Physics MCAT notes Flashcards
What are vectors? And what are the different vector quantities?
How are vectors added?
Numbers with magnitude and direction.
displacement, velocity, acceleration, and force
they are added tip to tail, • The X component of the resultant vector is the sum of the X components of the vectors being added. Similarly, the Y component of the resultant vector is the sum of the Y components of the vectors being added. • : 1. Resolve the vectors to be summed into their X and Y components.2. Add together the X components to get the X component of the resultant (Rx). In the same way, add the Y components to get the Y component of the resultant (Ry). 3. Find the magnitude of the resultant by using the Pythagorean theorem. If Rx and Ry are the components of the resultant, then Subtracting two vectors can be accomplished by adding the opposite of the vector that is being subtracted. By “ − B,” we mean a vector with the same magnitude of B but pointing in the opposite direction.
What are scalars? and what are the different scalar quantities?
numbers with quantity only, no direction
include distance, speed, energy, pressure and mass
Can a vector be multiplied by a scalar?
yes, to change either or both the length and direction. If we multiply vector A by the scalar value n, we produce a new vector, B, such that B = nA. To find the magnitude of the new vector, B, simply multiply the magnitude of A by the absolute value of n. To determine the direction of the vector B, we must look at the sign on n. If n is a positive number, then B and A are in the same direction. However, if n is a negative number, then B and A point in opposite directions. For example, if vector A is multiplied by the scalar +3, then the new vector B is three times as long as A, and A and B point in the same direction. If vector A is multiplied by the scalar -3, then B would still be three times as long as A but would now point in the opposite direction.
What is kinematics?
deals with the description of motion. study of motion with regard to what causes it.
What is displacement
vector quantity and, as such, has both magnitude and direction. The displacement vector connects (in a straight line) the object’s initial position and its final position. Understand that displacement does not account for the actual pathway taken between the initial and the final positions.
What is velocity and the difference between average velocity and instantaneous velocity?
it is a vector, is a vector. Its magnitude is measured as the rate of change of displacement in a given unit of time. The direction of the velocity vector is the same as the direction of the displacement vector. The SI units for velocity are meters/second. Speed, you will recall, is the rate of actual distance traveled in a given unit of time. The distinction is subtle, so let’s look at this a little more carefully. The instantaneous speed of an object will always be equal to the magnitude of the object’s instantaneous velocity, which is a measure of the average velocity as the change in time (Δ t) approaches 0. a measure of speed, instantaneous speed is also a scalar number. Average speed will not necessarily always be equal to the magnitude of the average velocity. This is because average velocity is the ratio of the displacement vector over the change in time (and is a vector), whereas average speed (which is scalar) is the ratio of the total distance traveled over the change in time. Average speed accounts for actual distance traveled.
- The average velocity of an object over an interval of time is the object’s displacement divided by the time elapsed: average velocity describes the motion of an object over a period of time, not at one particular instant. object has constant displacement, it is stationary. But when an object changes position, it does so at a certain rate — a concept we call velocity. The average speed is the distance traveled divided by the time elapsed. The average speed isn’t a vector quantity; it doesn’t depend on direction.
- An object’s instantaneous velocity is its velocity at any one moment in time. Instantaneous velocity, like average velocity, is a vector; it has both magnitude and direction. The instantaneous speed is the speed at any one moment in time. It doesn’t depend on direction like the instantaneous velocity. In fact, the instantaneous speed of an object at any time is the magnitude of the object’s instantaneous velocity vector at that time.
What is acceleration, and the difference between average and constant acceleration?
• is the rate of change of velocity over time. It is a vector quantity. acceleration results from application of force(s). Average acceleration,a, is the change in instantaneous velocity over the change in time. Instantaneous acceleration is defined as the average acceleration as t approaches 0. graph of velocity versus time, the tangent to the graph at any time t, which corresponds to the slope of the graph at that time, would indicate the instantaneous acceleration. If the slope is positive, the acceleration is positive and is in the direction of the velocity. If the slope is negative, the acceleration is negative and is in the direction opposite of the velocity, and it may be called deceleration.
acceleration is proportional to the force applied to it
objects experiencing translational or rotational equilibrium, in which the motional behavior of the object is constant. If an object’s motion is changing, as indicated by a change in velocity, then the object is experiencing acceleration, and that acceleration may be constant or itself changing
- acceleration to define the rate of change of velocity. An object at rest can also be described as moving at a constant velocity; that velocity happens to be zero. Whether or not an object is at rest or at some constant, non-zero velocity, the object has zero acceleration. An object only accelerates when the velocity is changing.
- Average acceleration- object’s average acceleration is much like its average velocity: average acceleration is the change in velocity, divided by the time elapsed. Acceleration is, in general, a vector quantity, the acceleration will be in one dimension, so keeping track of signs will be sufficient. At any particular moment, an object can have an instantaneous acceleration. The slope of a position versus time graph at a particular time gives the instantaneous velocity at that time. The slope of the velocity versus time graph at any single time is the object’s instantaneous acceleration.
- Constant acceleration. the acceleration is positive. Whatever the starting velocity is, the velocity is becoming more and more positive as time goesslope of the velocity versus time plot at any time is the instantaneous acceleration, the slope must be constant. Regardless of what position the object occupies at time zero, its acceleration is positive. Since the velocity is constantly becoming more and more positive, the slope of the position versus time plot must be increasing with time
What occurs when move along linear motion?
• linear motion, the object’s velocity and acceleration are along the line of motion. The pathway of the moving object is a straight line. Linear motion does not need to be limited to vertical or horizontal paths; the inclined surface of a ramp will provide a path for linear motion at some angle. Falling objects exhibit linear motion with constant acceleration. This one-dimensional motion. constant acceleration (the acceleration due to gravity (g), 9.8 m/s2) and would not reach terminal velocity. This is called free fall. Terminal velocity is due to the upward force of air resistance equaling the downward force of gravity. As the net force on the object at this point becomes zero, the acceleration is also zero. The object remains at a constant velocity until it is acted upon by another force.
What are the characteristics of projectile motion?
Projectile motion is motion that follows a path along two dimensions. The velocities and accelerations in the two directions (usually horizontal and vertical) are independent of each other and must, accordingly, be analyzed separately. Objects in projectile motion on Earth, such as cannonballs, baseballs, or bullets, experience the force and acceleration of gravity only in the vertical direction (“ along the y-axis” ). This means that vy will change at the rate of g but vx will not. assume that the horizontal velocity, vx, will be constant, because we assume that air resistance is negligible and, therefore, no measurable force is acting along the x-axis. When dealing with free fall problems, you can make “ down” either positive or negative, thus making the force of gravity either positive or negative. As long as you keep all forces upward with the opposite sign of all forces downward, you will get the correct answer. Though, for the sake of simplicity, ALWAYS make “ up” positive and “ down” negative. To demonstrate projectile motion and apply the kinematics equations to motion in two dimensions, we can turn our attention to cannonballs from a cannon. Projectiles display motion that can be analyzed with relatively simple mathematics. Whenever an object reaches its maximum height, its vertical velocity will be zero for the brief instant that it stops going up and starts falling down. As soon as an object is “ in flight,” the only force acting on it will be gravity; thus an object’s acceleration will be -9.8 m/s2 the entire time it is in flight. The amount of time that an object takes to get to its maximum height is the same time it takes for the object to fall back down; this fact makes solving these problems much easier. Because you can solve for the time to reach maximum height by setting your final velocity to zero, you can then multiply your answer by two, getting total time in flight. Because the only force acting on the object after it is launched is gravity, the velocity it has in the x-direction will remain constant throughout its time in flight. By multiplying the time by the x-velocity, you can find the horizontal distance traveled.
- The object’s motion in the horizontal direction (usually labeled the x-direction) has no acceleration, but the object’s motion in the vertical direction (the y-direction) has an acceleration of -g. When a projectile launches, it has the following initial properties: an initial height y0 (the ground level is usually y = 0), an initial speed v0, an initial angle of incline, θ, which divides the initial velocity into components: the x-component, v0x = v0 cos θ, and the y-component, v0y = v0 sin θ, Of course, as holds true throughout the entire flight of the projectile, the horizontal component of the acceleration, ax, is zero, and the magnitude of the vertical component, ay, equals g.
- As a projectile- The horizontal speed of the projectile, vx, doesn’ t change, because there is no horizontal acceleration. So the horizontal speed of the projectile is always equal to the initial horizontal speed: vx = v0 cos θ. The vertical speed of the projectile, vy, is always changing. That’ s because there is a constant vertical acceleration, g, pointing downward. So the projectile’ s upward motion slows down, stops, and then the projectile falls back to Earth. The important fact to remember about the motion of the projectile at the top of the arc is that the vertical speed is zero at that instant. The top of the arc is the place where the downward acceleration has reduced all of the initial vertical velocity to zero. only motion that the projectile undergoes at the top is horizontal motion; the horizontal speed is still vx = v0 cos θ. the horizontal distance it covered during the trip is called the range. If the object was launched and landed at the same height, then its motion is symmetric. This has two consequences: The time it took for the projectile to travel up to the top of the arc is equal to the time it took for the projectile come down from the top of the arc and land. The speed v at which the object lands is equal to the speed v0 at which the object took off. Furthermore, the vertical component of the speed at landing is equal in magnitude and opposite in direction to the initial vertical component of the speed, v0y.
What is force?
• experienced as pushing or pulling on objects. The amazing thing about forces is that they can exist between objects that aren’t even touching. While it is common in our experience for forces to be exerted by one object touching another, there are even more instances in which forces exist between objects nowhere near each other. On a grand scale, the oceanic tides are the result of the attractive gravitational force of the Moon on the water. On an even grander scale, the gravitational pull of planets orbiting a sun causes the sun to “ wobble” on its axis. On a more human scale, we can feel the repulsive force that exists between the north ends (or the south ends) of two bar magnets. The SI unit for force is the newton (N) and is equivalent to one kilogram · meter/second2.
What is the difference between mass and weight?
Mass and weight are not the same things! Mass (m) is a measure of a body’s inertia— the amount of matter in something, the amount of “ stuff.” Mass is a scalar quantity. (Remember, scalar numbers have magnitude only.) The SI unit for mass is the kilogram. Measurement of mass is independent of gravity. One kilogram of chocolate on Earth will have the same mass as one kilogram of chocolate on the Moon (and will be equally delicious). Weight (W) is a measure of gravitational force, usually that of the Earth, on an object’s mass. Weight is sometimes represented as Fg, or the force due to gravity. Because weight is a force, it is a vector quantity and has the same SI unit as any other force, the newton (N). Mass and weight are not the same thing. Weight: W = mg. N = (kg) (m/s2) W = weight = acceleration due to gravity, g, exerted on the mass, m. The weight of an object can be thought of as being applied at a single point in that object, called the center of gravity. Only for a homogeneous body (symmetrical shape and uniform density) can the center of gravity be located at its geometric center. For example, we can approximate the center of gravity for a metal shot-put ball as the geometric center of the sphere. The same cannot be said, however, for a human body, complex automobile, or any asymmetrical, non-uniform object.
What is Newton’s Laws of motion?
- Newton’s laws of motion- If there is no acceleration, then there is no net force on the object. This means that any object with a constant velocity has no net force acting on it. Where 1. F=ma=0. there is no acceleration, then there is no net force on the object. This means that any object with a constant velocity has no net force acting on it. A body either at rest or in motion with constant velocity will remain that way unless a net force acts upon it. law of inertia: “ A body in motion will stay in motion, and a body at rest will stay at rest, unless acted upon by an external force.” Newton’s first law ought to be thought of as a special case of his second law.
- The net force is the sum of all forces acting on an object. Even though the force of gravity is always acting on us, the net force on our bodies will be zero unless there is no ground below us pushing back up against gravity. The symbol in front of the F stands for “ sum of” and, in this case, means the “ vector sum of.” What Newton’s second law states is actually the corollary of the first: No acceleration of an object with mass m will occur when the vector sum of the forces results in a cancellation of those forces (vector sum equals zero). An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector. In a game of tug-of-war, one team will eventually end up in the mud pit because the uneven application of forces to the rope will cause an acceleration of the (losing) team toward the center. The net force is the sum of all forces acting on an object. Even though the force of gravity is always acting on us, the net force on our bodies will be zero unless there is no ground below us pushing back up against gravity.
- law of action and reaction: “ To every action, there is always an opposed but equal reaction.” More formally, the law states that for every force exerted by object B on object A, there is an equal but opposite force exerted by object A on object B. The mutual gravitational pull between the Earth and the Moon traverses hundreds of thousands of kilometers of space. our hand may have exerted quite the force against your desk, but it is an unavoidable law of Newtonian mechanics that your desk exerted the same force back against your hand
How are free body diagrams drawn?
• Drawing Free-Body Diagrams- When solving these problems, ALWAYS break each force that is not ONLY in the x- or y-direction into its x and y component parts using trigonometry. Looking at your forces, you know that there is more force in the negative y-direction than there is in the positive x-direction. Before jumping into the math, see if one of the answer choices has an angle that puts the vector closer to the negative y than to positive x. This would translate as an angle between 45 and 90 degrees below the x-axis. If you ever lose track of the angles, there’s a trick to finding which angle you’re dealing with. Drawing out vectors creates right triangles out of the vectors Wgravity, Wx, and Wy. Because you are breaking gravity into its component parts, it will be the largest value, making it the hypotenuse of both triangles. Wy, which goes perpendicular to the incline, will be equal to the normal force. By drawing the final force Wx, you see that it goes parallel to the incline. The angle theta will equal the angle between the force of gravity and Wy. By plugging Wx into F = ma, you can solve for the acceleration of the block in the x-direction. Because the block is neither breaking through the incline nor floating off of it, the normal force and Wy must be equal and opposite, meaning the net force in the y-direction is zero.
What is gravity?
• Gravity- Newton’s third law states that the force of gravity on m1 from m2 is equal and opposite of the force of gravity on m2 from m1. This means that the force of gravity on you from the Earth is equal and opposite of the force of gravity from you on the Earth. This may sound strange, but with Newton’s second law, you can make sense of it. Because the forces are equal but the masses are very different, you know that the accelerations must also be very different, from F = ma. Because your mass compared to that of the Earth is very small, you experience a large acceleration from it. In contrast, because the Earth is very massive and it feels the same force, it only experiences a tiny acceleration from you. Gravity is an attractive force that is felt by all forms of matter. We usually think of gravity as acting on us to keep us from floating off of the Earth’s surface, and of course, the planets of our solar system are kept in their orbits by the gravitational pull of the Sun. gravity is only one kind of force and it just happens to be the weakest of the four forces known to us. There are a lot of other forces that are working to oppose gravity (for example, friction, which is an electromagnetic force), magnitude of the gravitational force (F) between two objects is where G is the universal gravitational constant (6.67 × 10− 11 N· m2/kg2), m1 and m2 are the masses of the two objects, and r is the distance between their centers. magnitude of the gravitational force is inverse to the square of the distance (that is, if r is halved, then F will quadruple).
What are the other kinds of motion?
translational, rotational, and periodic
What is translational motion?
• Translational motion occurs when forces cause an object to move without any rotation about a fixed point in the object. The simplest pathways may be linear, such as when a child slides down a snowy hill on a sled, or parabolic, as in the case of a clown shot out of a cannon.
What is rotational motion?
Rotational motion- occurs when forces are applied against an object in such a way as to cause the object to rotate around a fixed pivot point, also known as the fulcrum. Application of force at some distance from the fulcrum, along the lever arm, generates torque,τ , or the moment of force. It is the torque that generates the rotational motion, not the mere application of the force itself. This is because torque depends not only on the magnitude of the force but also on the angle at which the force is applied against the lever arm as well as the distance between the fulcrum and the point of force application. where F is the magnitude of the force, r is the distance between the fulcrum and the point of force application, and theta (the Greek letter) is the angle between F and the lever arm.
What is circular motion?
Circular motion occurs when forces cause an object to move in a circular pathway. Upon completion of one cycle, the displacement of the object is zero. uniform circular motion, in which case the speed of the object is constant, you ought to know that there is also nonuniform circular motion. Nonuniform circular motion is covered briefly after we discuss uniform circular motion. For circular motion that demonstrates a constant speed at all points along the pathway. the instantaneous velocity vector is always tangent to the circular path. object moving in the circular motion has a tendency (inertia) to “ break out” of its circular pathway and move in a linear direction along the tangent. In all circular motion, we can resolve the forces into radial (center-seeking) and tangential components. In uniform circular motion, the tangential force is zero (because there is no change in the speed of the object). the resultant force is the radial force. This is known as the centripetal force, and according to Newton’s second law, this generates centripetal acceleration. Remember, also, from our discussion of Newton’s laws that both force and acceleration are vectors and the acceleration is always in the same direction as the resultant force. Thus it is this acceleration generated by the centripetal force that keeps an object in its circular pathway. When the centripetal force is no longer acting on the object, it will simply exit the circular pathway and assume a path tangential to the circle at that point. Examples of centripetal force in action are the force of gravity in maintaining a satellite’s orbit and the tension in a rope attached to an object that is being spun around. This is the force that keeps the object from flying off tangentially. the resultant force is the radial force. This is known as the centripetal force, and according to Newton’s second law, this generates centripetal acceleration. Remember, also, from our discussion of Newton’s laws that both force and acceleration are vectors and the acceleration is always in the same direction as the resultant force. Thus it is this acceleration generated by the centripetal force that keeps an object in its circular pathway. When the centripetal force is no longer acting on the object, it will simply exit the circular pathway and assume a path tangential to the circle at that point. where v2/r is the centripetal acceleration and F is the force necessary to keep an object of mass m in orbit with radius r. This means, then, that there is a tangential force acting to create a tangential acceleration. This force vector adds to the radial force vector to produce a resultant force (and resultant acceleration) that is not directed toward the center of the circle.
What is friction and what are the kinds of friction?
electromagnetic force opposing the movement of objects causes it to slow down or become stationary
static and kinetic
What is static friction?
Static friction (Fs) exists between a stationary object and the surface upon which it rests. where μ s is the coefficient of static friction and Fn is the normal force. Don’t forget that the normal force is the component of the contact force that is perpendicular to the plane of contact between the object and the surface upon which it rests. The maximum value of static friction can be calculated from the right side of the previous equation. Objects that are stationary ought not to be assumed to be experiencing that maximum value. In fact, one can demonstrate quite easily that the static friction between an object and a surface is not at its maximal value. Contact points are the places where friction occurs between two rough surfaces sliding past each other (top). If the “ normal load” — the force that squeezes the two together— rises, the total area of contact increases (bottom). That increase, and not the surface roughness, governs the degree of friction. The coefficient of static friction will always be larger than the coefficient of kinetic friction. It is always harder to get an object to start sliding than it is to keep an object sliding.
What is kinetic friction?
• Kinetic friction (Fk) exists between a sliding object and the surface over which the object slides. A wheel, for example, that is rolling along a road does not experience kinetic friction because the tire is not actually sliding against the pavement. The tire maintains an instantaneous point of static contact with the road and, therefore, experiences static friction! Only when the tire begins to slide on, say, an icy patch during the winter will kinetic friction come into play. To be sure, any time two surfaces slide against each other, kinetic friction will be present. μk is the coefficient of kinetic friction and Fn is the normal force. important distinction between this equation for kinetic friction and the previous equation for static friction. The kinetic friction equation has an equals sign, not the less-than-or-equals sign. This means that kinetic friction will have a constant value for any given combination of a coefficient of kinetic friction and normal force. It does not matter how much surface area is in contact or even the velocity of the sliding object.
What is mechanical equilibria?
• Mechanical Equilibria: examine mechanical equilibrium, which occurs when the vector sum of the forces or torques acting on an object is zero; that is, when all of the force or all of the torque vectors cancel out. Just because the net force equal zero does not mean the velocity equals zero;
What is translational equilibrium?
Translational equilibrium exists only when the vector sum of all of the forces acting on an object is zero. This is called the first condition of equilibrium. It’s merely an instance of Newton’s first law, which, remember, is only a special case of the second. When the resultant force upon an object is zero, the object will not accelerate. Its motional behavior will be constant. That may mean that the object is stationary, but it could just as well mean that the object is moving with a constant nonzero velocity. What is important to remember is that an object experiencing translational equilibrium will have a constant speed (which could be a zero or nonzero value) and a constant direction. Remember that sin 90° equals 1. This means that torque is greatest when the force applied is 90 degrees (perpendicular) to the length of the lever arm. Knowing that sin 0° equals 0 tells us that there is no torque when the force applied is parallel to the lever arm
What is rotational equilibriuM/
• Rotational equilibrium exists only when the vector sum of all the torques acting on an object is zero. This is called the second condition of equilibrium. Torques that generate clockwise rotation are conventionally negative, while torques that generate counterclockwise rotation are positive. Thus, in rotational equilibrium, it must be that all of the positive torques exactly cancel out all of the negative torques. Similar to the motional behavior defined by translational equilibrium, there are two possibilities of motion in the case of rotational equilibrium. Either the lever arm is not rotating at all (that is, it is stationary), or it is rotating with a constant angular frequency (analogous to a constant velocity)
What is energy?
Energy is a property or characteristic of a system to do work or more broadly, to make something happen. This broad definition helps us understand that different forms of energy have the capacities to do different things. For example, mechanical energy, such as that which Sisyphus transferred to the large rock, can cause things to move or accelerate through the process of work. An ice cube sitting on the kitchen counter at room temperature will eventually melt into water, undergoing the phase transformation from solid to liquid. Internal energy, or what a few textbooks call thermal energy (and what most of us sloppily call “ heat,” even though heat is actually a process of energy transfer, not energy itself), can make the ice cube on the counter melt. any time an object has a velocity, you should think about kinetic energy and the related concepts of work and conservation of mechanical energy
What is kinetic energy?
Energy is a property or characteristic of a system to do work or more broadly, to make something happen. This broad definition helps us understand that different forms of energy have the capacities to do different things. For example, mechanical energy, such as that which Sisyphus transferred to the large rock, can cause things to move or accelerate through the process of work. An ice cube sitting on the kitchen counter at room temperature will eventually melt into water, undergoing the phase transformation from solid to liquid. Internal energy, or what a few textbooks call thermal energy (and what most of us sloppily call “ heat,” even though heat is actually a process of energy transfer, not energy itself), can make the ice cube on the counter melt. any time an object has a velocity, you should think about kinetic energy and the related concepts of work and conservation of mechanical energy
What is potential energy?
• An object with mass is said to have potential energy when it has the potential to do something. Potential energy is another form of energy, and it can come in different types. One type of potential energy is gravitational potential energy, mechanical potential energy, which can be found in, say, a compressed spring, and chemical potential energy (or just chemical energy), which is found in the covalent and ionic bonds holding atoms together in molecules. Gravitational potential energy depends on a body’s position with respect to some level identified as “ ground,” or the zero potential energy position. this equation to solve for gravitational potential energy in situations relatively close to the Earth’s surface. where U is the potential energy, m is the mass in kg, g is the acceleration due to gravity, and h is the height of the object above the reference level. We see the potential energy is in a direct, linear relationship with all three of the variables, so changing any one of them by some given factor will result in a change in the potential energy by the same factor. Tripling the height of the pencil held in your hand above the floor would increase the pencil’s potential energy by a factor of three, and it would most likely require you to stand on the desk in order to do so (thereby also increasing your own potential energy and potential for injury should you lose your balance).
what is total mechanical energy?
total mechanical energy- sum of an object’s potential and kinetic energies. where E is total mechanical energy, U is potential energy, and K is kinetic energy. The first law of thermodynamics states that energy is never created or destroyed. It is merely transferred from one system to another. Yet this does not mean that the total mechanical energy will always remain constant. You’ll notice that the total mechanical energy equation accounts for potential and kinetic energies but not for other energies like thermal energy (“ heat” ) that is transferred as a result of friction. If frictional forces are present, some of the mechanical energy will be transformed into thermal energy and will be “ lost” — or, more accurately, not accounted for by the equation. Note that there is no violation of the first law of thermodynamics, as a full accounting of all the energies (kinetic, potential, thermal, sound, light, etc.) would reveal no net gain or loss of total energy, merely the transformation of some energy from one form to another.
What is the conservation of mechanical energy?
Conservation of Mechanical Energy: E = U + K = Constant- Mechanical energy is conserved when no dissipative forces (e.g., friction, air resistance) are present. In the absence of non-conservative forces, such as frictional forces, the sum of the kinetic and potential energies will be constant. Conservative forces are those that have potential energies associated with them. the two most commonly encountered conservative forces are gravitational and electrostatic. The spring system, which is mechanical, can also be approximated to be conservative. a. If the net work done to move a particle in any round-trip path is zero, the force is conservative. b. If the net work needed to move a particle between two points is the same regardless of the path taken, the force is conservative. an object that falls through a certain displacement in a vacuum will lose some measurable amount of potential energy but will gain exactly that same amount of potential energy when it is lifted back to its original height, regardless of whether the return pathway is the same as that of the initial descent. Furthermore, at all points during the fall through the vacuum, there will be a perfect conversion of potential energy into kinetic energy, with no energy lost to nonconservative forces (e.g., friction). Of course, in real life, outside of theoretical situations, nonconservative forces like friction and air resistance are impossible to avoid, and the balls that we throw know all too well the energy impact of nonconservative forces. When the work done by nonconservative forces is zero, or when there are no nonconservative forces acting on the system, the total mechanical energy of the system remains constant. The conservation of mechanical energy. When nonconservative forces, such as friction or air resistance, are present, total mechanical energy is not conserved. where W′ is the work done by the nonconservative forces only. The work done by the nonconservative forces will be exactly equal to the amount of energy “ lost” from the system. Where did this energy go? The first law of thermodynamics tells us that the energy wasn’t really lost. It simply was transformed into a form of energy, such as thermal energy, that isn’t accounted for in the mechanical energy equation.
What is work?
• Work- is used to mean another form of energy. Work is not actually a form of energy, but a process by which energy is transferred from one system to another. In fact, it’s one of only two ways in which energy can be transferred. The transfer of energy, by work or heat, is the only way in which anything can be done. We are familiar with both processes, each being something we experience every day of our lives, although, arguably, it’s easier to “ see” work than it is to “ see” heat. The chemical potential energy in the ATP was harnessed in the “ form” of heat. In fact, at the molecular level, this is no different from work, because it involves the movement of molecules and atoms, and each of them exert forces that do work on other molecules and atoms. Like any transfer of energy, it’s not a perfectly efficient process, and some of that energy is “ lost” as thermal energy. Our muscles quite literally “ warm up” when we contract them repeatedly. theta is the angle between the force and displacement vectors.
How are work and power calculated?
Calculating work and power- Energy is transferred through the process of work when something exerts forces on or against something else. where W is work, F is the force applied, d is displacement through which the force is applied, and theta is the angle between the applied force vector and the displacement vector. work is a function of the cosine of the angle, which means that only forces (or components of forces) parallel or antiparallel to the displacement vector will do work (i.e., transfer energy). We’ve already said that the SI unit for work is the joule, a fact suggesting that work and energy are the same thing, but remember they are not: Work is the process by which a quantity of energy is moved from one system to another. It takes force. Not just any force but force in the direction that we want the object to move. Every time we push, pull, tug, kick, or drag an object for the purpose of moving it from one place to another, we do work, and it’s not just humans that do work. Any machine designed to apply a force to generate movement is doing work. By pushing straight into the side of the box, meaning pushing parallel to the ground and thus parallel to its displacement, you get the best results. Remembering your trig, the cosine of 0 degrees is 1, meaning that all of the force is going into the work. If you were to change the angle at which you are pushing to 60 degrees (cosine of 60 is 0.5), then only half of your force would be going into the work. In summary, if in both situations you want the box to accelerate a certain distance, it will take double the force to move the box the same distance if the angle is 60 degrees instead of zero, though the same amount of work will be done.
. The unit for power, the watt, W. rate at which energy is transferred from one system to another is measured as power. where P is power, W is work, and t is the time over which the work is done. The SI unit for power is the watt (W), which as you can see from the equation is equal to J/s. Power is calculated in many different situations, especially those involving circuits, resistors, and capacitors. Power is always a measure of the rate of energy consumption, transfer, or transformation per unit time.
What is the work-energy theorem?
• Work-energy theorem- energy (the capacity to do something or make something happen). work-energy theorem is a powerful expression of the relationship between work and kinetic energy. In particular, it offers a direct relationship between the work done by all the forces acting on an object and the change in kinetic energy of that object. The net work done on or by an object will result in an equal change in the object’s kinetic energy. If you can calculate the change in kinetic energy experienced by an object, then by definition you can determine the net work done on or by an objectbrake pads exert frictional forces against the rotors, which are attached to the wheels. These frictional forces do work against the wheels, causing them to decelerate and bringing the car to a halt. The net work done by all these forces is equal to the change in kinetic energy of the car.
What is momentum?
• Momentum (p) is a quality of objects in motion. In classical mechanics, it is defined as the product of an object’s mass and velocity. Because it has magnitude and direction, it is a vector quantity, like velocity and acceleration. where p is momentum, m is mass, and v is velocity. For two or more objects, the total momentum is the vector sum of the individual momenta. All of these objects and all objects that have mass also have inertia. Inertia is the tendency of objects to resist changes in their motion and momentum. We can observe the sometimes disastrous results when objects encounter forces that cause them to change their motion• Momentum (p) is a quality of objects in motion. In classical mechanics, it is defined as the product of an object’s mass and velocity. Because it has magnitude and direction, it is a vector quantity, like velocity and acceleration. where p is momentum, m is mass, and v is velocity. For two or more objects, the total momentum is the vector sum of the individual momenta. All of these objects and all objects that have mass also have inertia. Inertia is the tendency of objects to resist changes in their motion and momentum. We can observe the sometimes disastrous results when objects encounter forces that cause them to change their motion
What is impulse?
• Impulse- As we have seen over and over again, the only manner by which an object’s motion can change is when there is net force acting on it to cause it to accelerate. When net force acts on an object, causing it to change its motion, this also results in change to the object’s momentum. This change in momentum is called impulse (I) and is a vector quantity. For a constant force applied through a period of time, impulse and momentum are related where I is impulse, F is force, Δ t is time, p is momentum, m is mass, and v is velocity. the setup of a typical momentum problem will involve changes to momentum in only one dimension, which allows us to treat the vectors as scalars along the number line. The variables are assigned positive or negative signs depending on whether the corresponding vectors are in the positive or the negative direction. inverse relationship between force magnitude and time if impulse is constant. In other words, given a particular change in momentum, the longer the period of time through which this impulse is achieved, the smaller the force necessary to achieve the impulse. front and side airbags and crumple zones in the front and rear of the car, are designed to increase the time through which the change in momentum associated with a collision will occur. Prolonging the duration of the collision allows the change in momentum to occur over a longer period of time, and this reduces the magnitude of the forces necessary to achieve the change in momentum. Reducing the forces exerted on the car and its occupants reduces the risk of severe injury or death.
What is the conservation of momentum mean?
• Conservation of momentum- situation with no external forces acting on a system, or if external forces are present, the vector sum of the external forces acting on that system is zero. In the absence of (nonzero) external forces, or in the case of the external forces canceling each other, the total (vector sum) momentum of a system will be constant.
What are collisions?
• Collisions- two or more objects collide in an idealized collision (instantaneous and in a specific location), we can say that momentum is conserved as long as no (net) external forces act on the objects. Conservation of momentum means that the vector sum of the momenta is constant: The total momentum after the collision is equal to the total momentum before the collision. This does not mean that the individual momenta will necessarily be constant. Objects that collide can sometimes experience dramatic changes in their momenta, even as the total momentum of the system is constant. Individual changes in momentum may occur (e.g., objects may experience changes in velocity as a result of the collision), but total momentum is conserved as long as no external forces, such as friction, are present. For a collision between two objects, a and b, this can be expressed. Use this equation for collisions after which the two objects, a and b, bounce apart and do not stick together. where pai and pbi are the momenta before the collision and paf and pbf are the momenta after the collision. Since we’ve already defined momentum as the product of mass and velocity, we can rewrite the conservation of momentum where vai and vbi are the velocities before the collision and vaf and vbf are the velocities after the collision. one-dimensional problems of collision can be treated as if the vectors were scalars along the number line. The signs on the velocities (and hence on the momenta) will be determined by the direction of the velocity and momentum vectors. You will decide, for each problem, which direction is given the positive sign.If the momentum problem is two-dimensional, then we will have to resolve the momentum vectors into their X and Y components using trigonometry, it’s inevitable that things are going to bump against each other. From cars to beams of high-energy particles directed onto thin sheets of gold foil, collisions are inevitable and frequent.In completely elastic collisions (objects don’t stick together), we have a perfect collision in which both momentum and kinetic energy are conserved. In both inelastic collisions (objects don’t stick together) and completely inelastic collisions (objects stick together), kinetic energy is not conserved, but momentum is. 1. Completely elastic collisions 2. Inelastic collisions 3. Completely inelastic collisions
What are completely elastic collision?
• Completely Elastic Collisions- Completely elastic collisions occur when two or more objects collide in such a way that both total momentum and total kinetic energy are conserved. This means that no energy of motion was transformed in the instance of the collision into another form, such as thermal, light, or sound. Nor was any energy used to change the shapes of the colliding objects. rarely do collisions occur without sound, light, or heat production or deformation of objects. can be analyzed as an instance of conservation of momentum and kinetic energy. Be careful not to assume that the velocities of the colliding objects remain constant. In fact, it is almost certain that the objects will experience changes in their velocities (magnitude and/or direction) upon impact. In completely elastic collisions, it is the total kinetic energy, not the individual velocities or even the individual kinetic energies of the objects, that remains constant. In equation form, the conservation of momentum. completely elastic collisions are the only type for which kinetic energy is conserved.
What are inelastic collision?
Inelastic Collisions- release of a tremendous amount of energy in the form of loud noises, blindingly bright explosions, ferociously hot fires, and/or bone-rattling vibrations. When a collision results in the production of light, heat, sound, or object deformation, there is necessarily a decrease in the total kinetic energy of the system. This type of collision is an inelastic collision and is closer to what we typically observe in everyday life. Momentum is conserved as long as no external forces are present (as in the case of totally elastic collisions) even as kinetic energy is transformed (“ lost” ). The conservation of momentum equation is identical to that displayed in the discussion of completely elastic collisions. However, the final kinetic energy will be less than the initial kinetic energy. change in kinetic energy will be equal to the amount of energy released from the system in the form of heat, light, or sound.
What are completely inelastic collision?
Completely Inelastic Collisions- Use this equation for collisions after which the two objects, a and b, stick together and move as one. not every collision results in mangled metal or mass extinction. Furthermore, we recognize that many collisions are necessary, even for the continuation of life. In fact, if it weren’t for completely inelastic collisions, the molecules that make up the matter of our universe would never have formed. In completely inelastic collisions, the objects that collide stick together rather than bouncing off each other and moving apart. When atoms are moving around and colliding with each other, they sometimes stick together to become compounds as the result of formation of covalent or ionic bonds. This is not that much different than the formation of a “ link” between two balls covered in Velcro that are rolled toward each other: Upon collision, they stick together and move as one object. totally inelastic collisions result in conservation of momentum as long as the vector sum of any external forces, such as frictional forces, is equal to zero. This is a variant of the inelastic collision, so total kinetic energy is not conserved. Because the objects stick together upon collision, ight side adds the masses of the two objects together and calculates a single final velocity, which is appropriate given that the objects move as a single mass after the collision.
What is the mechanical advantage?
• Mechanical Advantage- The difference is mechanical advantage. Sloping inclines, such as hillsides and ramps, make it easier for work to be accomplished. For a given quantity of work, any device (such as an inclined plane) that allows for work to be accomplished through a reduced applied force is said to provide mechanical advantage. In addition to the inclined plane, five other devices are considered the classic simple machines designed to provide mechanical advantage: wedge, axle and wheel, lever, pulley, and screw. Of these, the inclined plane, lever, and pulley. Mechanical advantage is the ratio of the force exerted on object by a simple machine (Fout) to the force actually applied on the simple machine (Fin). The mechanical advantage, because it is a ratio, is dimensionless. his reduction in necessary force for the purpose of accomplishing a given amount of work does have a “ cost” associated with it, however, and that is the distance through which the smaller force must be applied in order to do the work. Simple machines may provide mechanical advantage, but they do not violate the fundamental laws of physics! We know that energy can be neither created nor destroyed, merely changed from one form to another: energy “ in” (in one form) must equal energy “ out” (in another form). Inclined planes, levers, and pulleys do not “ magically” change the amount of work necessary to move an object from one place to another. In mechanical terms, that work is defined as the product of the object’s displacement and the magnitude of the force vector that is along the displacement vector. isplacement is pathway-independent, and for conservative systems, work doesn’t depend upon the actual distance traveled between the final position and the initial position. An inclined plane, as we will see in the following discussion, allows for masses to be displaced through the application of lower force over a greater distance to achieve the change in position. Pulleys and levers “ work,” in principle, in exactly the same way.
What are inclined planes?
Inclined planes- The ramp allows those using it to change their position (that is, achieve a displacement) from the street level to the elevated front door in a gradual manner. This displacement requires a given quantity of work defined, as we’ve seen, as the product of displacement and the force vector along the displacement. If we ignore friction forces, we can say that it makes no difference whether that displacement occurs in a straight-line pathway or in the back-and-forth pathway of the entrance ramp: The work required is the same. work equation an inverse relationship between applied force and distance for a constant value of work. Because the ramp is longer than a straight-line path from the street to the building door, the distance through which the ultimate displacement will be achieved is greater, and the force necessary to achieve that displacement is reduced. This is the mechanical advantage offered by an inclined plane to anyone using a wheelchair, pushing a baby carriage, or rolling a heavy object.
What are pulleys?
Pulleys- a reduction of necessary force at the “ cost” of increased distance to achieve a given value of work or energy transference. In practical terms, pulleys allow heavy objects to be lifted using a much-reduced force. Simply lifting a heavy object of mass m to a height of h will require an amount of work equal to mgh. If the displacement occurs over a distance equal to the displacement, then the force required to lift the object will equal mg. the distance through which the displacement is achieved is greater than the displacement, then setting W = Fd = mgh shows us that the applied force will be less than mg. In other words, we’ve been able to lift this heavy object to the desired height by using a lower force, but we’ve had to apply that lower force through a greater distance in order to lift this heavy object to its final height. Because the block is not accelerating, it is in translational equilibrium, and the force that the block exerts downward (its weight) is equaled by the sum of the tensions in the two ropes. For a symmetrical system, the tensions in the two ropes are the same and are each equal to half the weight of the block. epresents a heavy crate that must be lifted by a worker in a warehouse. Assuming that the crate is being held momentarily stationary, in midair, we again have a system in translational equilibrium: the weight (the load) is in balance with the total tension in the ropes. The tensions in the two vertical ropes are equal to each other (if they were unequal, the pulleys would turn until the tensions were equal on both sides) and each rope supports one-half of the crate’s total weight. Fortunately for the warehouse employee holding onto the free end of the rope, only half the force (the effort) is required to lift the crate to a high shelf. This is the mechanical advantage provided by the pulley, but as we’ve already discussed, mechanical advantage comes at the expense of distance. To lift an object to a certain height in the air (the load distance), one must pull through a length of rope (the effort distance) equal to twice that displacement. If, for example, the crate must be lifted to a shelf 3 meters above the ground, then both sides of the supporting rope must shorten by 3 meters, and the only way to accomplish this is by pulling through 6 meters of rope.
How are the efficiencies of simple machines measured?
All simple machines can be approximated as conservative systems if we ignore the usually small amount of energy that would be “ lost” due to external forces, such as friction. The idealized pulley is massless and frictionless, and under these theoretical conditions, the work put into the system (the exertion of force through a distance of rope) will exactly equal the work that comes out of the system (the displacement of the mass to some height). Real pulleys (and all real machines, for that matter) fail to conform to these idealized conditions to one degree or another and, therefore, do not achieve 100 percent efficiency in conserving energy output to input. We can define work input as the product of effort and effort distance; likewise, we can define work output as the product of load and load distance. Comparing the two, as a ratio of work output to work input, defines the efficiency of the simple machine. Efficiencies are often expressed as percentages by multiplying the efficiency ratio by 100 percent. The efficiency of a machine gives a measure of the amount of work you put into the system that “ comes out” as useful work. The corollary of efficiency is the percentage of the work that you put into the system that becomes unusable due to external forces. For every additional pair of pulleys, we can reduce the effort further still. In this case, the load has been divided among six lengths of rope, so the effort required is now only one-sixth the total load. Remember that we would need to pull through a length of rope that is six times the desired displacement, and too much of a good thing has its price. For pulleys, that price is lowered efficiency due to the added weight of each pulley and the additional friction forces.
What is the center of mass?
• Center of Mass- This point, which can be calculated using coordinate geometry, is the point within any two- or three-dimensional object at which the entire object’s mass could be represented as a single particle. Each part of the racket moves in its own way, so it’s not possible to represent the motion of the whole racket as a single particle. However, one point within the racket moves in a simple parabolic path, very similar to the flight of a ball. It is this point within the racket that is known as the center of mass. For a system of two masses, m1 and m2, lying along the x-axis at points x1 and x2, respectively, the center of mass is… For a system with several masses strung out along the x-axis, the center of mass is… For a system in which the particles are distributed in all three dimensions, the center of mass is defined by the three coordinates:
What is the center of gravity?
• center of gravity is the point at which the entire force due to gravity can be thought of as acting. It is found from similar formulas: The center of mass of a uniform object is at the geometric center of the object. Since W = mg, the center of gravity and the center of mass will be the same point as long as g is constant.
What is the zeroth law?
•zeroth law is based on a simple observation: When one object is in thermal equilibrium with another object, say a cup of warm tea and a metal stirring stick, and the second object is in thermal equilibrium with a third object, say the metal stirring stick and your hand, then the first and third object are also in thermal equilibrium and when brought into thermal contact (which doesn’t necessarily imply physical contact, by the way), no net heat will flow between them. transitive property of thermal equilibrium; if a = b and b = c, then a = c. No heat flows between objects in thermal equilibrium
What is temperature?
Temperature- average motional (kinetic) energy the difference in temperatures, determines the direction of heat flow. When allowed, heat moves spontaneously from materials that have higher temperatures to materials that have lower temperatures. Heat (energy) flows from hot to cold. If no net heat flows between two objects in thermal contact, then we can say that their temperatures are equal and they are in thermal equilibrium. Once we start talking about heat flowing from hotter to colder objects, physical property of matter, motional behavior of atoms and molecules making up matter, freezing and boiling temperatures of water are assigned the 0° and 100° values, respectively, for the Celsius scale. In spite of the fact that the Fahrenheit scale is also based on the phase transformations of water, it is clearly not as straightforward.
What occurs at absolute zero?
Kelvin is a scale based around “ absolute zero,” which is the temperature at which all random atomic motion stops. This occurs at zero degrees Kelvin. there are 180 degrees between water’s phase changes on the Fahrenheit scale, rather than 100 degrees as on both the Celsius and the Kelvin scales, the size of the Fahrenheit unit is smaller where TC stands for degrees Celsius, TK stands for degrees Kelvin, and TF stands for degrees
What is thermal expansion?
- thermal expansion- Length, volume, and even the conductivity of matter change as a function of temperature. The relationship between temperature and a physical property of some matter. The cold temperature caused the mercury to contract, and when the level in the glass tube stabilized at a lower level, he marked this as the zero reference on the scale. He then placed the same mercury thermometer in a mixture of ice and water (that is, at the freezing temperature for water). The slightly warmer temperature of this mixture caused the mercury to rise in the glass column, and when it stabilized at this higher level, Fahrenheit assigned a value of 32° . When he stuck the thermometer under his (or someone else’s) tongue, he marked the even higher mercury level as 96°. A change in the temperature of most solids results in a change in their length. Rising temperatures cause an increase in length, and falling temperatures cause a decrease in length. The amount of length change is proportional to the original length of the solid and the increase in temperature. where Δ L is the change in length, L is the original length, and Δ T is the change in temperature. The coefficient of linear expansion α is a constant that characterizes how a specific material’s length changes as the temperature changes. This usually has units of K− 1, though it may sometimes be quoted as ° C− 1.
- Liquids also experience thermal expansion, but the only meaningful parameter of expansion is volume expansion.
What is the first law of thermodynamics?
- first law of thermodynamics tells us that an increase in the total internal energy of a system is caused by transferring heat to the system or performing work on the system. The total internal energy of a system will decrease when heat is lost from the system or work is performed by the system. in the absence of friction forces, the sum of kinetic and potential energies is constant in a system. Essentially, the first law states that the change in the total internal energy of a system is equal to the amount of energy transferred in the form of heat to the system, minus the amount of energy transferred from the system in the form of work. The internal energy of a system can be increased by adding heat, doing work on the system, or some combination of both processes. where Δ U is the change in the system’s internal energy, Q is the energy transferred through heat to the system, and W is the work done by the system. sign convention: work done by the system is positive, while work done on the system is negative; heat flow into the system is positive, while heat flow out of the system is negative. The first law of thermodynamics is that energy is neither created nor destroyed. This means the energy of a closed system (such as the universe) will always remain constant.
- Examination of the first law of thermodynamics revealed that the energy of a closed system (up to and including the universe) is constant, such that the total internal energy of a system (the sum of all its potential and motional energies) equals the heat energy gained by the system minus the work energy done by the system, third law of thermodynamics, which states that absolute zero can never be actually reached,
What are systems and what do they describe?
Systems – object or material to which they are paying attention, everything else outside system is environment. energy is conserved even when friction is present. Energy can be neither created nor destroyed; it can only be changed from one form to another. Because the first law accounts for all work and all heat processes impacting the system, the presence of friction poses no problem, because the energy transfer associated with the friction will be accounted for in the first law equation.W here may be a “ loss” of energy from the car as a result of the friction, but that precise amount of energy can be “ found” elsewhere, as thermal energy in the atoms and molecules of the road and air.
What is heat?
•Heat is the process of energy transfer between two objects at different temperatures and will continue until the two objects come into thermal equilibrium (i.e., reach the same temperature). work and heat are the only two processes by which energy can be transferred from one object to another. Remember what the zeroth law says: Objects in thermal contact are in thermal equilibrium when their temperatures are the same. The corollary of this is the second law of thermodynamics: Objects in thermal contact and not in thermal equilibrium will exchange heat energy such that the object with a higher temperature will give off heat energy to the object with a lower temperature until both objects have the same temperature (and come to thermal equilibrium). Heat, then, is defined as the process by which a quantity of energy is transferred between two objects as a result of a difference in temperature. heat can never spontaneously transfer energy from a cooler object to a warmer one without work being done on the system. SI unit for heat is the joule (J),
How can heat be transferred?
Heat Transfer- energy to be transferred between objects, they must be in thermal contact with each other. Not necessarily physically touching, enery travels distances and doesn’t require a medium in order to move. conduction, convection, and radiation.
What is conduction?
Conduction is the direct transfer of energy from molecule to molecule through molecular collisions have to be in physical contact. the particles of the hotter matter transfer some of their motional energy to the particles of the cooler matter through collisions between the particles of the two materials. Metals are described as the best heat conductors because the density of atoms embedded in the “ sea of electrons” that characterizes the metallic bond facilitates the transfer of energy. Gases tend to be the poorest heat conductors because even though gas molecules are free to move around (in fact, the root mean square velocity of air molecules at room temperature and atmospheric pressure is around 500 m/s), there is so much space between individual molecules that energy transferming collisions occure relatively infrequently.
What is convection?
Convection is the transfer of heat by the physical motion of the heated material. Because convection involves flow, only fluids (liquids and gases) can transfer heat by this means. In convection, heated portions of the fluid rise from the heat source, while colder portions sink (because density decreases as temperature increases). Fans with circulating hot air
What is radiation?
• Convection is the transfer of heat by the physical motion of the heated material. Because convection involves flow, only fluids (liquids and gases) can transfer heat by this means. In convection, heated portions of the fluid rise from the heat source, while colder portions sink (because density decreases as temperature increases). Fans with circulating hot air
What is specific heat?
- vacuum. For this reason, the energy from the sun is able to warm the earth
- Specific Heat- One calorie (little c) is the amount of heat required to raise 1 g of water one degree Celsius. One Calorie (big C) is the amount of heat required to raise 1 kg of water 1 degree Celsius. heat energy is added or removed from a system, the temperature of that system will change in proportion to the amount of heat, unless the system is undergoing a phase change during which the temperature is constant. This relationship between heat and temperature for a substance is called specific heat (c). The specific heat of a substance is defined as the amount of heat energy required to raise 1 kg of a substance by 1° C or 1 K. with the specific heat for a substance changes according to its phase. where m is the mass of the object and c is the specific heat. Because the unit size for the Celsius and Kelvin scales is the same, the change in temperature will be the same for temperatures measured in Celsius or Kelvin
What is the heat of transformation?
• Heat of Transformation- a substance is undergoing a phase change, such as from solid to liquid or liquid to gas, the heat that is added or removed from the system does not result in a change in temperature. phase changes occur at constant temperature, and the temperature will not begin to change until all of the substance has been converted from one phase into the other. water melts at 0° C. No matter how much heat is added to a mass of ice at 0° C, the temperature will not rise until all the ice has been melted into liquid water. We’ve determined that adding heat raises the temperature of a system because the particles in that system now have a greater average kinetic energy, and it’s true that molecules have greater degrees of freedom of movement in the liquid state than in the solid state (and even more so in the gas state). However, phase changes are related to changes in potential energy, not kinetic energy.
What is the characteristic structure and motion of frozen things and what micro state do they undergo?
The molecules of water in ice, for example, aren’t “ frozen” in place and unable to move. Actually, there’s a lot of movement. The molecules rotate, vibrate, and wiggle around. The bonds within each molecule are also free to bend and stretch. Of course, the molecules are held in relatively stable positions by the hydrogen bonds that form between them, but they still have a fairly significant amount of motional (kinetic) energy. The potential energy, however, is quite low because of the stability provided by the relative closeness of one molecule to another and by the hydrogen bonds. add heat to ice that is at 0° C. The heat energy causes the water molecules to begin to break away from each other by breaking free of the hydrogen bonds between them. Not all of the hydrogen bonds and liquid water molecules still want to form hydrogen bonds, but because the water molecules are being held less rigidly in place, they now have greater degrees of freedom of movement (statistical mechanics says that these contribute to a greater number of “ microstates” ) and their average potential energy increases. However, their average kinetic energy stays the same because they “ redirect” some of their previously limited motion to other directions. Instead of only jumping up and down or swaying side to side, the molecules begin to move forward and backward. Nevertheless, to start moving forward, they have to decrease their up-and-down jumping. In this way, the average motional (kinetic) energy is constant even as the molecules begin to “ enjoy” greater degrees of freedom of movement (a greater number of possible microstates)
What are the different phase changes?
Phase changes are sublimation (solid to gas), deposition (gas to solid), fusion (solid to liquid), freezing (liquid to solid), condensation (gas to liquid), and finally vaporization (liquid to gas).
What is work?
When work is done by a system, the work is said to be positive, and when work is done on a system, the work is noted as negative. From the first law of thermodynamics, you can see that when work is done by the system, the internal energy of the system decreases, and when work is done on the system, the internal energy of the system increases. process of energy transfer by application of force through some distance. pressure can be thought of as an “ energy density.” During any thermodynamic process, a system goes from some initial equilibrium state with an initial pressure, temperature, and volume to some other equilibrium state, which may be at a different final pressure, temperature, or volume.
when a gas expands, we say that work was done by the gas and the work is positive; when a gas is compressed, we say that work was done on the gas and the work is negative. There are an infinite number of paths between an initial and final state. Different paths require different amounts of work. You can calculate the work done on or by a system by finding the area under the pressure-volume curve. Note that if volume stays constant as pressure changes (that is, Δ V = Δ x = 0), then no work is done because there is no area to calculate. On the other hand, if pressure remains constant as volume changes (that is, Δ P = Δ y = 0), then the area under the curve is a rectangle of length P and width Δ V (Vf− Vi). For processes in which pressure remains constant,
How does a piston work?
Ex. When the gas expands, it pushes up against the piston, exerting a force (F = PA), causing the piston to move up and the volume of the system to increase. When the gas is compressed, the piston pushes down on the gas, exerting a force (F = PA), and the volume of the system decreases. Because the volume of the system has changed due to an applied pressure, we can say that work has been done. much more work to change volume at high pressures. This makes sense when you think of pressurized cylinders. To put more gas into an already pressurized cylinder would take an incredible amount of work. Conversely when a pressurized cylinder is broken, it quickly does a lot of work on its environment. takes much more work to change volume at high pressures. put more gas into an already pressurized cylinder would take an incredible amount of work. Conversely when a pressurized cylinder is broken, it quickly does a lot of work on its environment.
What is a closed cycle?
closed cycle in which, after certain interchanges of work and heat, the system returns to its initial state. Because work is positive when the gas expands and negative when the gas is compressed, the work done is the area enclosed by the curve.
What are some special cases of the first law of thermodynamics?
special cases of the first law of thermodynamics- some physical property is held constant through the process. These processes are isovolumetric (constant volume), adiabatic (no heat exchange), and closed cycle (constant internal energy). Isovolumetric processes are also known as isochoric; closed cycle processes are also known as isothermal, meaning the temperature stays constant.
What is the second law of thermodynamics and energy and what is an example of that?
- Second Law of Thermodynamics and Entropy- Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so. second law states that energy will spontaneously disperse. It does not say that energy can never be localized or concentrated
- Ex. The chemical energy in the bonds of elemental iron and oxygen is released and disperses as a result of the formation of the more stable (lower energy) bonds of iron oxide (rust). The potential energy of the building is released and dispersed in the form of light, sound, and heat (motional energy) of the ground and air as the building crumbles and
What is entropy?
Entropy- measure of the spontaneous dispersal of energy at a specific temperature: how much energy is spread out or how widely spread out energy becomes in a process. where Δ S is the change in entropy, Q is the heat that is gained or lost, and T is the temperature in Kelvin. When energy is distributed into a system at a given temperature, its entropy increases. When energy is distributed out of a system at a given temperature, its entropy decreases. the entropy of the universe is always increasing. The more space that appears with the expansion of the universe, the more space there is for the entire universe’s energy to be distributed and the total entropy of the universe to increase irreversibly.
Work must usually be done to concentrate energy. energy in a closed system will spontaneously spread out and entropy will increase if it is not hindered from doing so. the second law ultimately claims that the entropy of the universe is increasing. That is, energy concentrations at any and all locations in the universe are in the process of becoming distributed and spread out.
What is an example of ran increase in entropy?
Ex. hot object is brought into thermal contact with a cold object, the hot object will transfer heat energy to the cold object until both are in thermal equilibrium (that is, at the same temperature). This is a natural process and also one that we would describe as irreversible: unsurprised that the two objects eventually reach a common temperature, but not possible if all of a sudden the hot object became hotter and the cold object became colder.. ice and liquid water in equilibrium at 0° C. If we place this mixture of ice and liquid water into a thermostat that is also at 0° C and allow infinitesimal amounts of heat to be absorbed by the ice from the thermostat so that the ice melts to liquid water at 0° C and the thermostat remains at 0° C, then the increase in the entropy (+Q/T) of the system (the water) will be exactly equal to the entropy decrease (− Q/T) of the surroundings (the thermostat). The net change in the entropy of the system and its surroundings is zero. Under these conditions, the process is reversible. The key to a reversible reaction is making sure that the process goes so slowly— requiring an infinite amount of time— that the system is always in equilibrium and no energy is lost or dissipated (by friction). To be frank, no real processes are reversible; we can only approximate a reversible process. Ice that melts on the warm countertop will not be expected to “ reverse course” and freeze if it remains in the warm environment. The liquid water will need to be placed in an environment that is cold enough to cause the water to freeze, and once frozen in the cold environment, the ice would not be expected to begin melting spontaneously. The freezing and melting of water in real life is essentially an irreversible process. reversible process, the entropy where L is the latent heat (either heat of fusion or heat of vaporization), m is mass, and T is the constant temperature of the system and environment in Kelvin.
What are electrostatics?
• study of stationary charges and the forces that are created by and act upon these charges.
What are charges?
• One, the proton, has a positive charge; the other, the electron, has a negative charge. While opposite charges exert attractive forces (that is, attracting forces), like charges, those that have the same sign, exert repulsive forces (that is, repelling forces). Unlike the force of gravity, which is always an attractive force, the electrostatic force may be repulsive or attractive, depending on the signs of the charges that are interacting. The fundamental unit of charge is e =1.60 × 10− 19 coulombs. A proton and an electron each have this amount of charge; the proton is positively charged (q = +e), while the electron is negatively charged (q = − e). Most matter is electrically neutral: A balance of positive and negative charges ensures a relative degree of stability. When charges are out of balance, the system can become electrically unstable. SI unit of charge is the coulomb, and the fundamental unit of charge. proton and an electron each have this amount of charge, although as we’ve already stated, the proton is positively charged (q = +e) while the electron is negatively charged (q = − e). Please note that even though the proton and the electron share the same magnitude of charge, they do not share the same mass. The proton has a mass much greater than that of the electron.
What does Colulumb’s Law state?
Coulomb’s Law- Coulomb’s law gives us the magnitude of the electrostatic force F between two charges q1 and q2 whose centers are separated by a distance r in meters. direction of the force may be obtained by remembering that unlike charges attract and like charges repel. The force always points along the line connecting the centers of the two charges.
What is an electric field?
• electric field- Every electric charge sets up a surrounding electric field. Electric fields make their presence known by exerting forces on other charges that move into the space of the field. Whether the force exerted through the electric field is attractive or repulsive depends on whether the stationary test charge qo (i.e., the charge placed in the electric field) and the stationary source charge (i.e., the charge that sets up the electric field) are opposite charges (attractive) or like charges (repulsive). Electric fields are produced by source charges (q). When a test charge (q0) is placed in an electric field (E), it will experience an electrostatic force (F) equal to q0E. where E is the electric field magnitude, F is the force felt by the test charge qo, k is the electrostatic constant, q is the source charge magnitude, and r is the distance between the charges. Electric field is a vector. The first method is to place a test charge qo at some point within the electric field, measure the force that the test charge feels, and define the electric field at that point in space as the ratio of the force magnitude to test charge magnitude. This is F/qo test charge must actually be present in order for a force to be generated (and measured). Sometimes, however, no test charge is actually within the electric field, so we need another way to measure the magnitude of that field because charges produce electric fields whether or not other charges are present to feel them. need to know the magnitude of the source charge and the distance between the source charge and point in space at which we want to measure the electric field. This is kq/r2. Field lines are used to represent the electric field vectors for a charge. They point away from a positive charge and point toward a negative charge. Field lines look like the spokes of a bicycle wheel, and the field lines of a single charge never cross each other. By convention, the direction of the electric field vector is given as the direction that a positive test charge +qo would move in the presence of the source charge. If the source charge is positive, then +qo would experience a repulsive force and would accelerate away from the positive source charge. On the other hand, if the source charge is negative, then +qo would experience an attractive force and would accelerate toward the negative source charge. Therefore, positive charges have electric field vectors that radiate outward (that is, point away) from the charge, whereas negative charges have electric field vectors that radiate inward toward (that is, point to) the charge. representation of the electric field vectors using field lines, also known as lines of force. These are imaginary lines that represent how a positive test charge would move in the presence of the source charge. The field lines are drawn in the direction of the actual electric field vectors. Field lines also indicate the relative strength of the electric field at a given point in the space of the field. The lines are closer together near the source charge and spread out at distances farther from the charge. Where the field lines are closer together, the field is stronger; where the lines are farther apart, the field is weaker. Since every charge exerts its own electric field, a collection of charges will exert a net electric field at a point in space that is equal to the vector sum of all the electric fields. When a test charge is placed in an electric field, a force will be generated on the test charge by the electric field, the magnitude. maintain the sign on the charge so that the direction of the force vector is in the direction of qoE. In other words, if the charge is positive, then the force will be in the same direction as the electric field vector; if the charge is negative, then the force will be in the direction opposite to the field vector.
What is electric potential energy?
give an example
• Electric Potential Energy- there are different “ flavors” of potential energy; gravitational, chemical, and mechanical are three forms. electric potential energy. In a manner similar to gravitational potential energy, this is a form of potential energy that is related to the relative position of one charge with respect to another charge or to a collection of charges. Just as a ball that is held high above the ground has a relatively large amount of gravitational potential energy, when one charge q is separated from another charge Q by a distance, r, the charges will have an electric potential energy equal to calculate the electric potential energy between two charges separated in space. If the charges are like charges (both positive or both negative), then the potential energy will be positive. If the charges are unlike (one positive and the other negative), then the potential energy will be negative. Remember that work and energy have the same unit (the joule), so we can define electrical potential energy for a charge at a point in space in an electric field as the amount of work necessary to bring the charge from infinity to that point. Electric potential energy is the work necessary to move a test charge from infinity to a point in space in an electric field surrounding a source charge. and W = Fd, if we define d as the distance r that separates two charges, then. The electric potential energy of a system will increase when two like charges move toward each other or when two opposite charges move apart. Conversely, the electric potential energy of a system will decrease when two like charges move apart or when two opposite charges move toward each other.
Opposite charges will have negative potential energy, and this energy will become increasingly negative as the charges are brought closer and closer together. Increasingly negative numbers are actually decreasing, because they are moving farther to the left of 0 on the number line. As like charges, these will exert repulsive forces, and the potential energy of the system will be positive. Since like charges repel each other, the closer they are to each other, the “ unhappier” (that is, less stable) they will be. Remember that unlike gravitational systems, the forces of electrostatics can be either attractive or repulsive. In this case, the like charges will become more stable the farther apart they move. When like charges are moved toward each other, the electric potential energy of the system increases; when like charges move apart, the electric potential energy of the system decreases. When unlike charges move toward each other, the electrical potential energy of the system decreases; when unlike charges are moved apart, the electrical potential energy of the system increases. This is the basic concept; the equation just helps you quantify the energy! This concept also helps you predict the direction of spontaneous movement of a charge: If allowed, a charge will always move in whatever direction results in a decrease in the system’s electric potential energy.
What is electric potential?
• Electric potential- the ratio of the work done to move a test charge from infinity to a point in an electric field surrounding a source charge divided by the magnitude of the test charge. electric potential energy. electric potential is defined as the ratio of the magnitude of a charge’s electric potential energy to the magnitude of the charge itself. Electric potential can also be defined as the work necessary to move a charge qo from infinity to a point in an electric field divided by the magnitude of the charge qo. where V is the electric potential measured in volts (V) and 1 volt = 1 joule/coulomb. Even if there is no test charge qo, we can still calculate the electric potential of a point in space in an electric field as long as we know the magnitude of the source charge and the distance from the source charge to the point in space in the field. Electric potential is a scalar quantity whose sign is determined by the sign of the charge qo. For a positive test charge, V is positive, but for a negative test charge, V is negative. For a collection of charges, the total electric potential at a point in space is the scalar sum of the electric potential due to each charge. Since electric potential is inversely proportional to the distance from the source charge, a potential difference will exist between two points that are at different distances from the source charge. If Va and Vb are the electric potentials at points a and b, respectively, then the potential difference, known as voltage, between a and b is Vb– Va. where Wab is the work needed to move a test charge qo through an electric field from point a to point b. The work depends only on the potentials at the two points a and b and is independent of the actual pathway taken between a and b. The “ plus” end of a battery is the high-potential end, and the “ minus” end of a battery is the low-potential end. Positive charge moves (the definition of current) from + to − while negative charge moves from − to +. When a positive charge moves spontaneously though an electric field, it will move from a position of higher electric potential (higher electric potential energy divided by the positive charge) to a position of lower electric potential (lower electric potential energy divided by the positive charge). Positive charge moves spontaneously from high voltage to low voltage. When a negative charge moves spontaneously through an electric field, it will move from a position of lower electric potential (higher electric potential energy divided by the negative charge) to a position of higher electric potential (lower electric potential energy divided by the negative charge). Negative charge moves spontaneously from low voltage to high voltage.
What are equipotential lines?
Equipotential Lines- the potential at every point is the same. That is, the potential difference between any two points on an equipotential line is zero. Since the work to move a charge from one equipotential line to another does not depend on the path, we know that we are dealing with conservative forces. In three-dimensional space, these equipotential lines would actually be spheres surrounding the source charge. From the equation for electric potential, you can see that no work is done when moving a test charge qo from one point to another on an equipotential line. Work will be done in moving a test charge qo from one line to another, but the work depends only on the potential difference of the two lines and not on the pathway taken between them. This is entirely analogous to the displacement of an object horizontally above a constant surface. Since the object’s height above the surface has not changed (the object has only moved, say, to the left or to the right of its original position), its gravitational potential energy is unchanged. Furthermore, the change in the object’s gravitational potential energy will not depend on the pathway taken from one height to another but only on the actual height displacement.
One very important equipotential line that you should be aware of is the plane that lies halfway between +q and – q, called the perpendicular bisector of the dipole. Since the angle between this plane and the dipole axis is 90° (and cos 90° = 0), the electric potential at any point along this plane is 0. The electric field produced by the dipole at any point in space is the vector sum of each of the individual electric fields produced by the two charges. Along the perpendicular bisector of the dipole, the magnitude of the electric field can be approximated. The electric field vectors at the points along the perpendicular bisector will point in the direction opposite to p (as defined directionally by physicists).
What is an electric dipole?
The electric dipole, which results from two equal and opposite charges being separated a small distance d from each other, can be transient (as in the case of the moment-by-moment changing distribution of electrons in the electron cloud of an atom or molecule) or permanent (as in the case of the molecular dipole of water or the carbonyl functional group). The equal weights on either end of the bar represent the equal and opposite charges separated by a small distance, represented by the length of the bar. charges +q and – q separated by a distance d. Given the dipole, we want to calculate the electric potential P at some point surrounding the dipole. The distance between the point in space and +q is r1; the distance between the point in space and – q is r2; the distance between the point in space and the midpoint of the dipole is r. We know that for a collection of charges, the electric potential P is the scalar sum of the potentials due to each charge at that point. For points in space relatively distant from the dipole (compared to d), the product of r1 and r2 is approximately equal to the square of r, and the r2– r1 is approximately equal to dcosθ.
The product of qd is defined as the dipole moment p with SI units of C· m. The dipole moment is a vector. ector along the line connecting the charges (the dipole axis), with the vector pointing from the negative charge toward the positive charge. Chemists usually reverse this convention, having p point from the positive charge toward the negative charge. Sometimes, you’ll see chemists draw a crosshatch at the tail end of the dipole vector to indicate that the tail end is at the positive charge. In terms of the dipole moment p, we can rewrite the equation for calculating the potential at a point in space near a dipole.
• when the electric dipole is placed in a uniform external electric field (strength of field everywhere the same), each of the equal and opposite charges of the dipole will feel a force exerted on it by the field. Since the charges are equal and opposite, the forces acting on the charges will also be equal and opposite, resulting in a situation of translational equilibrium. where p is the magnitude of the dipole moment (p = qd), E is the magnitude of the uniform external electric field, and theta is the angle the dipole moment makes with the electric field. This torque will cause the dipole to reorient itself by rotating so that its dipole moment, p, aligns with the electric field E.
What is magnetism? and how are magnetic fields created?
- Magnetism- the two necessary conditions for the generation of magnetic fields are charge and movement of that charge. Likewise, the two necessary conditions for the generation of magnetic forces are charge and movement of that charge. Both magnetic and electric fields describe the direction a positive charge would travel. If you are ever given a negative charge, continue to solve as if it were a positive test charge. However, flip your answer 180° at the very end.
- Any moving charge creates a magnetic field. Magnetic fields may be set up by the movement of individual charges, such as an electron moving through space; by the mass movement of charge in the form of a current though a conductive material, such as a copper wire; or by the “ flow” of charge in permanent magnets. single electron through space or a current through a conductive material, creates a magnetic field. The SI unit of magnetic field is the tesla (T). SI unit of the magnetic field is the tesla (T) for which 1 T = 1 N· s/m· C. The size of the tesla unit is quite large, so small magnetic fields are sometimes measured in gauss, for which 1 T = 104 gauss. For magnetic field vectors that are “ along the plane of the page,” draw field lines as arrows with the tip of the arrow pointing in the direction of the field vector. For magnetic field vectors that are “ coming out of the page,” draw a dot to represent the tip of the field vector (the tip of the arrow). And for magnetic field vectors that are “ going into the page,” draw an X to represent the tail of the field vector (the tail of the arrow). The spacing between magnetic field lines is reflective of the strength of the field at that point in space: The farther out from the moving charge, the weaker the magnetic field, and the further apart the field lines will be spaced. At any point along a field line, the magnetic field vector itself is tangential to the line.
What are magnetic materials?
- Magnetic materials include- diamagnetic, paramagnetic, or ferromagnetic. Diamagnetic materials are made of atoms with no unpaired electrons and that have no net magnetic field. Diamagnetic materials will be repelled by either pole of a bar magnet and so can be called weakly antimagnetic. In layperson terms, diamagnetic materials are “ nonmagnetic” and include common materials that you wouldn’t ever expect to get stuck to a magnet: wood, plastics, water, glass, and skin, just to name a few.
- both paramagnetic and ferromagnetic materials have unpaired electrons, so these atoms do have a net magnetic moment dipole, but the atoms in these materials are usually randomly oriented so that the material itself creates no net magnetic field. Paramagnetic materials will become weakly magnetized in the presence of an external magnetic field, which causes the permanent magnetic dipoles of the individual atoms to align with the external field. Paramagnetic materials will be attracted toward the pole of a bar magnet, so they are sometimes called weakly magnetic. Upon removal of the external magnetic field, the thermal energy of the individual atoms will cause the individual magnetic dipoles to reorient randomly, and the material will cease to be magnetized. Some paramagnetic materials that we commonly work with include aluminum, copper, and gold.
What are ferromagnetic materials?
Ferromagnetic materials, like paramagnetic materials, have unpaired electrons and permanent atomic magnetic dipoles that are normally oriented randomly so that the material has no net magnetic dipole. However, unlike paramagnetic materials, ferromagnetic materials will become strongly magnetized when exposed to a magnetic field or under certain temperatures. For all ferromagnetic materials, there is a critical temperature, called the Curie temperature, above which the material is paramagnetic but below which the material is magnetized as a result of a high degree of alignment of the magnetic fields of the individual atoms (which are assembled into large groups of atoms [1012-1018] called magnetic domains). When the ambient temperature (i.e., room temperature) is below the Curie temperature, the material is permanently magnetized. The common metal bar magnet that holds our grocery lists, photos, and holiday cards against the refrigerator door is made of permanently magnetized material, typically including iron. (Interestingly, the thin flexible magnets that have also found a home on your refrigerator are made of ground-up magnetite, a crystalline ferrimagnetic material that is weakly magnetic.) Other ferromagnetic materials are nickel and cobalt. They are sometimes called strongly magnetic because they have a large and positive susceptibility to external magnetic fields, are strongly attracted to magnetic fields, and can retain their magnetic properties for varying amounts of time after the external magnetic field has been removed. Common examples of ferromagnetic items, in addition to the ubiquitous bar magnet, include paper clips, safety pins, and sewing needles.
• All bar magnets have a north and south pole. Field lines exit the north pole and enter the south pole. Because magnetic field lines are circular, it is impossible to have a monopole magnet (but it is possible for magnets to have more than two poles). If two bar magnets are allowed to interact, opposite poles will attract each other, while like poles will repel each other.
What does current-carrying wire create?
Current-Carrying Wires- Because any moving charge creates a magnetic field, we would certainly expect that a collection of moving charge, in the form of a current through a conductive material such as a copper wire, would produce a magnetic field in its vicinity. As with the net electric field of multiple charges, the net magnetic field of a current is equal to the vector sum of the magnetic fields of all the individual moving charges that comprise the current. The configuration of the magnetic field lines surrounding a current-carrying wire will depend on the shape of the wire. when two points at different electric potentials are connected with a conductor (such as a copper wire), charge flows between the two points. The flow of charge is called an electric current. The magnitude of the current i is the amount of charge Δ q passing through the conductor per unit time Δ t, and it can be calculated
What is current?
SI unit of current is the ampere (1 A = 1 coulomb/second). Charge is transmitted by a flow of electrons in a conductor, and because electrons are negatively charged, they move from a point of lower electric potential to a point of higher electric potential (and in doing so reduce their electrical potential energy). By convention, however, the direction of current is the direction in which positive charge would flow from higher potential to lower potential. Thus, the direction of current is opposite to the direction of actual electron flow.
What are the specificities of a magnetic field when a infinitely long and straight current-carrying wire are used?
infinitely long and straight current-carrying wire, we can calculate the magnitude of the magnetic field produced by the current i in the wire at a perpendicular distance, r, from the wire. where B is the magnetic field at a distance r from the wire, and μ o is the permeability of free space (4π × 10− 7 tesla · meter/ampere = 1.26 × 10− 6 T · m/A). The equation demonstrates an inverse relationship between the magnitude of the magnetic field and the distance from the current. shape of the magnetic fields surrounding a current is concentric perpendicular circles of magnetic field vectors. To determine the direction of the field vectors, you can use a right-hand rule. This right-hand rule is one of three right-hand rules that you will use in the context of magnetism. In this rule, your right thumb points in the direction of the current. Your other right-hand fingers mimic the circular magnetic field lines, curling around your thumb in the same direction that the magnetic field lines curl around the current. Your fingers show you the direction of the magnetic field lines and the direction of B itself at any point. This right-hand rule works for both a straight-line wire and a circular loop of wire. (You must use your right hand for this and all other right-hand rules.
What are the specificities of a magnetic field when a circular loop of current-carrying wire are used?
For a circular loop of current-carrying wire of radius r, the magnitude of the magnetic field at the center of the circular loop. The less obvious difference is that the first expression gives the magnitude of the magnetic field at any perpendicular distance, r, from the current-carrying wire, while the second expression gives the magnitude of the magnetic field only at the center of the circular loop of current-carrying wire with radiusr.
What is the magnetic force due to a magnetic field?
The Magnetic Field Force- magnetic field lines never cross. created by magnets or moving charge, and magnetic fields exert forces only on other moving charges. Charges do not “ sense” their own fields; they only sense the field established by some other charge or collection of charges. That is to say, charges feel forces only from external electric or magnetic fields. presence of a fixed and uniform magnetic field B. This field is produced, of course, by some external source, such as a magnet or arrangement of moving charge (such as a configuration of current-carrying wires), only concerned with the strength and direction of the external field
What is the magnetic force on a moving charge?
• Force On A Moving Charge- When a charge moves in a magnetic field, a magnetic force may be exerted on it, the magnitude of which can be calculated. where q is the charge (including the sign of the charge), v is the velocity of the charge, B is the magnitude of the magnetic field, and θ is the smallest angle between the vector qv and the magnetic field vector B. Notice that the magnetic force is a function of the sine of the angle, which means that the charge must have a perpendicular component of velocity in order to experience a magnetic force. If the charge is moving with a velocity that is parallel or antiparallel to the magnetic field vector, it will experience no magnetic force. sin 0° and sin 180° equal zero. This means that any charge moving parallel or antiparallel to the direction of the magnetic fi eld will experience no force from the magnetic fi eld.
What is the second right hand rule?
• Second right hand rule- To determine the direction of the magnetic force on a moving charge, you must position your right-hand thumb in the direction of the vector qv. The vector qv takes into account not only the direction of the velocity vector but also the sign on the charge. If the charge is positive, then your thumb will point in the direction of v, but if the charge is negative, your thumb will point in the direction opposite to v. Of course, if either q or v is zero, then you have either no charge or stationary charge, your thumb has nowhere to point, and there is no magnetic force to be calculated. Once you’ve figured out what direction your thumb needs to point, extend your fingers in the direction of the magnetic field. Your fingers should point away from you if the magnetic field vector is going “ into the page” and represented by Xs; they should point toward you if the magnetic field vector is coming “ out of the page” and represented by dots. You may need to rotate your wrist this way or that to get the correct configuration of thumb and fingers. Once your thumb and fingers are in their proper positions, your palm, which has no choice but to face a particular direction, will indicate the direction of the magnetic force vector F on the moving point charge q. has your thumb point in the direction of velocity, your index finger in the magnetic field, and then the palm of your hand in the direction of force. As long as your own method works for you, use it! Charged particles moving perpendicular to a constant, uniform magnetic field travel in uniform circular motion, with constant speed in the plane perpendicular to the magnetic field. For a charge moving in uniform circular motion due to an external magnetic field, a change in the strength of the external magnetic field will result in a change of the radius of the circular pathway of the charged particle but not in the magnitude of its velocity.
What is the third right-hand rule?
third right hand-rule: applies to current-carrying wire placed in an external magnetic field. It’s actually the same right-hand rule you will use to determine the force exerted by a magnetic field on a point charge; the only difference is that the right-hand thumb always points in the direction of the current, never opposite to that direction. Because current, by convention, is the direction of movement of positive charge, it makes sense that the thumb will always point in the same direction as current. The other fingers of your right hand are positioned so that they point in the same direction as the magnetic field vector B. The palm of your right hand will automatically be facing in the direction of the magnetic force vector. The force acting on the current-carrying wire will always be perpendicular to the plane defined by B and the direction of the current. Your palm will indicate which of the two perpendicular directions the force is acting.
What direction does a charged particle move in a magnetic field?
When a charged particle moves perpendicular to a constant, uniform magnetic field, the resulting motion is circular motion with constant speed in the plane perpendicular to the magnetic field. Charged particles assume circular motion with constant speed when they move into a constant, uniform magnetic field perpendicular to the field vector. A centripetal force is always associated with circular motion. In other words, an external force, which we call the centripetal force, must always be applied to an object demonstrating circular motion since that object must constantly change direction. The centripetal force may be the tension in a string, the restoring force of a spring, gravitational force between a planet and a satellite, or the force of a magnetic field (just to name a few). In this case, the centripetal force is the magnetic force (F = qvB). solve for the orbit radius (r), the magnetic field (B), and the velocity (v). assuming constant mass and charge of the charged particle, both the velocity and radius of the uniform circular motion seem to be a function of the magnetic field. This is to say, it seems to be the case that changing the magnitude of the magnetic field will either result in an increase in the velocity or a decrease in the radius (or some combination of both). We know that work is done when a force is applied through some distance and there is a dependency of work on the cosine of the angle between the force vector and the displacement vector. In circular motion, the centripetal force is always perpendicular to the instantaneous velocity vector (angle equals 90° ; cos 90° = 0); therefore, no work is done by the centripetal force on the moving charged particle. According to the work-energy theorem, if no (net) work is done on an object, its kinetic energy will not change, and there will be no change in the magnitude of the object’s velocity. This is exactly what happens in uniform circular motion: The speed of the object is constant as it travels through its circular pathway. For this charged particle, which demonstrates uniform circular motion, it must be the case that the magnitude of its velocity is constant. Thus, a change in the strength of the magnetic field will result in a change in the radius of the circular pathway of the charged particle but not in the magnitude of the velocity.
