Book 2: Force and Motion Flashcards
What are the SI units of length and time?
length: metre (m)/kilometre (km), centimetre (cm), millimetre (mm)
time: second (s)/microsecond (μs), millisecond (ms)
What is the average reaction time of a person?
0.2s
How can we overcome the limits of reaction time?
We can measure the duration of repeating events for more cycles or use automatic devices like light-gates connected to a timer-scaler or data-logger.
What is displacement and what type of measurement is it?
Displacement is the change in position relative to the starting position, and it requires both magnitude (size) and direction. Therefore, it is a vector.
What is the difference between vectors and scalars?
Vectors require both magnitude and direction, but scalars only require magnitude.
How can the total displacement be calculated?
If the displacement is along a straight line, the total displacement has the magnitude and direction of the arrow pointing from the starting point to the finishing point. If the displacement is along a plane, Pythagoras’ theorem and trigonometry can be used to find its magnitude and direction.
What is speed and what is its unit? Is it a vector or scalar?
Speed is the distance travelled per unit time, measured in an SI unit of ms^-1 (m/s). It is a scalar because it does not require direction.
What are average speed and instantaneous speed?
Average speed measures how fast an object moves over a whole journey. It is obtained by dividing the total distance travelled by the time taken. Instantaneous speed is the average speed over an extremely short time; the shorter the time period, the more accurate the measurement.
What is velocity and what is its unit? Is it a vector or scalar?
Velocity is the displacement per unit time, measured in an SI unit of ms^-1. It is a vector because it has both magnitude and direction.
What are average velocity and instantaneous velocity?
Average velocity measures the displacement of an object over a whole journey. It is obtained by dividing the total displacement travelled by the time taken. It may not be equal to the average speed. Instantaneous velocity is the average displacement over an extremely short time; the shorter the time period, the more accurate the measurement. Its magnitude is always equal to that of instantaneous speed.
What does it mean when an object is in uniform motion?
It is moving in constant velocity, which means it is moving at a constant speed in a fixed direction.
What is acceleration and what is its unit? Is it a vector or scalar?
Acceleration is the change in velocity per unit time, measured in an SI unit of ms^-2. It is a vector because an object has acceleration when its direction changes as well.
What is average acceleration?
Average acceleration is the total change of velocity in the total time travelled.
How can we tell whether an object is speeding up or slowing down from its velocity and acceleration?
If the velocity and acceleration have the same sign, the object is speeding up. If they have opposite signs, then the object is slowing down. We cannot tell the direction or acceleration of an object from only the sign of its velocity, or only the sign of its acceleration.
What is a s-t graph and what are its features?
An s-t graph is a displacement-time graph, with the displacement being plotted on the y-axis against the time. Its slope give the velocity of the object.
What is a v-t graph and what are its features?
A v-t graph is a velocity-time graph, with the velocity being plotted on the y-axis against the time. The slope of a v-t graph gives the acceleration of an object. When the graph is a straight line or curve, the sign of the slope gives the direction of acceleration and the steeper the slope, the greater the magitude of acceleration. The area under a v-t graph is the total displacement of the object.
What is an a-t graph?
An a-t graph is an acceleration-time graph, with the acceleration being plotted on the y-axis against the x-axis.
What are the looks of the s-t, v-t, and a-t graphs when an object is in uniform motion?
The s-t graph is a straight line, the v-t graph is a horizontal line (y=v, where v is the constant velocity), and the a-t graph is a horizontal line (y=0)
What are the looks of the s-t, v-t, and a-t graphs when an object is uniformly accelerated?
The s-t graph is a curved line curved upwards, the v-t graph is a straight line with a slope, and the a-t graph is a horizontal line (y=a, where a is the constant acceleration)
What are the looks of the s-t, v-t, and a-t graphs when an object is uniformly accelerating with direction opposite to its velocity?
The s-t graph is a downward-opening parabola, the v-t graph is a straight line with slope from positive to negative, and the acceleration is a horizontal line (y=a, where a is the constant acceleration and a<0)
What are the equations of uniformly accelerated motion?
v=u+at, s=1/2(v+u)t=ut+1/2at^2, v^2=u^2+2as
Why do objects fall at different speeds?
Objects fall due to gravity, and they fall at different speeds because of air resistance. If air is removed, objects fall at the same rate.
What is the acceleration due to gravity?
9.81 ms^-2 near the earth’s surface and pointing downwards, denoted by g
What is a force and its unit? Is it a vector or scalar?
Force is a push or pull on an object by another object, and it exists in pairs. Its SI unit is newton (N), and it is a vector because it has both magnitude and direction.
How are forces measured?
They can be measured using spring balances or force sensors. A spring balance can only measure a pulling force while a force sensor conected to a data-logger can measure both pulls and pushes.
What are some examples of contact forces?
Friction: friction occurs when an object slides or tends to slide over another object. Its direction is opposite to that of the relative motion of the object.
Tension: when a rope is stretched, tension is developed and pulls objects along the stretched object.
Normal force: the force acting perpendicularly on an object by the surface in contact with it (supporting force)
What are some examples of non-contact forces?
Weight: weight is a gravitational pull by the Earth towards the centre of the earth.
Electrical force: exists between electric charges
Magnetic force: exists between magnets and magnetic objects
What is net force?
Net force is the added result of all forces exerted on an object.
What is inertia?
Inertia is the tendency of an object to maintin its state of rest or of uniform motion/constant velocity.
How is inertia related to mass?
Mass is a measure of an object’s inertia. The greater the mass, the greater the inertia.
What is Newton’s first law of motion?
Every object remains in a state of rest or uniform motion unless acted on by a net force or unbalanced force.
What is Newton’s second law of motion?
The acceleration of an object is directly proporitonal to, and in the same direction as, the net force acting on it, and inversely proporitonal to the mass of the object. (F=ma)
1N=?kg
1N=1kg m s^-2
What is weight (on earth)?
Weight is the gravitational force acting on an object. W=mg, where g is the acceleration due to gravity (9.81m s^-2)
How is mass different from weight?
Mass measures the inertia of an object while weight is the gravitational force acting on an object. Mass is measured in kg while weight is measured in N. The value of mass does not depend on location, but weight varies with location.
Why doesn’t an object resting on a plane move if the applied force is too small? Why does it start to move when the applied force increases to a certain magnitude?
The net force acting on the object is equal to 0, which means that the friction between the object and the plane has the same magnitude as the applied force. Friction increases accordingly when the applied force increases but there is a maximum value for friction. Therefore, when the applied force is large enough, the object starts moving.
What is fluid resistance and what is its relaitonship with the speed and shape of an object?
Fluid resistance is the resistive force experienced by objects when they move through fluids. It increases with the speed of moving objects, and streamlined bodies can reduce the resistance.
What is Newton’s third law of motion?
To every action, there is an equal and opposite reaction. The action and reaction forces act on different interacting objects simultaneously.
What are some characteristics of an action-and-reaction pair?
They act on different objects that interact with each other, have an equal magnitude at all times, and act in opposite directions.
What is resultant force?
Resultant force is the combination of two or more forces acting on an object that provides the same total effect of the original forces.
How do we resolve one force into two forces?
We usually resove them to components that are perpendicular to each other. Fx=F cosa, Fy=F sina, where a is the angle of F (the original force).
What is the moment of force and what is its unit? Is it a scalar or vector?
Moment of force/torque measures the turning effect of a force about a certain point. It is represented by τ and has a unit of newton-metre (N m). It is a vector and measures turning effect in clockwise and anticlockwise directions.
What is the formula for obtaining moment?
Moment of force=force*perpendicular distance from the point
How do we obtain the length of the moment arm?
When the force is perpendicular to the rod, the moment arm is equal to the length of the rod (attains its maximum). When the force makes an acute angle a with the rod, the moment arm can be found by lsina (l is the length of the rod). When the force is parallel to the rod, the moment arm is equal to 0 (attains its minimum).
What is a pivot?
A pivot is the point an object turns about when it is acted on by a moment.
What is net moment?
Net moment is the sum of all moments acting on a body. Taking the clockwise direction as positive, the net moment is all clockwise moment-all anticlockwise moment.
What is a couple?
A couple forms when two equal and oppoite parallel forces apply simultaneously to the same body and do not act in the same line.
How can the net moment of a couple be obtained?
net moment=force*perpendicular distance between the forces
What is equilibrium and what are its conditions?
A rigid body stays in equilibrium when it is at rest, that is, when it has no net force acting on it and no net moment acting on it.
What is the centre of gravity and how can it be located?
The centre of gravity is a fixed point on every rigid body where its weight seems to act. For a uniform symmetrical object, its centre of gravity i is located at its centre, whereas the centre of gravity of a non-uniform object can be found experimentally.
What is work and what is its unit? Is it a scalar or a vector?
Work, or mechanical work, is the energy transferred due to a force. It is measured in joules (J) and it is a scalar. W=F//s, 1J=1N m (1J of work is done when a force of 1N pushes an object resulting in displacement of 1m)
What happens when work is done on an object by F, and when work is done against an object by F?
When work is done on an object by F, the object speeds up when it is acted on by F in the same direction, making it speed up and gain kinetic energy. When work is done against an object by F, the object is acted on by F in the opposite direction, making it slow down and lose kinetic energy.
What happens to the work done when the applied force is not parallel to the displacement of the object?
W=Fscosa, where F// (parallel force) is the only force counted, obtained by using trigonometric ratios to find the horizontal component (F//).
How can the total work done be calculated?
The total work done=net parallel force*displacement
How can we find the kinetic energy increase through the work done?
W=Fs=ma*v^2/2a=1/2mv^2
What are two types of potential energy and how are they posessed?
Elastic potential energy, possessed by an elastic object when stretched/compressed/bent; and gravitational potential energy, possessed by an object due to gravity.
What is the formula for gravitational potential energy?
GPE=mgh (massheightg)
What is the law of conservation of energy?
Energy can be converted from one form to another, but it canot be created or destroyed.
What are some examples where the sum of kinetic and potential energy is constant?
Simple pendulum and bungee jumping, when air resistance is negligible
Which quantities of energy are conserved in a system where air resistance is not negligible?
The total amount of GPE, EPE, KE, and Wf (work done against air resistance that turns energy into internal energy)
What are some examples where the sum of kinetic energy and potential energy is not constant?
Braking, roller coasters, diving
What is horsepower?
Horsepower is a unit of power that measures the power of a typical horse. It is equal to about 746 watts.
What is the relationship between power and force?
P=Fv (power=force*velocity)
What is momentum and what is its unit? Is it a scalar or vector?
Momentum is defined as mass*velocity, and it is measured in kg m s ^-1 (kilogram metre per second). It is a vector, and its direction is equivalent of that of velocity.
Under which collisions are the total momentum conserved?
elastic collision, inelastic collision, perfectly inelastic collision, explosion
Under which collisions are the total kinetic energy conserved?
elastic collision
What is the law of conservation of momentum and under which circumstances does it hold true?
The law of conservation of momentum states that the total momentum of a system is conserved provided that there is no external net force acting on the system. It should be noted that an external forces refers to a force exerted by an object outside the system, while all forces acting between objects within a system are internal forces. Also, the momentum of each object in the system is not conserved.
What are some examples of conservation of momentum?
Newton’s cradle, recoil of guns and cannons, and spacecrafts (SAFER)
How can Newton’s second law of motion be restated with momentum?
The net force acting on an object is equal to the rate of change in momentum of an object. (F=(mv-mu)/t)
How is a F-t graph related to the change in momentum? How can we utilise this relationship?
The area under a F-t graph is equal to the change in momentum. Therefore, we can estimate the average force F acting on the object in a collision, if the change in momentum and time are given.
What are some applications of the relationship between impact time, force, and momentum?
A larger net force or a longer time of impact results in a larger change in momentum. Therefore, a follow-through motion in playing tennis increases the time of impact, so it increases the speed of the ball. For a fixed change in momentum, the net force is larger if the time of impact is shorter. Therefore, crumple zones on cars and crash cushion systems on roads increase the time of impact, and lower the possibility of serious injury.
What is projectile motion?
Projectile motion is performed by a projected object that is moving freely in the air. The object is called a projectile.
What are the properties of a horizontally projected object?
When air resistance is negligible, a projectile moves at a uniform velocity horizontally and at a uniform acceleration due to gravity vertically. The horizontal and vertical motion are independent of each other.
What is the shape of the trajectory of a horizontally projected object?
It is a part of a parabola.
How do we calculate the velocity of an object projected at an angle a?
Like forces, velocity can be resolved into components in the xy- directions respectively.
horizontal velocity=vcosa
vertical velocity=vsina
What are the properties of the trajectory and projectile when it is projected at an angle under negligible air resistance?
- The trajectory is symmetrical about the vertical line passing through its vertex.
- The speeds of the projectile for the upward and downward motion are the same at the same height.
- The time of upward flight is equal to the time of downward flight.
- The range depends on the angle of projection. It is the maximum when the angle of projection is 45 degrees.
What are the energy changes in projectile motion?
If air resistance is negligible, the sum of kinetic energy and potential energy of a projectile is constant during its flight. The minimum kinetic energy of the projectile is 1/2mu^2, while the maximum potential energy of the projectile is mgh, both attained at the highest point of the projectile.
How is the trajectory of a projectile different with air resistance?
The trajectory becomes asymmetrical, and the range and maximum height are both reduced.
What is uniform circular motion?
An object is in uniform circular motion when it is moving in a circle at uniform speed.
What is angular displacement and angular velocity? What are their units? Are they scalars or vectors?
Angular displacement describes the angle sweeped out by an object in uniform circular motion. It is measured in radians (rad). Angular velocity measures the angular displacement per unit time. It is measured in radian per second (rad s^-1). Its magnitude is equal to the magnitude of angular speed. Both angular displacement and angular velocity are vectors.
What is linear speed?
Linear speed is the uniform speed an object has in uniform circular motion. It is equal to the radius multipled by the angular speed.
What is the period in uniform circular motion?
The period is the time that the object takes to complete one revolution. It is equal to the circumference/linear speed or 2pi/angular speed.
What is centripetal acceleration?
Centripetal acceleration in uniform circular motion is an acceleration that always points to the centre of the circle. Its magnitude is given by a=v^2/r=rw^2 (linear speed^2/radius, or radius*angular speed^2)
What is centripetal force?
According to Newton’s second law of motion, when an object accelerates, the net force must point in the same direction as the acceleration. Therefore, there is a net force pointing inward towards the centre of the circle. The force is called centripetal force. It is calulated by F=ma: F=mv^2/r or F=mrw^2.
Is centripetal force a new force and does it do work on the obejct?
Centripetal force is not a new force. It is the combined result of all forces acting on an object in uniform circular motion. It does not do work on the object, because it is always perpendicular to the direction of motion of the object.
What will happen to a ball tied to a string moving in uniform ciruclar motion if the string breaks suddenly?
According to Newton’s first law, the ball will continue with the original speed along its direction of motion just before the string broke. Therefore, it will fly off tangentially to the circle.
What are some daily examples of uniform circular motion?
Cars making turns on a level road: the friction by the tyres and the road provide the centripetal force which depends on the radius of curvature, mass, and linear speed. If the friction required is larger than the maximum friction that the road can provide, the car skids off the road.
Cars making turns on banked roads: banking of the roads reduces the reliance on friction between the road and the tyres.
Aeroplanes making turns: An aeroplane turns when it is flying at a tilted angle.
Rotors in amusement parks: It is a vertical cylindrical room that rotates at a high speed. At a certain speed, the floor is lowered and the riders remain stuck to the wall.
What is Newton’s law of universal gravitation?
Every particle in the universe attracts every other particle with a gravitational force. The gravitational force between two particles is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. F=Gm1m2/r^2
What is G?
G is the universal gravitational constant, which is 6.67*10^-11nm^2kg^-2.
What is the gravitational force exerted on an object by the Earth?
W=mg or F=mg0(Re^2/r^2)
(force=mass9.81radius of the earth^2/object’s distance from Earth’s centre^2)
How can gravitational force be explained?
Gravitational force is a non-contact force. Therefore, we use a concept of a field. An object of mass M establishes a gravitational field in the region around it. Any object located in the field will experience a gravitational force F.
What is gravitational field strength?
Gravitational field strength is the strength of the field, which determines the magnitude of the gravitational force F an object located in the field experiences. It is equal to the gravitational force/mass (g=F/m0=GM/r^2)
What is the unit of gravitational strength? is it a scalar or a vector?
The unit of gravitational strength is N kg^-1. It is a vector, and its direction is the same as the direction of the gravitational force acting on the test mass.
Which objects can the formulas for gravitation and gravitational field apply to?
Particles, or spherically symmetrical objects, which are spherical objects with layers of spherical shells, with each shell having uniform density.
What are all meanings of ‘g’?
g can stand for the acceleration of an object due to gravity at a point, of it can also stand for the gravitational field strength at that point. For example, near the Earth’s surface, an object in a free fall experiences an acceleration of g(9.81ms^-2), and an object of mass 1kg experiences a gravitational force of 9.81N at that point (in thie case, g=9.81Nkg^-1)
How can orbital motion be explained?
The gravitational force between two objects may provide the requires centripetal force. Therefore, many objects in space moving under gravity can be considered as performing uniform circular motion (orbital motion).
In orbital motion, what is the relationship of speed, angular velocity, and gravitational force?
GMm/r^2=mv^2/r=mrw^2
Therefore,
v=sqrt(GM/r), and w=sqrt(GM/r^3)
For an object orbiting the Earth, why must the centre of orbit be at the centre of the Earth? Does there have to be a required speed for an object to orbit the Earth?
The net force acting on the object (centripetal force) has to point towards the Earth’s centre.
If the speed is not large enough, the object will move in projectile motion. However, if the speed is large that it equals sqrt(GMe/r)//the required velocity to provide enough centripetal force, the projectile motion becomes orbital motion.
Does gravitational force do any work on the orbiting object?
No, because it is always perpendicular to the direction of motion of the object (similar to the case of centripetal force). Therefore, there is no energy transfer between the orbiting object and the Earth, and the orbiting object moves with constant kinetic energy (at a constant speed)
