This lecture will help you understand:
Momentum Impulse
Impulse–Momentum Relationship Conservation of Momentum
Work Energy Power
Potential Energy Kinetic Energy
The Work-Energy Theorem
Kinetic Energy and Momentum Conservation of Energy
Momentum
Momentum
—is
mass in motion
defined as the product of mass and velocity:
Momentum
Momentum = mass
velocity
= mass x length/time
Units are kg m/s
is a vector quantity
Momentum increases when
mass and/or velocity increases
A moving object has
A. momentum. B. energy.
C. speed.
D. all of the above.
Momentum
A moving object has
A. momentum. B. energy.
C. speed.
D. all of the above.
Momentum
When the speed of an object is doubled, its momentum
A. remains unchanged in accord with the conservation of momentum.
B. doubles.
C. quadruples. D. decreases.
Momentum
When the speed of an object is doubled, its momentum
A. remains unchanged in accord with the conservation of momentum.
B. doubles. C. quadruples. D. decreases.
Momentum
It takes more force to stop a fast ball than a
slow one.
It takes more force to stop a real truck than a
toy one.
The change in momentum of an object is equal
to the force applied to it multiplied by the time
interval during which the force is applied.
Force x time interval = change in momentum
Ft = m
D
v
Impulse
Impulse
—the product of force and contact time.
Equation for impulse:
Impulse = force
time =
Ft
When the force that produces an impulse acts for twice
as much time, the impulse is
A. not changed. B. doubled.
C. increased by four times. D. decreased by half.
Impulse
When the force that produces an impulse acts for twice
as much time, the impulse is
A. not changed. B. doubled.
C. increased by four times. D. decreased by half.
Impulse
Impulse–Momentum Relationship
Equation derivation:
a F
m
a
D
v
t
a = a
F
m
D
v
t
Impulse–Momentum Relationship
Momentum change
increases
when force
and/or time increase.
Examples in which time increases:
Long-range cannons have long barrels for maximum range.
A cannonball shot from a cannon with a long barrel will
emerge with greater speed, because the cannonball
receives a greater
A. average force. B. impulse.
C. both of the above. D. neither of the above.
A cannonball shot from a cannon with a long barrel will
emerge with greater speed, because the cannonball
receives a greater
A. average force. B. impulse.
C. both of the above. D. neither of the above.
Explanation:
The force on the cannonball will be the same for a short- or long-barreled cannon. The longer barrel provides for a longer
time for the force to act and therefore a greater impulse.
(The long barrel also provides a longer distance that the force acts, providing greater work and greater KE of the
cannonball.)
Impulse–Momentum Relationship
Force is reduced
when the time interval of an
impact increases.
F x
t = mΔv
Examples:
A truck hitting a haystack takes more time to stop than a truck hitting a brick wall.
Jumping into a safety net versus onto solid ground Go with the ball when catching.
Force is increased
when the time interval of an
impact is decreased.
F x
t = mΔv
Stopping time vs. stopping force
Stopping time- time required to stop a moving
object.
A fast-moving car hitting a haystack or hitting a cement
wall produces vastly different results. Both experience
A. the same change in momentum. B. the same impulse.
C. the same force. D. A and B.
A fast-moving car hitting a haystack or hitting a cement
wall produces vastly different results. Both experience
A. the same change in momentum. B. the same impulse.
C. the same force. D. A and B.
Explanation:
Although stopping the momentum is the same
whether done slowly or quickly, the force is vastly different. Be sure to distinguish between
momentum, impulse, and force.
When a dish falls, will the change in momentum be less
if it lands on a carpet than if it lands on a hard floor?
(Careful!)
A. No, both are the same.
B. Yes, less if it lands on the carpet. C. No, less if it lands on a hard floor. D. No, more if it lands on a hard
floor.
When a dish falls, will the change in momentum be less
if it lands on a carpet than if it lands on a hard floor?
(Careful!)
A. No, both are the same.
B. Yes, less if it lands on the carpet. C. No, less if it lands on a hard floor. D. No, more if it lands on a hard
floor.
Explanation: The momentum becomes zero in both cases, so both change by the same amount. Although the momentum change and impulse are the same, the force is less when the time of momentum change is extended. Be careful to distinguish between force, impulse, and momentum.
Conservation of Momentum
The total momentum of all objects interacting
with one another remains constant in an
isolated system.
Equation form:
(total momentum)
before= (total momentum)
afterConservation of Momentum
Collisions
When objects collide in the absence of external forces,
net momentum before collision = net momentum after collision
Examples:
Conservation of Momentum
Consider a collision between two objects - object 1 and object 2.
The time that the force acts upon object 1 is equal to the time that the force acts upon object 2.
the impulses experienced by the two objects are also equal in magnitude and opposite in direction.
they must also experience equal and opposite
Check your understanding
Consider a karate expert. During a
talent show, she executes a swift blow to a cement block and breaks it with
her bare hand. During the collision between her hand and the block, the ___.
A. time of impact on both the block and the expert's hand is the same
B. force on both the block and the expert's hand have the same magnitude
C. impulse on both the block and the expert's hand have the same magnitude
Check your understanding
Consider a karate expert. During a
talent show, she executes a swift blow to a cement block and breaks it with
her bare hand. During the collision between her hand and the block, the ___.
A. time of impact on both the block and the expert's hand is the same
B. force on both the block and the expert's hand have the same magnitude
C. impulse on both the block and the expert's hand have the same magnitude
D. all of the above.
Check your understanding
Suppose that you're driving down the highway and a bug crashes into the windshield of your car. Which undergoes the greater change is momentum?
A. the bug B. your car
Check your understanding
Suppose that you're driving down the highway and a bug crashes into the windshield of your car. Which undergoes the greater change is momentum?
A. the bug B. your car
C. both the same
In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the
Conservation of Momentum
Elastic collision
is
defined as a collision whereupon objects
collide without permanent deformation or
the generation of heat.
The colliding
objects
rebound
Examples:
Conservation of Momentum
Moving Ball A strikes Ball B, initially at rest.
Ball A comes to rest, and Ball B moves away with a velocity equal to the initial velocity of Ball A.
Momentum is transferred from Ball A to Ball B.
Moving Ball A strikes Ball B, initially at rest.
Ball A comes to rest, and Ball B moves away with a velocity equal to the initial velocity of Ball A.
Check your Understanding
Car 1 rolls at certain speed and collides elastically with car 2 at rest of the same mass. The collision brings car 1 to rest. How does the speed of car 2 after the
collision compare with the initial speed of car 1?
A. Car 2 has twice the initial speed of car 1.
B. Car 2 has the same speed as the initial speed of car 1. C. Car 2 has half the speed as car 1.
Check your Understanding
Car 1 rolls at certain speed and collides elastically with car 2 at rest of the same mass. The collision brings car 1 to rest. How does the speed of car 2 after the
collision compare with the initial speed of car 1?
A. Car 2 has twice the initial speed of car 1.
B. Car 2 has the same speed as the initial speed of car 1.
Conservation of Momentum
Inelastic collision
Two objects collide and move together as
one mass.
Freight Car A is moving toward identical Freight Car B that is at rest. When they collide, both freight cars couple together.
Compared with the initial speed of Freight Car A, the speed of the coupled freight cars is
A. the same.
B. half. C. twice.
D. none of the above.
Freight Car A is moving toward identical Freight Car B that is at rest. When they collide, both freight cars couple together.
Compared with the initial speed of Freight Car A, the speed of the coupled freight cars is
A. the same.
B. half.
C. twice.
D. none of the above.
Explanation:
After the collision, the mass of the moving freight cars has doubled. Can you see that their speed is half the initial
velocity of Freight Car A?
Work
Work is done on an object when a force causes
a displacement of the object.
W = Fd
If you push against a stationary brick wall for several minutes, you do no work
A. on the wall.
B. at all.
C. both of the above. D. none of the above.
Work
If you push against a stationary brick wall for several minutes, you do no work
A. on the wall.
B. at all.
C. both of the above. D. none of the above.
Explanation:
You may do work on your muscles, but not on the wall.
Work
Work is done in lifting a barbell. How much work is done in lifting a twice-as-heavy barbell the same distance?
A. Twice as much. B. Half as much. C. The same.
D. Depends on the speed of the lift.
Work
Work is done in lifting a barbell. How much work is done in lifting a twice-as-heavy barbell the same distance?
A. Twice as much.
B. Half as much. C. The same.
D. Depends on the speed of the lift.
Explanation:
This is in accord with work = force distance. Twice the force for the same distance means twice the work done on the
barbell.
Work
You do work when pushing a cart with a constant force. If you push the cart twice as far, then the work you do is
A. less than twice as much. B. twice as much.
C. more than twice as much. D. zero.
Work
You do work when pushing a cart with a constant force. If you push the cart twice as far, then the work you do is
A. less than twice as much.
B. twice as much.
C. more than twice as much. D. zero.
Work
Work
Which of the following will result in more work?
Running straight up hill, or taking a zigzag path up the hill?
The work will be the same for both paths. The force (gravity) is vertical,
so the distance (h) measured is also vertical. The work = Fd, or in this case, Fgh
h
Power
Power is the rate at which work is done.
Units are Watts(W) which = J/s
t
W
P
A job can be done slowly or quickly. Both may require the same amount of work, but different amounts of
A. energy.
B. momentum. C. power.
D. impulse.
Power
A job can be done slowly or quickly. Both may require the same amount of work, but different amounts of
A. energy.
B. momentum.
C. power.
D. impulse.
Comment:
Power is the rate at which work is done.
Power
Potential Energy
Potential Energy
is the stored energy due to position, shape or state (solid, liquid, gas).
An object with potential energy has the potential to do work.
Chemical energy – energy absorbed or released during chemical reactions.
Examples:
Drawn bow
Stretched rubber band
Potential Energy
Gravitational potential energy is the energy
stored in an object as the result of its vertical
position or height.
PE of an elevated object
= the work done against gravity to lift it
=F
gd; since F
g=mg, then
PE = mgh
Potential Energy
Gravitational potential energy examples: Water in an elevated reservoir
Does a car hoisted for repairs in a service station have increased potential energy relative to the floor?
A. Yes. B. No.
C. Sometimes.
D. Not enough information.
Potential Energy
Does a car hoisted for repairs in a service station have increased potential energy relative to the floor?
A. Yes.
B. No.
C. Sometimes.
D. Not enough information.
Comment:
And if the car were twice as heavy, its increase in potential energy would be twice as much.
Potential Energy
Kinetic Energy
Kinetic energy is energy of motion
Depends on mass (m) and speed (v)
That means that for a twofold increase in speed, the kinetic energy will increase by a factor of four. For a threefold increase in speed, the kinetic energy will increase by a factor of nine.
Must a car with momentum have kinetic energy?
A. Yes, due to motion alone.
B. Yes, when motion is nonaccelerated.
C. Yes, because speed is a scalar and velocity is a vector quantity.
D. No.
Kinetic Energy
Must a car with momentum have kinetic energy?
A. Yes, due to motion alone.
B. Yes, when momentum is nonaccelerated.
C. Yes, because speed is a scalar and velocity is a vector quantity.
D. No.
Explanation:
Acceleration, speed being a scalar, and velocity being a vector quantity, are irrelevant. Any moving object has both
momentum and kinetic energy.
Kinetic Energy
The Work-Energy Theorem
When work is done on an object by an external force, there is a change in the total mechanical energy (TME) (which is KE+PE) of the object.
Equation for work-energy theorem:
Net work = change in TME
The work done in braking a moving car to a stop is the force of tire friction stopping distance. If the initial speed of the car is doubled, the stopping distance is
A. actually less.
B. about the same. C. twice.
D. none of the above.
The work done in braking a moving car to a stop is the force of tire friction stopping distance. If the initial speed of the car is doubled, the stopping
distance is
A. actually less.
B. about the same. C. twice.
D. none of the above.
Explanation:
Twice the speed means four times the kinetic energy and four times the stopping distance.
Kinetic Energy and Momentum
Comparison of Kinetic Energy and Momentum
Both depend on mass and velocity—
Momentum depends on mass and speed.
KE depends on mass and the square of its speed.
Momentum is a vector quantity.
Conservation of Energy
Conservation
is defined in everyday language as “to save”—in
physics, to “remain unchanged.”
Law of conservation of energy:
In the absence of external work input or output,
the energy of a system remains unchanged.
Conservation of Energy
A situation to ponder…
Consider the system of a bow and arrow. In
drawing the bow, we do work on the system and
give it potential energy. When the bowstring is
released, most of the potential energy is
Suppose the potential energy of a drawn bow is 50 joules, and the kinetic energy of the shot arrow is 40 joules. Then
A. energy is not conserved.
B. 10 joules go to warming the bow. C. 10 joules go to warming the target. D. 10 joules is mysteriously missing.
Suppose the potential energy of a drawn bow is 50 joules, and the kinetic energy of the shot arrow is 40 joules. Then
A. energy is not conserved.
B. 10 joules go to warming the bow.
C. 10 joules go to warming the target. D. 10 joules is mysteriously missing.
Explanation:
The total energy of the drawn bow, which includes the poised arrow, is 50 joules. The arrow gets 40 joules and the remaining 10 joules warms the bow—still in the initial system.