1. Energy, Work, and Power

2. What is Energy?
Energy, in physics, is defined as the capacity to do work.
There are many different forms of energy. List some types of energy…
In this chapter, we are going to focus on gravitational potential and kinetic energy.

3. If energy is the ability to do work, what is work?
Mechanical energy transferred by a force (e.g. gravitational force, friction, applied force) acting on an object over a measured displacement
I.e., if work is done on an object, the object’s mechanical energy changes as a result.
Measured in Newton∙Metres (N∙m) or Joules (J)
Scalar quantity
Is work being done in these pictures?
What force is doing work?
What on?

4. Defining Work: When Force is Constant
W = F Δd cosθ
W = Work (N∙m or J)
F = Force doing the work (N)
Δd = displacement (m)
Θ = angle between F and Δd when placed tail to tail, always less than 180˚

5. Positive Work W = F Δd cosθ
When W > 0, the object has gained mechanical energy due to the force acting on it.
W = F Δd cosθ
If 0 ≤ θ < 90˚ (i.e., the force has a component that acts in the same direction as the displacement)
Identify situations in which positive work is done.

6. Zero Work
When W = 0, zero mechanical energy has been transferred to the object
W = F Δd cosθ
If F = 0
If Δd = 0
If θ = 90˚ (i.e., F Δd)
Describe situations in which zero work is done.

7. Negative Work W = F Δd cosθ
When W < 0, the object has lost mechanical energy due to the force acting on it
W = F Δd cosθ
If 90˚< θ ≤ 180˚ (i.e., the force has a component that acts in the opposite direction as the displacement)
Describe situations in which zero work is done.

8. Work Examples
A 0.90 kg book on a level table is pushed with a force of 15 N over a distance of 6.0 m. A force of friction of 2.0 N opposes this motion.
How much work does the normal force do on the book?
How much work does the applied force do on the book?
How much work does friction do on the book?

9. Work Examples
A hockey puck (m = 0.20 kg) slides along a patch of rough ice (µk = 0.060) and stops after travelling for 25 m.
Draw a FBD for the puck.
Determine the work done by the friction.
What work is done by the normal force?

10. Defining Work: When Force Varies
When force varies over the displacement, the work done is the area beneath the force-displacement graph
Positive area = positive work done Negative area = negative work done

11. Homework on Work
Pg. 229 # 1-5, 7-8

12. Kinetic Energy
Kinetic Energy (Ek) is the energy of an object due to its motion.
Ek = ½ mv2
Ek = kinetic energy (J)
m = mass (kg)
v = velocity (m/s)

13. KE Example
A 95 g donut falls from a table and hits the floor. The maximum KE of the donut during its fall is 2.6 J.
When does the donut achieve maximum KE?
Calculate the donut’s maximum speed.

14. KE Conceptual Questions
As a car leaves a small town, the driver presses on the accelerator until the speed doubles. By what factor did the car’s kinetic energy increase?
Two cars are travelling at the same speed. Car A is twice the mass of car B. How does car A’s KE compare to car B’s?

15. KE Conceptual Questions
Examine the pictures which follow, and answer the following questions:
Which object has the greatest velocity?
Work is being done on which of the objects in the photos?
What force is doing the work in each case?
Which objects are probably losing kinetic energy?
Which object has the greatest amount of kinetic energy?

16. KE Conceptual Questions

17. Relating Kinetic Energy & Work
W = ΔEk
Assumptions:
All work done gives the system kinetic energy only
Constant force provides constant acceleration
Force and displacement are parallel
The formula for kinetic energy is derived using work

18. Homework on Kinetic Energy
Pg. 207, 11A-D
Pg. 216, 19-21
Pg. 226, 23-26

19. Gravitational Potential Energy
Gravitational Potential Energy (Eg) is the energy of an object because of its position relative to a lower position.
Δ Eg = mg Δh
Δ Eg = change in gravitational potential energy (J)
m = mass (kg)
Δh = change in height (m)

20. GPE Examples
Jose Guerra, an 85 kg Olympic diver from Cuba, climbs to the top of a diving platform at constant velocity. As a result, he gains 15 kJ of energy, with respect to the ground. How high is the platform from the ground?

21. The Importance of Reference Points
Δ Eg = mg Δh
E.g. A 75 kg skydiver jumps from a plane 1.5 km from the ground. What is her GPE with respect to:
a) the airplane? b) the ground?
The amount of GPE an object has is relative.

22. W = ΔEg Relating GPE and Work Assumptions:
Work done gives system GPE only
Object is lifted at constant velocity
Force and displacement are parallel (θ = 0º)
The formula for gravitational potential energy is derived using work.

23. GPE Conceptual Questions
Object A has twice the mass of object B. B is 4.0 m above the ground, and A is 2.0 m above the ground. Which has the greater amount of GPE?
For A and B of the previous question: Both A and B are lowered 1.0 m. Which has the greater amount of GPE now?

24. GPE Conceptual Questions
You carry a heavy box up a flight of stairs at constant velocity. Your friend carries an identical box on an elevator to reach the same floor as you. Who did the greatest amount of work (against gravity)? Explain.

25. GPE Conceptual Questions
Examine the pictures which follow, and answer the following questions:
What object do you think has the greatest amount of GPE?
Which objects clearly illustrate that GPE may be converted into KE?
What other forms of potential energy can you think of, besides GPE?

26. GPE Conceptual Questions

27. Homework on GPE
p. 235 # 3-6

28. Law of Conservation of Energy
Energy is neither created nor destroyed.
It may only be converted from one form to another or transferred from one object to another.

30. Law of Conservation of Mechanical Energy
The total mechanical energy is the sum of the gravitational and potential energy.
Total mechanical energy is conserved (so long as work is done by conservative forces):
ET = ET’
Eg + Ek = Eg’ + Ek’
ET = total mechanical energy (J)
Eg = gravitational potential energy (J)
Ek = kinetic energy (J)

31. Conservation Conceptual Questions
How does the car’s total mechanical energy, kinetic energy, and gravitational potential energy compare A, B and C? A C B

32. Conservation of Mechanical Energy

33. Conservation of Mechanical Energy

34. Conservation Conceptual Question
The masses of the cars in the picture below are identical. All four cars are released from rest simultaneously from point A. Which car is travelling the fastest by point B?

35. Example Problem
An astronaut on the moon, stands on a cliff and drops a 20 kg boulder from a height of 30 m. On the moon, g is 1.6 N/kg. Use conservation of energy to calculate the speed of the boulder:
a) Just before it hits the ground.
b) 10 m from the top of the cliff.

36. Homework on Energy Conservation
p. 241 # 1-3

37. Conservative and Non-Conservative Forces
The box shown can travel any one of four paths to get to its final destination, shown.
A then B
C then D E F
In the absence of friction, how does the amount of work done by gravity compare along each path?
If friction is present, how does the amount of work is done by friction compare along each path?

38. Conservative and Non-Conservative Forces
The work done by a conservative force does not depend on the length of the path taken.
E.g. Gravity
The work done by a non-conservative force depends on the length of the path taken.
E.g. Friction, air resistance
The longer the path, the more work done (more energy removed) from the system by the force.

39. Non-Conservative Forces, Work and Energy
The amount of work done by the non-conservative force equals the change in the total mechanical energy of the system:
Wnc=ET’-ET
Wnc = Work done by non-conservative force (N·m)
ET’= Total energy after interaction (J)
ET = Total energy before interaction (J)

40. Example
A 65.0 kg skydiver jumps from an airplane at an altitude of 5.00 × 102 m from the ground. Several minutes later, she reaches the ground travelling at a terminal velocity of 8.00 m/s.
What is the skydiver’s total mechanical energy, relative to the ground, just after she jumps?
What is the skydiver’s total mechanical energy just before she lands?
How much work did the non-conservative frictional force do?

41. Mid-Point Assessment
What do the vocabulary terms below mean? Discuss in your small groups.
Work Total Mechanical Energy Kinetic Energy
Potential Energy Positive Work Zero Work
Negative Work Constant Force Variable Force

42. How are these terms related? What do you know about these terms?
Assessment
How are these terms related?
What do you know about these terms?
Instructions:
WITHOUT TALKING, in your small groups, you will pass around a piece of paper on which you will construct a mind map.
Your mind maps will show how these terms are related AND what you’ve learned about the terms.
After 10 minutes, you will be allowed to talk about what you’ve come up with as a group.
Create a good copy in your groups to post in class.
Don’t forget to copy down your good copy in your notes too!

43. Mid-Point Assessment
Example of concept maps:

44. Mid-Point Assessment Some key questions to consider:
How are work and energy related?
If zero work is done on an object, does it affect the energy? What is positive work is done? Negative work?
How do you calculate work?

45. POWER & EFFICIENCY

46. What is Power? Rate at which work is done
Measured in Watts (W) (1 Watt = 1 Joule/second) or
P = Power (W)
W = work done (N∙m or J)
ΔE = change in energy (J)
Δ t = time (s)

47. Power Example
When doing a chin-up, a physics student lifts her 40 kg body a distance of 0.25 m in 2.00 s. What is the power delivered by the student's biceps?

48. What is Efficiency?
Transforming energy from one form to another always involves some “loss” of useful energy
The efficiency of a device describes the amount of input energy that is converted into the intended output energy or work.

49. Efficiency Efficiency = x 100% Efficiency = x 100%
How much of the input energy goes towards a “useful” output?
Efficiency = x 100%
Efficiency = x 100%
Eo = useful output energy (J)
Ei = input energy (J)
Wo = useful output work (N∙m)
Wi = input work (N∙m)

50. Efficiency Example
An electric kettle uses 2000 J of electrical energy to produce 500 J of heat energy.
What is the efficiency of the kettle?

51. Homework
p. 254 # 1-5

52. Energy, Work & Power Equations1) 2) 3) 4) 5) 6) 7)

53. Test your Knowledge with this MINI-TEST!
Work, Energy & Power
Test your Knowledge with this MINI-TEST!

54. MINI-TEST
Question 1:
Units for work are joules. This can also be written as:
N/m
N∙m
N/m2
N2∙m

55. MINI-TEST
Question 2:
Which one of the following statements about work is correct?
Work is a vector quantity
Work has no units
Work is a measure of how much energy is created in a process
Work is a scalar quantity

56. MINI-TEST
Question 3:
Which one of these following statements about power is correct?
Power is the rate of doing work
Power is the rate of change of velocity
Power is a vector
Power is the potential energy gained when the mass is raised

57. MINI-TEST
Question 4:
The power used by a hoist lifting a 50.0 kg mass through a vertical distance of 4.5 m in 5.0 s is:
10W
45W
100W
450W

58. MINI-TEST
Question 5:
A theme park roller-coaster carriage starts to run down a slope. Which of the following statements are true, ignoring friction and air resistance?
Kinetic energy is transformed to potential energy
Energy is destroyed as heat
Potential energy is transformed into kinetic energy
The total energy at e beginning is bigger than at the end

59. MINI-TEST Question 6: Which one of the following statements is TRUE:
An object at rest has no energy.
Gravitational potential energy depends only on the height of an object.
Doubling the speed of a moving object quadruples its kinetic energy.
Things "use up" energy.

60. Agree or Disagree?
“Heat”, “temperature” and “thermal energy” each describe the same thing.
Heat is a substance that resides within an object.
A piece of wood and a piece of steel, both removed from a pot of boiling water and placed in a sealed container, will cool to different temperatures.
Increasing thermal energy will increase temperature.

61. Thermal Energy & Heat Heat: Kinetic molecular theory: Thermal energy:
How do the motion of particles in solids, liquids and gases compare?
Link 1, Link 2
Thermal energy:
Measure of the kinetic energy of particles due to their constant random motion.
Depends on mass, and number of particles in a substance.
Heat:
Transfer of thermal energy (through the collision of particles).
Solid
Liquid
Gas

62. Discussion Question
The picture shows a kettle of boiling water, and a mug of boiling hot tea.
Compare these objects using kinetic molecular theory, thermal energy and heat.

63. Temperature
Measure of the average speed (kinetic energy) of the atoms or molecules of a substance.
Measured in units of Celsius (°C), Fahrenheit (°F) or Kelvin (K).
0°C and 100°C are defined by the freezing and boiling points of water.
0K is defined as absolute zero, when the kinetic energy of particles is zero (no movement). 0K = °C
TK = TC
T = temperature in Kelvin TC = temperature in Celsius

64. Kinetic Molecular Theory & Temperature

65. First Law of Thermodynamics
The change in energy of a system is the sum of the work and heat exchanged between a system and its surroundings:
ΔE = W + Q
ΔE = change in energy (J)
W = Work done on a system (J)
Q = heat (J)

66. Heat & Temperature

67. Thermal Equilibrium
Energy flows from “warmer” objects to “cooler” objects until they both achieve thermal equilibrium (the same temperature).
Transfer of energy occurs through the collision of particles.

68. Specific Heat Capacity
Amount of energy that must be added to raise 1.0 kg of a substance by 1.0 K.
Larger masses require more heat to achieve a specific rise in temperature
Different materials have varying capacities to absorb heat.
Table 1: Some Specific Heat Capacities
Substance
Specific Heat Capacity (J/kg·°C)
Aluminum (solid)
900
Ice (-15°C)
2000
Ethyl alcohol (liquid)
2450
Mercury (liquid)
139
Water (15°C)
4196
Substance
Specific Heat Capacity (J/kg·°C) at Constant Pressure
Carbon dioxide gas
833
Nitrogen gas
1040
Water vapour (100°C)
2020

69. Specific Heat Capacity

70. Heat Required for Temperature Change
To calculate the amount of heat required to raise the temperature of a quantity of a substance:
Q = mcΔT
Q = heat transferred [J]
m = mass of substance [kg]
c = specific heat capacity of substance
ΔT = temperature change [K or °C]*
*Since K and °C are 1:1, when temperature changes are used, both scales give the same result.

71. Examples
A 2.5 kg pane of glass, initially at 41°C, loses 4.2 × 104 J of heat. What is the new temperature of the glass?
A 120 g mug at 21°C is filled with 210 g of coffee at 91°C. All the heat lost by the coffee is transferred to the mug. The specific heat capacity of the mug is 7.8 × 102 J/kg·°C.
Write an equation representing the heat gained by the mug.
Write an equation representing the heat lost by the coffee.
Calculate the final temperature of the coffee.

72. Phase Changes
A beaker of ice is placed on a hot plate. Its temperature is monitored with a thermometer.
What will happen to the beaker of ice over time?
How do you expect the beaker’s temperature to change, as more and more heat is added by the hot plate? Why?
Temperature (K)
Heat (J)
Temperature (K)
Heat (J)
Temperature (K)
Heat (J)
Temperature (K)
Heat (J)

73. Phase Changes As the ice is heated,
Temperature (K)
Heat (J)
Thermal
energy added
to ice
Increased
av. kinetic energy
of particles
Increase in temperature
Temperatures do not increase during phase changes
When the ice temperature reaches 0°C, thermal energy goes towards melting the ice, instead of increasing temperature.
Once the ice has melted, the temperature increases once more.
Temperature (K)
Heat (J)

74. Phase Changes Phase changes require a change in internal energy.
The amount of energy needed for a phase change is called the latent heat.

75. Homework
Pg. 287 #1-10