1. Chapter 5
Energy

2. Forms of Energy Mechanical Chemical Electromagnetic Nuclear
Focus for now
May be kinetic (associated with motion) or potential (associated with position)
Chemical
Electromagnetic
Nuclear

3. Slide 10-3

4. Slide 10-4

5. Slide 10-5

6. Reading Quiz If a system is isolated, the total energy of the system
increases constantly.
decreases constantly.
is constant.
depends on work into the system.
depends on work out of the system.
Answer: C
Slide 10-6

7. Answer If a system is isolated, the total energy of the system
increases constantly.
decreases constantly.
is constant.
depends on work into the system.
depends on work out of the system.
Answer: C
Slide 10-7

8. Reading Quiz Which of the following is an energy transfer?
Kinetic energy
Heat
Potential energy
Chemical energy
Thermal energy
Answer: B
Slide 10-8

9. Answer Which of the following is an energy transfer? Kinetic energy
Heat
Potential energy
Chemical energy
Thermal energy
Answer: B
Slide 10-9

10. Reading Quiz
If you raise an object to a greater height, you are increasing
kinetic energy.
heat.
potential energy.
chemical energy.
thermal energy.
Answer: C
Slide 10-10

11. Answer If you raise an object to a greater height, you are increasing
kinetic energy.
heat.
potential energy.
chemical energy.
thermal energy.
Answer: C
Slide 10-11

12. Forms of Energy Mechanical Energy Thermal Energy Other forms include
Slide 10-12

13. Some Energy Considerations
Energy can be transformed from one form to another
Essential to the study of physics, chemistry, biology, geology, astronomy
Can be used in place of Newton’s laws to solve certain problems more simply

14. The Basic Energy Model
Slide 10-13

15. Energy Transformations
Kinetic energy K = energy of motion
Potential energy U = energy of position
Thermal energy Eth = energy associated with temperature
System energy E = K + U + Eth + Echem + ...
Energy can be transformed within the system without loss.
Energy is a property of a system.
Slide 10-14

16. Some Energy Transformations
Echem  Ug
K  Eth
Echem  Ug
Us  K  Ug
Slide 10-15

17. Checking Understanding
A skier is moving down a slope at a constant speed. What energy transformation is taking place?
A. K  Ug
B. Ug Eth
C. Us  Ug
D. Ug  K
E. K  Eth
Answer: B
Slide 10-16

18. Answer
A skier is moving down a slope at a constant speed. What energy transformation is taking place?
A. K  Ug
B. Ug Eth
C. Us  Ug
D. Ug  K
E. K  Eth
Answer: B
Slide 10-17

19. Checking Understanding
A child is on a playground swing, motionless at the highest point of his arc. As he swings back down to the lowest point of his motion, what energy transformation is taking place?
A. K  Ug
B. Ug Eth
C. Us  Ug
D. Ug  K
E. K  Eth
Answer: D
Slide 10-18

20. Answer
A child is on a playground swing, motionless at the highest point of his arc. As he swings back down to the lowest point of his motion, what energy transformation is taking place?
A. K  Ug
B. Ug Eth
C. Us  Ug
D. Ug  K
E. K  Eth
Answer: D
Slide 10-19

21. Work Provides a link between force and energy
The work, W, done by a constant force on an object is defined as the product of the component of the force along the direction of displacement and the magnitude of the displacement

22. Work, cont. F is the magnitude of the force
Δ x is the magnitude of the object’s displacement
q is the angle between

23. Work, cont. This gives no information about Work is a scalar quantity
the time it took for the displacement to occur
the velocity or acceleration of the object
Work is a scalar quantity

24. Units of Work SI US Customary Newton • meter = Joule foot • pound
N • m = J
J = kg • m2 / s2
US Customary
foot • pound
ft • lb
no special name

25. More About Work
The work done by a force is zero when the force is perpendicular to the displacement
cos 90° = 0
If there are multiple forces acting on an object, the total work done is the algebraic sum of the amount of work done by each force

26. When Work is Zero Displacement is horizontal Force is vertical
cos 90° = 0

27. More About Work, cont. Work can be positive or negative
Positive if the force and the displacement are in the same direction
Negative if the force and the displacement are in the opposite direction (friction, for instance)

28. Work Can Be Positive or Negative
Work is positive when lifting the box
Work would be negative if lowering the box
The force would still be upward, but the displacement would be downward

29. Work and Dissipative Forces
Work can be done by friction
The energy lost to friction by an object goes into heating both the object and its environment
Some energy may be converted into sound
For now, the phrase “Work done by friction” will denote the effect of the friction processes on mechanical energy alone

30. Energy Transfers These change the energy of the system.
Interactions with the environment.
Work is the mechanical transfer of energy to or from a system via pushes and pulls.
Slide 10-20

31. Kinetic Energy Energy associated with the motion of an object
Scalar quantity with the same units as work - joules
Work is related to kinetic energy

32. Kinetic Energy Example
At rest, KE = ½m(0)2= 0, but with the presence of an instantaneous velocity, the car has KE.
If the velocity is constant, then KE is constant.
If acceleration is present, then the final velocity is determined and used to calculate the KE of the car at the point of time or distance being considered.

33. Work-Kinetic Energy Theorem
When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy
Speed will increase if work is positive
Speed will decrease if work is negative

34. Work and Kinetic Energy
An object’s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest
The moving hammer has kinetic energy and can do work on the nail

35. Energy Transfers: Work
W K
W Eth
W Us
Slide 10-21

36. The Work-Energy Equation
Slide 10-22

37. Types of Forces There are two general kinds of forces Conservative
Work and energy associated with the force can be recovered
Examples are gravity, springs, electromagnetism
Non-conservative
The forces are generally dissipative and work done against it cannot easily be recovered
Examples include friction, propulsive forces, and sound

38. Conservative Forces
A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points
The work depends only upon the initial and final positions of the object (displacement)
Any conservative force can have a potential energy function associated with it

39. More About Conservative Forces
Examples of conservative forces include:
Gravity
Spring force
Electromagnetic forces
Potential energy is another way of looking at the work done by conservative forces

40. Nonconservative Forces
A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points.
Examples of nonconservative forces
kinetic friction, air drag, propulsive forces, and sound

41. Friction as a Nonconservative Force
The friction force is transformed from the kinetic energy of the object into a type of energy associated with temperature
The objects are warmer than they were before the movement
Internal Energy is the term used for the energy associated with an object’s temperature

42. Friction Depends on the Path
The blue path is shorter than the red path
The work required is less on the blue path than on the red path
Friction depends on the path and so is a non-conservative force

43. Potential Energy
Potential energy is associated with the position of the object within some system
Potential energy is a property of the system, not the object
A system is a collection of objects interacting via forces or processes that are internal to the system

44. Potential Energy Example
At position A, the elephant has no potential energy, while at B, its mass has been elevated within a system and has PE= mgh

45. Work and Potential Energy
For every conservative force a potential energy function can be found
Evaluating the difference of the function at any two points in an object’s path gives the negative of the work done by the force between those two points

46. Gravitational Potential Energy
Gravitational Potential Energy is the energy associated with the relative position of an object in space near the Earth’s surface
Objects interact with the earth through the gravitational force
Actually the potential energy is for the earth-object system

47. Work and Gravitational Potential Energy
PE = mgy
Units of Potential Energy are the same as those of Work and Kinetic Energy

48. Work-Energy Theorem, Extended
The work-energy theorem can be extended to include potential energy:
If other conservative forces are present, potential energy functions can be developed for them and their change in that potential energy added to the right side of the equation

49. The Law of Conservation of Energy
Slide 10-23

50. The Basic Equation Kf  Uf  Eth  Ki  Ui A few things to note:
Work can be positive (work in) or negative (work out)
We are, for now, ignoring heat.
Thermal energy is…special. When energy changes to thermal energy, this change is irreversible.
Slide 10-24

51. Checking Understanding
Three balls are thrown off a cliff with the same speed, but in different directions. Which ball has the greatest speed just before it hits the ground?
Ball A
Ball B
Ball C
All balls have the same speed
Answer: D
Slide 10-26

52. Checking Understanding
Three balls are thrown off a cliff with the same speed, but in different directions. Which ball has the greatest speed just before it hits the ground?
Ball A
Ball B
Ball C
All balls have the same speed
Answer: D
Slide 10-26

53. Energy Transfers These change the energy of the system.
Interactions with the environment.
Work is the mechanical transfer of energy to or from a system via pushes and pulls.
Slide 10-20

54. Energy Transfers: Work
W Eth
W K
W Us
Slide 10-21

55. The Work-Energy Equation
Slide 10-22

56. The Law of Conservation of Energy
Slide 10-23

57. The Basic Equation Kf  Uf  Eth  Ki  Ui A few things to note:
Work can be positive (work in) or negative (work out)
We are, for now, ignoring heat.
Thermal energy is…special. When energy changes to thermal energy, this change is irreversible.
Slide 10-24

58. Checking Understanding
Three balls are thrown off a cliff with the same speed, but in different directions. Which ball has the greatest speed just before it hits the ground?
Ball A
Ball B
Ball C
All balls have the same speed
Answer: D
Slide 10-26

59. Answer
Three balls are thrown off a cliff with the same speed, but in different directions. Which ball has the greatest speed just before it hits the ground?
Ball A
Ball B
Ball C
All balls have the same speed
Answer: D
Slide 10-27

60. Reference Levels for Gravitational Potential Energy
A location where the gravitational potential energy is zero must be chosen for each problem
The choice is arbitrary since the change in the potential energy is the important quantity
Choose a convenient location for the zero reference height
often the Earth’s surface
may be some other point suggested by the problem
Once the position is chosen, it must remain fixed for the entire problem

61. Conservation of Mechanical Energy
Conservation in general
To say a physical quantity is conserved is to say that the numerical value of the quantity remains constant throughout any physical process
In Conservation of Energy, the total mechanical energy remains constant
In any isolated system of objects interacting only through conservative forces, the total mechanical energy of the system remains constant.

62. Conservation of Energy, cont.
Total mechanical energy is the sum of the kinetic and potential energies in the system
Other types of potential energy functions can be added to modify this equation

63. Problem Solving with Conservation of Energy
Define the system
Select the location of zero gravitational potential energy
Do not change this location while solving the problem
Identify two points the object of interest moves between
One point should be where information is given
The other point should be where you want to find out something

64. Problem Solving, cont Verify that only conservative forces are present
Apply the conservation of energy equation to the system
Immediately substitute zero values, then do the algebra before substituting the other values
Solve for the unknown(s)

65. Work-Energy With Non-conservative Forces
If non-conservative forces are present, then the full Work-Energy Theorem must be used instead of the equation for Conservation of Energy
Often techniques from previous chapters will need to be employed

66. Potential Energy Stored in a Spring
Involves the spring constant, k
Hooke’s Law gives the force
F = - k x
F is the restoring force
F is in the opposite direction of x
k depends on how the spring was formed, the material it is made from, thickness of the wire, etc.

67. Potential Energy in a Spring
Elastic Potential Energy
related to the work required to compress a spring from its equilibrium position to some final, arbitrary, position x

68. Work-Energy Theorem Including a Spring
Wnc = (KEf – KEi) + (PEgf – PEgi) + (PEsf – PEsi)
PEg is the gravitational potential energy
PEs is the elastic potential energy associated with a spring
PE will now be used to denote the total potential energy of the system

69. Conservation of Energy Including a Spring
The PE of the spring is added to both sides of the conservation of energy equation
The same problem-solving strategies apply

70. Nonconservative Forces with Energy Considerations
When nonconservative forces are present, the total mechanical energy of the system is not constant
The work done by all nonconservative forces acting on parts of a system equals the change in the mechanical energy of the system

71. Nonconservative Forces and Energy
In equation form:
Wnc = (KEf – KEi) + (PEf – PEi) or
Wnc = (KEf + PEf) - (KEi + PEi)
The energy can either cross a boundary or the energy is transformed into a form of non-mechanical energy such as thermal energy

72. Transferring Energy By Work By applying a force
Produces a displacement of the system

73. Transferring Energy Heat
The process of transferring heat by collisions between molecules
For example, the spoon becomes hot because some of the KE of the molecules in the coffee is transferred to the molecules of the spoon as internal energy

74. Transferring Energy Mechanical Waves
A disturbance propagates through a medium
Examples include sound, water, seismic

75. Transferring Energy Electrical transmission
Transfer by means of electrical current
This is how energy enters any electrical device

76. Transferring Energy Electromagnetic radiation
Any form of electromagnetic waves
Light, microwaves, radio waves

77. Notes About Conservation of Energy
We can neither create nor destroy energy
Another way of saying energy is conserved
If the total energy of the system does not remain constant, the energy must have crossed the boundary by some mechanism
Applies to areas other than physics

78. Power
Often also interested in the rate at which the energy transfer takes place
Power is defined as this rate of energy transfer
SI units are Watts (W)

79. Power, cont. US Customary units are generally hp
Need a conversion factor
Can define units of work or energy in terms of units of power:
kilowatt hours (kWh) are often used in electric bills
This is a unit of energy, not power

80. Power
Slide 10-39

81. Power Same final kinetic energy, but Same mass...
different times mean different powers.
Same mass...
Both reach 60 mph...
Slide 10-40

82. Checking Understanding
Four toy cars accelerate from rest to their top speed in a certain amount of time. The masses of the cars, the final speeds, and the time to reach this speed are noted in the table. Which car has the greatest power?
Car
Mass (g)
Speed (m/s)
Time (s) A
100 3 2 B
200 C D
300 E 1 4
Answer: A
Slide 10-41

83. Answer
Four toy cars accelerate from rest to their top speed in a certain amount of time. The masses of the cars, the final speeds, and the time to reach this speed are noted in the table. Which car has the greatest power?
Car
Mass (g)
Speed (m/s)
Time (s) A
100 3 2 B
200 C D
300 E 1 4
Answer: A
Slide 10-42

84. Checking Understanding
Four toy cars accelerate from rest to their top speed in a certain amount of time. The masses of the cars, the final speeds, and the time to reach this speed are noted in the table. Which car has the smallest power?
Car
Mass (g)
Speed (m/s)
Time (s) A
100 3 2 B
200 C D
300 E 1 4
Answer: E
Slide 10-43

85. Answer
Four toy cars accelerate from rest to their top speed in a certain amount of time. The masses of the cars, the final speeds, and the time to reach this speed are noted in the table. Which car has the smallest power?
Car
Mass (g)
Speed (m/s)
Time (s) A
100 3 2 B
200 C D
300 E 1 4
Answer: E
Slide 10-44

86. Example Problem
A typical human head has a mass of 5.0 kg. If the head is moving at some speed and strikes a fixed surface, it will come to rest. A helmet can help protect against injury; the foam in the helmet allows the head to come to rest over a longer distance, reducing the force on the head. The foam in helmets is generally designed to fail at a certain large force below the threshold of damage to the head. If this force is exceeded, the foam begins to compress.
If the foam in a helmet compresses by 1.5 cm under a force of N (below the threshold for damage to the head), what is the maximum speed the head could have on impact?
Use energy concepts to solve this problem.
Slide 10-46

87. Work Done by Varying Forces
The work done by a variable force acting on an object that undergoes a displacement is equal to the area under the graph of F versus x

88. Spring Example
Spring is slowly stretched from 0 to xmax
W = ½kx²

89. Spring Example, cont.
The work is also equal to the area under the curve
In this case, the “curve” is a triangle
A = ½ B h gives W = ½ k x2

90. Work
Slide 10-28

91. Work Done by Force at an Angle to Displacement
Slide 10-29

92. Energy Equations
Slide 10-30

93. Checking Understanding
Each of the boxes, with masses noted, is pulled for
10 m across a level, frictionless floor by the noted force. Which box experiences the largest change in kinetic energy?
Answer: D
Slide 10-31

94. Answer Each of the boxes, with masses noted, is pulled for
10 m across a level, frictionless floor by the noted force. Which box experiences the largest change in kinetic energy?
Answer: D D.
Slide 10-32

95. Checking Understanding
Each of the boxes, with masses noted, is pulled for
10 m across a level, frictionless floor by the noted force. Which box experiences the smallest change in kinetic energy?
Answer: C
Slide 10-33

96. Answer Each of the boxes, with masses noted, is pulled for
10 m across a level, frictionless floor by the noted force. Which box experiences the smallest change in kinetic energy?
Answer: C C.
Slide 10-34

97. Slide 10-37

98. Summary
Slide 10-48

99. Summary
Slide 10-49

100. Additional Questions
Each of the 1.0 kg boxes starts at rest and is then pushed for 2.0 m across a level, frictionless floor by a rope with the noted force. Which box has the highest final speed?
Answer: E
Slide 10-50

101. Answer
Each of the 1.0 kg boxes starts at rest and is then pushed for 2.0 m across a level, frictionless floor by a rope with the noted force. Which box has the highest final speed?
Answer: E E.
Slide 10-51

102. Additional Questions
Each of the 1.0 kg boxes starts at rest and is then pushed for 2.0 m across a level, frictionless floor by a rope with the noted force. Which box has the lowest final speed?
Answer: D
Slide 10-52

103. Answer
Each of the 1.0 kg boxes starts at rest and is then pushed for 2.0 m across a level, frictionless floor by a rope with the noted force. Which box has the lowest final speed?
Answer: D D.
Slide 10-53

104. Additional Questions
A 20-cm-long spring is attached to a wall. When pulled horizontally with a force of 100 N, the spring stretches to a length of 22 cm. What is the value of the spring constant?
5000 N/m
500 N/m
454 N/m
Answer: C
Slide 10-58

105. Answer
A 20-cm-long spring is attached to a wall. When pulled horizontally with a force of 100 N, the spring stretches to a length of 22 cm. What is the value of the spring constant?
5000 N/m
500 N/m
454 N/m
Answer: C
Slide 10-59

106. Homework Assignment Pages 151 – 154
Problems 5, 8, 12, 14, 18,21, 23, 30, 41, 51, 54