Ch. 1: Kinematics and Dynamics Flashcards
what are the 7 SI units and the corresponding “thing” that they measure?
- METER –> length
- KILOGRAM –> mass
- SECOND –> time
- AMPERE –> current
- MOLE –> amount of substance
- KELVIN –> temperature
- CANDELA –> luminous intensity
defn: base unit vs. derived unit
BASE UNIT = the standard units around which the system itself is designed
DERIVED UNIT = created by associating base units with each other (i.e. a Newton)
what is an angstrom in terms of meters?
1 A = 10^-10 m
what is a nanometer in terms of meters?
1 nm = 10^-9 m
what is an electron-volt in terms of Joules? what does an eV represent?
1 eV = 1.6 x 10^-19 J
the amount of energy gained by an electron accelerating through a potential difference of one volt
defn: vectors (4 examples) vs. scalars (5 examples)
VECTOR = numbers that have magnitude and direction
1. displacement 2. velocity 3. acceleration 4. force
SCALAR = numbers that have magnitude only, not direction
1. distance 2. speed 3. energy 4. pressure 5. mass
defn: resultant
the sum or difference of two or more vectors
defn + process: tip to tail method
one method of finding the resultant of two vectors
place the tail of B at the tip of A without changing the length or direction of either arrow
the lengths of the arrows must be proportional to the magnitudes of the vectors
the vector sum of A + B is the vector joining the tail of A to the tip of B and pointing toward the tip of B
defn: component method of vector addition
break each vector into perpendicular components (most often x and y), however in some circumstances it makes more sense to define them as parallel and perpendicular to some other surface
what is a simple way of describing the x and y components of a resultant vector?
the x component is the sum of the x components of the vectors being added
the y component is the sum of the y components of the vectors being added
how do you subtract one vector from another? what does this look like mathematically?
by adding a vector with equal magnitude but opposite direction to the first vector
A - B = A + (-B) where -B represents a vector with the same magnitude as B but pointing in the opposite direction
how does the component method work for vector subtraction?
the x-component of the resultant vector is the difference of the x-components of the vectors being subtracted
the y-component of the resultant vector is the difference of the y-components of the vectors being substracted
what is the result of a vector A being multiplied by a scalar n (magnitude and direction)?
new vector B = nA
magnitude: |n|A
direction: look at the sign of n
- if n is positive: B and A are in the same direction
- if n is negative: B and A point in opposite directions
defn + equation: dot product
does this generate a vector or scalar product?
the dot product is how we multiply vectors by other vectors
SCALAR product: A dot B = |A| |B| cos theta
defn + equation: cross product
does this generate a vector or scalar product?
the cross product is another way of how we multiply vectors by other vectors
VECTOR product: A x B = |A| |B| sin theta
once we have the magnitude we use the right-hand rule to determine its direction
what direction is the resultant of a cross product in relation to the plane created by the two vectors? what does this mean physically on the MCAT?
resultant of a cross product will ALWAYS BE PERPENDICULAR to the plane created by the two vectors
on the MCAT: usually means the vector of interest is going into or out of the screen
what are the three steps of applying the right hand rule when considering a resultant C where C = A x B?
- Point your thumb in direction of vector A
- Extend your fingers in the direction of vector B (you may need to rotate your wrist to get the correct configuration)
- Your palm establishes the plane between the two vectors –> the direction your palm points is the direction of the resultant C
what is a secondary method (not the palm method) of using the right hand rule for a resultant C = A x B?
- Point the right index finger in the direction of A
- Point the right middle finger in the direction of B
- Hold the thumb perpendicular to these two fingers, it is the direction of C
defn: displacement (x or d)
is this a vector or scalar quantity?
displacement = an object in motion may experience a change in its position in space
this is a vector quantity (has both magnitude and direction)
what does the displacement vector connect?
the object’s initial and final position
does displacement consider the path?
NO! only the net change in position from initial to final
defn: distance
how does this differ from displacement?
a scalar quantity that considers the pathway taken
magnitude + SI unit + direction: velocity
magnitude: the rate of change of displacement in a given unit of time
SI units: meters/second
direction: the same direction of the displacement vector
defn: speed
the rate of actual distance traveled in a given unit of time
what is the relationship between an object’s instantaneous speed and an object’s instantaneous velocity?
the instantaneous speed of an object will always be equal to the magnitude of the object’s instantaneous velocity
defn: instantaneous velocity
a measure of the average velocity as the change in time (delta t) approaches zero
defn: average speed vs. average velocity
average SPEED = a measure of distance traveled in a given period of time
average VELOCITY = a measure of the displacement of an object over a given period of time
every change in velocity is motivated by a what?
a push or a pull (a force
defn + SI unit: Force (F)
a vector quantity that is experienced as pushing or pulling on objects (they do not need to touch!)
SI unit: newton (N) = kg.m/s^2
defn: gravity
an attractive force that is felt by all forms of matter
all objects exert gravitational forces on each other (no matter how small!)
why do gravitational forces usually not have much significance on a small scale?
other forces tend to be much larger in magnitude
they only really take on a significant value on the planetary level
defn: friction
a type of force that opposes the movement of objects and cause it to slow down or become stationary
what are the two types of friction?
static
kinetic
defn: static friction (fs)
exists between a stationary object and the surface upon which it rests
defn: coefficient of static friction (us)
a unitless quantity that is dependent on the two materials in contact
defn: normal force
the component of the force between two objects in contact that is perpendicular to the plane of contact between the object and the surface upon which it rests
what does it mean when static friction = 0?
an object is resting on a surface with no applied forces
if an object is stationary, is it necessarily experiencing a maximal static force of friction?
no
what will any applied force below the threshold of the maximal value of static friction to the the object?
it will not be sufficient to move the object as there will be an equal but opposite force of static friction opposing the object’s motion
defn: kinetic friction (fk)
exists between a sliding object and the surface over which the object slides
any time two surfaces slide against each other, there will be kinetic friction present
what are the two main distinctions between the equations for static and kinetic friction and what do these differences imply?
KINETIC FRICTION EQUATION HAS AN EQUALS SIGN –> kinetic friction will have a constant value for any given combination of a coefficient of kinetic friction and normal force
DIFFERENT COEFFICIENTS OF FRICTION –> us is always larger than uk (the max value for static friction will always be greater than the constant value for kinetic friction –> objects will stick until they stat moving and then will slide more easily over each other)
does the amount of surface area in contact or the velocity of the sliding object affect the value of kinetic friction?
no! the value of kinetic friction is a constant for any given combo of a coefficient of kinetic friction and normal force
defn: mass vs. weight
+ (scalar vs. vector, SI unit)
mass (m) = a measure of a body’s inertia = the amount of matter in the object
- scalar
- SI unit: kilogram
weight (Fg) = a measure of the gravitational force (usually of Earth) on an object’s math
- vector
- unit: newtons (N)
defn: center of mass or gravity
the weight of an object can be though of as being applied at a single point in that object
defn: acceleration (a)
vector or scalar?
SI units?
the rate of change of velocity that an object experiences as a result of some applied force
vector
Si units: meters/s^2
defn: deceleration
acceleration in the direction opposite the initial velocity
on the graph of velocity vs. time, what is the tangent to the graph at any time t (the slope of the graph at that time)
the instantaneous acceleration
Newton’s first law
Fnet = ma = 0
where Fnet = net force, m = mass, a = acceleration
A body either at rest or in motion with constant velocity will remain that way unless a net force acts upon it (the law of inertia)
Newton’s second law
Fnet = ma
An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector
note: the net force and acceleration vectors necessarily point in the same direction
Newton’s third law
FAB = - FBA
the law of action and reaction
To every action, there is always an opposed but equal reaction
More formally: for every force exerted by object A on object B, there is an equal but opposite force exerted by object B on object A
remember: physical contact is not necessary
defn: linear motion
the object’s velocity and acceleration are along the line of motion, so the pathway of the moving object continues along a straight line
value: acceleration due to gravity
g = 9.8 m/s^2
defn: free fall
an object would fall with constant acceleration (g) and would not reach terminal velocity
char: air resistance (2)
- opposes the motion of an object
- its value increases as the speed of the object increases
proc: drag force
an object in free fall will experience a growing drag force as the magnitude of its velocity increases
defn: terminal velocity
eventually, the drag force will be equal in magnitude to the weight of the object and the object will fall with constant velocity according to Newton’s first law
defn + char: projectile motion
motion that follows a path along two dimensions
the velocities and accelerations in the two directions are INDEPENDENT of each other and must be analyzed separately
for projectile motion, is the acceleration of gravity felt in the vertical direction? in the horizontal direction?
what does this imply
ONLY in the vertical direction
that only means that vy will change at the rate of g but vx will remain constant
why can we generally assume that horizontal velocity in freefall is 0 on the MCAT?
we usually assume that air resistance is negligible and thus no measurable force is acting along the x-axis
approach: inclined planes
divide force vectors into components that are parallel and perpendicular to the plane
most often, gravity must be split into components
Fg parallel = mg sin theta –> the component of gravity parallel to the plane (oriented down the plane)
Fg perpendicular = mg cos theta –> the component of gravity perpendicular to the plane (oriented into the plane)
defn: 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
char (6): uniform circular motion (traditional focus on MCAT)
- speed of the object is constant
- the instantaneous velocity vector is always tangent to the circular path
- the object moving in the circular path has a tendency (inertia) to break out of its circular pathway and move in a linear direction along the tangent
- it is kept from doing so by a centripetal force (always points radially inward)
- we can resolve the forces into radial and tangential components
- the tangential force is zero because there is no change in the speed of the object
defn: centripetal acceleration
generated by centripetal force
this acceleration keeps an object in its circular pathway (remember: the acceleration is always in the same direction as the net force)
defn: dynamics
the study of forces and torques
defn: translational motion
occurs when forces cause an object to move without any rotation
what are the two things needed to solve any translational motion problem?
- free body diagrams
- Newton’s three laws
when does translational equilibrium exist? what is this called?
exists only when the vector sum of all the forces acting on an object is zero
this is called the first condition of equilibrium
why does an object experiencing translational equilibrium have constant velocity?
- when the resultant force upon an object is zero, the object will not accelerate (so the object is stationary OR is moving with a constant nonzero velocity)
- THUS an object experiencing translational equilibrium will have a constant velocity
defn: 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 (the fulcrum)
defn + aka: torque
application of force at some distance from the fulcrum
aka: moment of force
defn: lever arm
the distance between the applied force and the fulcrum
why is torque what generates rotational motion NOT the mere application of the force itself?
because torque depends not only on the magnitude of the force but also on the length of the lever arm and the angle at which the force is applied
defn + aka: rotational equilibrium
exists only when the vector sum of all the torques acting on an object is zero
aka: second condition of equilibrium
pair clockwise (cw) and counterclockwise (ccw) torques with positive and negative
CW = negative
CCW = positive
what are the two possibilities of motion in the case of rotational equilibrium?
which is more common on the MCAT?
- not rotating at all (stationary) –> almost always the case on the MCAT
- rotating with a constant angular velocity
