1. Momentum and Energy
© 2013 Pearson Education, Inc.

2. 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
Machines
Efficiency
© 2013 Pearson Education, Inc.

3. Momentum = mass x velocity
Momentum is inertia in motion, defined as the product of mass and velocity:
Momentum = mass x velocity
p = m x v
© 2013 Pearson Education, Inc.

4. Momentum Momentum = mass  velocity or
Momentum = mass  speed (when direction is unimportant)
Momentum = mv
High mass or high velocity  high momentum
High mass and high velocity  higher momentum
Low mass or low velocity  low momentum
Low mass and low velocity  lower momentum
© 2013 Pearson Education, Inc.

5. Momentum
© 2013 Pearson Education, Inc.

6. Momentum CHECK YOUR NEIGHBOR
A moving object has
momentum.
energy.
speed.
all of the above
Explain your answer to your neighbor.
D. all of the above
© 2013 Pearson Education, Inc.

7. Momentum CHECK YOUR NEIGHBOR
When the speed of an object is doubled, its momentum
remains unchanged in accord with the conservation of momentum.
doubles.
quadruples.
decreases.
Explain your answer to your neighbor.
B. doubles.
© 2013 Pearson Education, Inc.

8. Impulse Impulse is the product of force and contact time.
Equation for impulse:
Impulse = force  time = Ft
Great force for long time  large impulse
Same force for short time  smaller impulse
© 2013 Pearson Education, Inc.

9. Impulse CHECK YOUR NEIGHBOR
When the force that produces an impulse acts for twice as much time, the impulse is
not changed.
doubled.
increased by four times.
decreased by half.
Explain your answer to your neighbor.
B. doubled.
© 2013 Pearson Education, Inc.

10. Impulse–Momentum Relationship
The greater the impulse exerted on something, the greater will be its change in momentum.
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.
© 2013 Pearson Education, Inc.

11. Impulse–Momentum Relationship
Equation:
Impulse = change in momentum or
Force  time =  momentum
Greater force, greater change in velocity  greater change in momentum
Same force for short time  smaller change in momentum
Same force for longer time  more change in momentum
© 2013 Pearson Education, Inc.

12. Impulse–Momentum Relationship
Impulse may be viewed as causing momentum change, or momentum change may be viewed as causing impulse.
It doesn’t matter which way you think about it, as long as you know that impulse and change of momentum are always linked.
© 2013 Pearson Education, Inc.

13. Impulse–Momentum Relationship
Cases of momentum changes
Increasing momentum: Apply the greatest force for the longest time (impulse) to produce the maximum increase in momentum.
Examples:
Long-range cannons have long barrels for maximum range.
A golfer follows through while teeing off.
© 2013 Pearson Education, Inc.

14. Impulse–Momentum Relationship CHECK YOUR NEIGHBOR
Compared to a cannonball shot from a cannon with a short barrel, a cannonball shot from a cannon with a long barrel emerges with greater speed because the cannonball receives a greater
average force.
impulse.
both of the above
neither of the above
Explain your answer to your neighbor.
B. impulse.
© 2013 Pearson Education, Inc.

15. Impulse–Momentum Relationship
Cases of momentum changes (continued)
Decreasing momentum: The impulse with the longer time that decreases momentum has a smaller force.
Examples:
Driving into a haystack versus a brick wall
Jumping into a safety net versus onto solid ground
© 2013 Pearson Education, Inc.

16. Impulse–Momentum Relationship
© 2013 Pearson Education, Inc.

17. Impulse–Momentum Relationship
© 2013 Pearson Education, Inc.

18. Impulse–Momentum Relationship
By hitting the haystack instead of a wall, you extend the time of contact.
The longer contact time therefore provides you with a lesser force acting on you.
The reverse is also true.
Short contact time gives you a higher force.
© 2013 Pearson Education, Inc.

19. Impulse–Momentum Relationship
Whether you hit the wall or the haystack, your momentum will be decreased by the same amount.
This means that the impulse required to stop you is the same.
© 2013 Pearson Education, Inc.

20. Impulse–Momentum Relationship CHECK YOUR NEIGHBOR
A fast-moving car produces vastly different results when it hits a haystack than when it hits a cement wall. But, in both cases, the car experiences
the same change in momentum.
the same impulse.
the same force.
both the same change in momentum and the same impulse.
Explain your answer to your neighbor.
D. both the same change in momentum and the same impulse.
© 2013 Pearson Education, Inc.

21. Impulse–Momentum Relationship CHECK YOUR NEIGHBOR
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!)
No, both are the same
Yes, less if it lands on the carpet
No, less if it lands on a hard floor
No, more if it lands on a hard floor
Explain your answer to your neighbor.
A. No, both are the same
© 2013 Pearson Education, Inc.

22. Impulse–Momentum Relationship in Sports
When the boxer moves away (rides the punch), he extends the time and diminishes the force.
© 2013 Pearson Education, Inc.

23. Impulse–Momentum Relationship in Sports
If the boxer moves into the punch, the time is reduced and he must withstand a greater force
© 2013 Pearson Education, Inc.

24. Impulse–Momentum Relationship in Sports
Imparting a large impulse to the bricks in a short time produces considerable force.
© 2013 Pearson Education, Inc.

25. Conservation of Momentum
In every case, the momentum of a system cannot change unless it is acted on by external forces.
A system has the same momentum both before and after the interaction occurs. When the momentum does not change, we say it is conserved.
© 2013 Pearson Education, Inc.

26. Conservation of Momentum
Law of conservation of momentum:
In the absence of an external force, the momentum of a system remains unchanged.
Equation form:
(Total momentum)before = (Total momentum)after
© 2013 Pearson Education, Inc.

27. Conservation of Momentum
The momentum before firing is zero
After firing, the net momentum is still zero
Because the momentum of the cannon is equal and opposite to the momentum of the cannonball
© 2013 Pearson Education, Inc.

28. Conservation of Momentum
A) external force acts on the 8 ball, increasing its p
B) external force acts on the cue-ball, and its p decreases
C) no external force acts on the cue-ball-plus-8-ball, and the p is conserved (it’s just transferred)
© 2013 Pearson Education, Inc.

29. Conservation of Momentum
Collisions
When objects collide in the absence of external forces,
Net momentum before collision = Net momentum after collision
Examples:
Elastic collisions
Inelastic collisions
© 2013 Pearson Education, Inc.

30. Conservation of Momentum
An elastic collision is defined as a collision in which objects collide without permanent deformation or the generation of heat.
© 2013 Pearson Education, Inc.

31. Conservation of Momentum
Moving ball A strikes ball B, which was 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.
© 2013 Pearson Education, Inc.

32. Conservation of Momentum
An inelastic collision is a collision in which colliding objects don’t rebound, but become tangled or coupled together, generating heat.
© 2013 Pearson Education, Inc.

33. Conservation of Momentum CHECK YOUR NEIGHBOR
Freight car A is moving toward identical freight car B, which is at rest. When the cars collide, they couple together. Compared with the initial speed of freight car A, the speed of the coupled freight cars is
the same.
half.
twice.
none of the above
Explain your answer to your neighbor.
B. half.
© 2013 Pearson Education, Inc.

34. Work
Work
is defined as the product of the force exerted on an object and the distance the object moves (in the same direction as the force).
is done only when a force succeeds in moving the body it acts upon.
© 2013 Pearson Education, Inc.

35. Work Two things enter where work is done:
Application of force
Movement of something by that force
The work done on the object is the average force multiplied by the distance through which the object is moved.
© 2013 Pearson Education, Inc.

36. Work CHECK YOUR NEIGHBOR
If you push against a stationary brick wall for several minutes, you do no work
on the wall.
at all.
both of the above
none of the above
Explain your answer to your neighbor.
A. on the wall.
© 2013 Pearson Education, Inc.

37. Work
The quantity of work done is equal to the amount of force times the distance moved in the direction in which the force acts.
W = F x d
Units for work are in joules (J)
Work falls into two categories:
Work done against another force
Work done to change the speed of an object
© 2013 Pearson Education, Inc.

38. Work CHECK YOUR NEIGHBOR
Work is done in lifting a barbell. How much work is done in lifting a twice-as-heavy barbell the same distance?
Twice as much
Half as much
The same
It depends on the speed of the lift.
Explain your answer to your neighbor.
A. Twice as much
© 2013 Pearson Education, Inc.

39. Work CHECK YOUR NEIGHBOR
You do work when you push a cart with a constant force. If you push the cart twice as far, then the work you do is
less than twice as much.
twice as much.
more than twice as much.
zero.
Explain your answer to your neighbor.
B. twice as much.
© 2013 Pearson Education, Inc.

40. Energy Energy is defined as that which produces changes in matter.
The effects of energy are observed only when it is being transferred from one place to another or
transformed from one form into another.
Unit for energy: joule
Both work and energy are measured in joules.
© 2013 Pearson Education, Inc.

41. Power Power is a measure of how quickly work is done or
the rate at which energy is changed from one form into another.
Equation for power:
Units for power: joule per second, or watt
(One watt = 1 joule of work per second)
© 2013 Pearson Education, Inc.

42. Power CHECK YOUR NEIGHBOR
A job can be done slowly or quickly. Both may require the same amount of work but different amounts of
energy.
momentum.
power.
impulse.
Explain your answer to your neighbor.
C. power.
© 2013 Pearson Education, Inc.

43. Potential Energy
Potential energy is stored energy due to position, shape, or state. In its stored state, energy has the potential for doing work.
Examples:
Drawn bow
Stretched rubber band
Raised ram of a pile driver
© 2013 Pearson Education, Inc.

44. Potential Energy
The amount of gravitational potential energy possessed by an elevated object is equal to the work done against gravity in raising it.
The work done on an object equals the force required to move it upward times the vertical distance moved (W = Fd). The upward force when moved at constant velocity is the weight, mg, of the object. So, the work done in lifting an object through height h is the product mgh.
© 2013 Pearson Education, Inc.

45. Potential Energy Equation for gravitational potential energy:
PE = weight  height or
PE = mgh
Examples of gravitational potential energy:
Water in an elevated reservoir
The elevated ram of a pile driver
© 2013 Pearson Education, Inc.

46. Potential Energy Which diagram has the greatest potential energy?
© 2013 Pearson Education, Inc.

47. Potential Energy CHECK YOUR NEIGHBOR
Does a car hoisted for repairs in a service station have increased potential energy relative to the floor?
Yes No
Sometimes
There is not enough information.
Explain your answer to your neighbor.
A. Yes
© 2013 Pearson Education, Inc.

48. Kinetic Energy Kinetic energy is the energy of a moving body.
Equation for kinetic energy:
Kinetic energy = 1/2 mass  speed2 or
Kinetic energy = 1/2 mv2
Small changes in speed  large changes in kinetic energy
© 2013 Pearson Education, Inc.

49. Kinetic Energy
© 2013 Pearson Education, Inc.

50. Kinetic Energy
© 2013 Pearson Education, Inc.

51. Kinetic Energy CHECK YOUR NEIGHBOR
Must a car with momentum have kinetic energy?
Yes, due to motion alone
Yes, when motion is nonaccelerated
Yes, because speed is a scalar and velocity is a vector quantity No
Explain your answer to your neighbor.
A. Yes, due to motion alone
© 2013 Pearson Education, Inc.

52. The Work–Energy Theorem
When work is done on an object to change its kinetic energy, the amount of work done is equal to the change in kinetic energy.
Equation for the work–energy theorem:
Net work = change in kinetic energy
If there is no change in an object's energy, then no work is done.
The theorem applies to potential energy: For a barbell held stationary, no further work is done, so there is no further change in energy.
The theorem applies to decreasing energy: The more kinetic energy something has, the more work is required to stop it.
© 2013 Pearson Education, Inc.

53. The Work–Energy Theorem CHECK YOUR NEIGHBOR
Consider a problem that asks for the distance needed for a fast-moving crate sliding across a factory floor to come to a stop. The most useful equation for solving this problem is
F = ma.
Ft = mv.
KE = 1/2mv2.
Fd = 1/2mv2.
Explain your answer to your neighbor.
D. Fd = 1/2mv2.
© 2013 Pearson Education, Inc.

54. The Work–Energy Theorem CHECK YOUR NEIGHBOR
The work done in braking a moving car to a stop is the force of tire friction times the stopping distance. If the initial speed of the car is doubled, the stopping distance will be
actually less.
about the same.
twice.
none of the above
Explain your answer to your neighbor.
D. none of the above
© 2013 Pearson Education, Inc.

55. 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. Kinetic energy is a scalar quantity.
© 2013 Pearson Education, Inc.

56. 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. Energy cannot be created or destroyed.
© 2013 Pearson Education, Inc.

57. Conservation of Energy
© 2013 Pearson Education, Inc.

58. Conservation of Energy
Will all the Energy be transferred or converted completely to the new type of Energy?
© 2013 Pearson Education, Inc.

59. Conservation of Energy
6CO2 + 6H2O + sunlight  C6H12O6 + 6O2
© 2013 Pearson Education, Inc.

60. 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 transferred to the arrow as kinetic energy and some as heat to the bow.
© 2013 Pearson Education, Inc.

61. A situation to ponder… CHECK YOUR NEIGHBOR
Suppose the potential energy of a drawn bow is 50 joules and the kinetic energy of the shot arrow is 40 joules. Then
energy is not conserved.
10 joules goes to warming the bow.
10 joules goes to warming the target.
10 joules is mysteriously missing.
Explain your answer to your neighbor.
B. 10 joules goes to warming the bow.
© 2013 Pearson Education, Inc.

62. Machines
A machine is a device for multiplying force or changing the direction of force.
No machine can
put out more energy than is put into it.
create energy; it can only transfer or transform energy.
© 2013 Pearson Education, Inc.

63. Machines Equations: Work input = work output
(Force  distance)input = (force  distance)output
Example: a simple lever
Small input force over a long distance  large output force over a short distance
© 2013 Pearson Education, Inc.

64. Machines
© 2013 Pearson Education, Inc.

65. Machines
Pulleys allow you to exert a small force through a large distance to lift a heavy object
© 2013 Pearson Education, Inc.

66. Machines CHECK YOUR NEIGHBOR
In an ideal pulley system, a woman lifts a 100-N crate by pulling a rope downward with a force of 25 N. For every 100-centimeters length of rope she pulls downward, the crate rises
50 centimeters.
45 centimeters.
25 centimeters.
none of the above
Explain your answer to your neighbor.
C. 25 centimeters.
© 2013 Pearson Education, Inc.

67. Machines
A. A machine that does work with only one movement is a simple machine.

68. Machines
B. Lever—bar that is free to pivot about a fixed point called the fulcrum
1. Input arm is part of the lever on which effort force is applied.
2. Output arm is part of the lever that exerts the resistance force.

69. Machines
3. Three classes of levers based on positions of effort force, resistance force, and fulcrum
a. First-class lever—fulcrum is located between the effort and resistance forces; multiplies and changes direction of force
b. Second-class lever—resistance force is located between the effort force and fulcrum; always multiplies force
c. Third-class lever—effort force is between the resistance force and fulcrum; doesn’t multiply force but does increase distance over which force is applied

73. Machines
4. Calculating ideal mechanical advantage (IMA) of a lever—IMA equals length of input arm divided by length of output arm

74. Machines
C. Grooved wheel with a rope, simple chain, or cable running along the groove is a pulley, which is a modified first-class lever.
1. A fixed pulley is attached to something that doesn’t move; force is not multiplied but direction is changed; IMA = 1.
2. A movable pulley has one end of the rope fixed and the wheel free to move; multiplies force; IMA = 2.

77. Machines
3. Block and tackle—system of pulleys consisting of fixed and movable pulleys; IMA = number of ropes supporting resistance weight

78. Machines
D. Wheel and axle—machine with two wheels of different sizes rotating together; modified lever form
1. IMA = radius of wheel divided by the radius of axle
2. Gears are a modified form of the wheel and axle.

81. Machines
E. Inclined Plane—sloping surface that reduces the amount of force required to do work
1. IMA = length of slope (effort distance) divided by height of slope (resistance distance)
2. Less force is required if a ramp is longer and less steep.

83. Machines
F. Screw—inclined plane wrapped in a spiral around a cylindrical post

85. Machines
G. Inclined plane with one or two sloping sides is a wedge.

90. Machines
H. Compound machine—uses a combination of two or more simple machines

93. Efficiency
Efficiencyis how effectively a device transforms or transfers useful energy.
Equation for efficiency:
A machine with low efficiency  greater amount of energy wasted as heat
Some energy is always dissipated as heat, which means that no machine is ever 100% efficient.
© 2013 Pearson Education, Inc.

94. Efficiency
© 2013 Pearson Education, Inc.

95. Efficiency CHECK YOUR NEIGHBOR
A certain machine is 30% efficient. This means the machine converts
30% of the energy input to useful work—70% of the energy input will be wasted.
70% of the energy input to useful work—30% of the energy input will be wasted.
as strange as it may seem, both of the above
none of the above
Explain your answer to your neighbor.
A. 30% of the energy input to useful work—70% of the energy input will be wasted.
© 2013 Pearson Education, Inc.