1. Unit 7:
Work, Power, and
Mechanical Energy

2. I. Work Depends on: Force Displacement the force is applied for
Question: If we apply a force to an object and it doesn’t move, how much work has been done?
None, the force did not cause displacement 2

3. I. Work
By doing work on an object, you transfer __________ from one object to another.
energy
Equation:
W = Fd
Units –
N*m = Joule (J)
scalar
no direction
Work is a ______ quantity(____________) 3

4. I. Work
Example: A 50 kg crate is pulled 40 m across a horizontal surface in 120 s by a force of 150 N. Find the work done. 4

5. A. Work Done Against Gravity
Use the ___________________ (weight) of an object that is being moved to find the amount of work done in lifting the object
force due to gravity 5

6. A. Work Done Against Gravity
How much work is done lifting a 3 kg backpack a distance of 1.25 m?
How many Calories did you burn? (1 kilocalorie = 4184 J) (kcal vs. J article)
Calories : ( 6

7. B. Work and the Direction of the Force
Work is done when a force is applied
New modified Formula
parallel
________to the motion
W = Fcos(θ)d 7

8. B. Work and the Direction of the Force
Example: A 2.3 kg block rests on a horizontal surface. A force of 5 N is applied to the block at an angle of 30 degrees to the horizontal. Determine the work done in moving the block a distance of 2 m. 8

9. C. Finding Work from a Force vs. Distance Graph
Area Under Line= 9

10. II. Power
rate
Definition: _________ of doing ________ (how quickly work is done)
Power is _________ quantity
work
scalar
Equations (see Reference Tables):
Units: 10

11. II. Power
Example: An electric motor lifts an elevator that weighs 1.20 x 10 4 N a distance of 9 m in 15 s. What is the power of the motor? 11

12. II. Power
Example: A person applies a force of 25 N to a toy car and it moves at an average velocity of 10 m/s. What is the power developed by the car? 12

13. Work and Power Whiteboard Problems:
If a 25 kg mass is dropped from a height of 5 m, find the following: A) Work done by gravity B) If the average velocity of the mass is 7 m/s, what power was developed by gravity?
A constant force of 5 N acting at an angle of 25 degrees from the horizontal is applied to a box to move it at a constant speed. Determine how much power is dissipated in moving the box 5 m along the floor in 2 seconds.
A kg rubber hockey puck slows down from 20.0 m/s to 10.0 m/s as it slides along ice for 102 m. Calculate the following: A) Force of friction (hint: see ref. tabs). B) Average Velocity C) Power developed by friction D) Work done by friction
A) 1,226 J B) 1,717 W
11.3 W
A) N, B) 15.0 m/s, C) 2.76 W, D) 18.8 J 13

14. III. Kinetic Energy Definition: “Energy of __________” motion
Equation (see ref. tabs.)
KE = ½ mv2 KE
Units:
Joule (J) v 14

15. III. Kinetic Energy
Example: A 75 kg skydiver is falling through the air at 60 m/s. What is the kinetic energy of the skydiver?

16. A. Gravitational Potential Energy (GPE)
IV. Types of Potential Energy
Definition: ______energy (based on _______)
stored
position
A. Gravitational Potential Energy (GPE)
Definition: _______energy due to ________in a gravitational field
stored
height 16

17. A. Gravitational Potential Energy (GPE)
Equation (see ref. tabs.)
PE = mgh
PE (J)
Slope = mg
(weight)
Units:
Joule (J)
h (m)
Reference Point: Position where gravitational energy equals _________
zero 17

18. A. Gravitational Potential Energy (GPE)
Example: What is the gravitational PE of a 100 kg skydiver that is in a plane 1000 m above the ground? 18

19. B. Elastic Potential Energy
Restoring Force: force required to return spring to ___________ position
its original
Spring Constant: (k) (Phet Sim) “stiffness” of spring
Larger the spring constant, larger the _________
force 19

20. B. Elastic Potential Energy
Hooke’s Law (see ref. tabs)
Fs = k x
Slope = k
Fs (N)
x = displacement (m)
k = spring constant (N/m)
x (m) 20

21. B. Elastic Potential Energy
Why does this happen? 21

22. B. Elastic Potential Energy
Factors that affect how much elastic PE an object has:
1) Displacement of spring
2) Spring constant 22

23. B. Elastic Potential Energy
Equation (see ref. tables)
PEs = ½ k x2
PEs (J)
Units: Joules (J)
x (m) 23

24. B. Elastic Potential Energy
Example: A kg mass is hung from a spring causing it to stretch m.
What is the spring constant?
B) What is the PE stored in the spring? 24

25. 1630 kg 91.8 N/m 2670 N/m A) 2.08 x 10 5 J, B) 9.81 x 10 4 J _____
Types of Energy Whiteboard Problems:
1. A car has a kinetic energy of 4.32 X 10 5 J when traveling at a speed of 23 m/s. What is its mass?
2. A spring is 1.5 meters long and is stretched to a length of 4.3 meters, producing 360 joules of elastic potential energy. What is the spring constant?
3. A force of 32 N is required to pull a horizontal spring m from its equilibrium position. What is the spring’s k?
4. A 50 kg shell is shot from a cannon at Earth’s surface to a height of 425 m. A) What is the GPE of the shell when it is at this height? B) What is the change in the GPE when the shell falls to a height of 225 m?
5. A ball is thrown upward from the Earth’s surface. While the ball is rising, its GPE is increases/decreases/remains the same.
1630 kg
91.8 N/m
2670 N/m
A) 2.08 x 10 5 J, B) 9.81 x 10 4 J
_____ 25

26. V. Conservation of Energy
created
Energy cannot be _______nor _________. It is transferred from one from to another.
Therefore, total energy before = ___________________
destroyed
total energy after
Equation:
MEbefore = MEafter (Mechanical E = KE + PE)
KEi + PEi = KEf + PEf
Larger Pendulum Version Video 26

27. V. Conservation of Energy
More conservation of Energy Animations 27

28. Example: A B C
40 m
10 m
If the cart starts from rest, has a mass of 100 kg and assuming no friction, find the following:
A) The amount of KE and speed at position B.
B) The speed at position C. 28

29. A) The amount of KE and speed at position B.
Example:
If the cart has a mass of 100 kg and assuming no friction, find the following:
A) The amount of KE and speed at position B. 29

30. B) The speed at position C.
Example:
If the cart has a mass of 100 kg and assuming no friction, find the following:
B) The speed at position C. 30

31. Conservation of Energy Whiteboard Problems:
A 40.0 kg test rocket is fired vertically on a level surface. Its fuel gives it a kinetic energy of 3.00 x103 J before it leaves the pad. What is the maximum height the rocket will reach?
A 20.0 kg object is dropped off of a 30.0 m cliff. How fast is the object going when it hits the ground?
A 150. kg roller coaster is released from rest at the top of a 50.0 m hill. How fast will it be going if the second hill is 10 m high?
A kg toy has a spring attached to it so it can be shot straight up into the air. The spring is compressed m and has a spring constant of 300. N/m. A) Find the KE of the object when it is shot into the air. B) Find the maximum height of the toy (relative to the end of the barrel).
7.65 m
24.3 m/s
28.0 m/s
A) J, B) m 31

32. VI. Conservation of Energy and the Motion of a Pendulum
A. What does the work on a pendulum?
Gravity
________(does not take away from total ME)
Mechanical Energy is conserved (neglecting friction) 32

33. NEGLECTING FRICTION h = max h = max PE = max PE = max v = 0 h h v = 0
KE = 0
KE = 0
ME = PE
v = max
h = 0
ME = PE
KE = max
PE = 0
ME = KE 33

34. Energy vs. Horizontal Position Graph for a Frictionless Pendulum34

35. VII. Work-Energy Theorem
Definition: When work is done in a system, mechanical energy can be __________or __________ in the system
added
removed
Equation (see ref. tabs.)
W = Fd = ΔET 35

36. VII. Work-Energy Theorem
Example: A 1000 kg car traveling 40 m/s slows to 20 m/s.
What is the initial KE?
B) What is the final KE?
C) How much work is done on the car in slowing it down? 36

37. VII. Work-Energy Theorem
Even though work is a _________ quantity, it can be positive or negative.
SCALAR
If work is applied in the same direction of motion it is ________ because it is adding mechanical energy to the object.
POSITIVE
If work is applied in the opposite direction of motion it is ________ because it is taking away mechanical energy from the object.
NEGATIVE
Friction applies _________ amount of work to objects.
NEGATIVE 37

38. VII. Work-Energy Theorem38

39. VII. Work-Energy Theorem
Example: A 15 N block rests at the bottom of an incline that is 0.2 m high. If it takes 4 J of work to push the block up an incline, how much work was done against friction? 39

40. VII. Work-Energy Theorem
Whiteboard: A kg baseball bat strikes a kg ball at rest on a tee with an average force of 2.00 x 10 4 N. If the bat stays in contact with the ball for a distance of 5.00 x m, A) what kinetic energy will the ball acquire from the bat? B) What will be the ball’s speed after contact? 40

41. VIII. Conservation of Energy when Work is Done
Problem: A 0.1 kg apple falls from the tree at a height 2 m and compresses the spring 0.3 m. What is the spring constant of the spring (ignore air resistance) 41

42. VIII. Conservation of Energy when Work is Done
When work is done by a non-conservative force (friction, outside push), mechanical energy can be added or taken away from the initial mechanical energy of the object
Conservation of Energy when Work is done Equation:
KEi + PEi + W = KEf + PEf
+ W = energy added
- W = energy lost
Total Energy (ET) =
PE + KE + Q
Q = Internal Energy (energy of molecules/particles – excluding KE + PE) 42

43. VIII. Conservation of Energy when Work is Done
If mechanical energy (KE and PE) is lost, it can go into __________ energy. For example, if an object slides across a rough level floor and comes to a stop, it loses ____________ energy (specifically, _____________ energy). Friction generates __________ energy (molecules rub against each other and increase the temperature of the object).
INTERNAL
MECHANICAL
KINETIC
INTERNAL 43

44. VIII. Conservation of Energy when Work is Done44

45. VIII. Conservation of Energy when Work is Done
Example: A 30.4 N force is used to slide a 40.0 N crate a distance of 6.00 m at a constant speed along a 30.0 degree incline to a vertical height of 3.00 m
A) Determine the total work done by the 30.4 N force. 45

46. VIII. Conservation of Energy when Work is Done
Example: A 30.4 N force is used to slide a 40.0 N crate a distance of 6.00 m at a constant speed along a 30.0 degree incline to a vertical height of 3.00 m
B) Calculate the total increase in gravitational potential energy of the crate after it has slid 6.00 m along the incline. 46

47. VIII. Conservation of Energy when Work is Done
Example: A 30.4 N force is used to slide a 40.0 N crate a distance of 6.00 m at a constant speed along a 30.0 degree incline to a vertical height of 3.00 m
C) State what happened to the kinetic energy, potential energy, mechanical energy, and internal energy of the crate as it slides along the incline.
Kinetic: ___________ Potential: ____________
Mechanical: ____________ Internal: _____________
Constant
Increased
Increased
Increased 47

48. VIII. Conservation of Energy when Work is Done
Example: A 100 kg sled is located at top of an incline that is 20 m long and 5 m high. The force of friction between the sled and the incline is 45 N. What is the speed of the sled at the bottom of the incline, if the sled starts down the incline at 5 m/s? 48

49. A) 392 J, B) 8.85 m/s, C) 8.51 m/s (8.27 m/s) 0.0612 m/s 283,000 J
Conservation of Energy When Work is Done Whiteboard Problems:
A 10.0 kg block rests at the top of an incline that is 4.00 m high and 5.00 m long. A) Find the potential energy of the block when it is at the top of the incline. B) What is the speed of the block at the bottom of the incline, if it is frictionless? C) If the incline is not frictionless, and the block experiences a constant 10.0 N force of friction as it moves down the incline, find the speed of the block at the bottom.
A 10.0 kg block is pushed against a horizontal spring that has a spring constant of 15.0 N/m. If the spring is displaced m, find the speed of the block after it is released from the spring.
A 100. kg skier starts at the top of a 300. m double-black diamond slope. How much energy was lost to friction if his velocity at the bottom of the hill is 15.0 m/s?
A 5.00 kg ball is dropped from a height of 10.0 m and 10.0 J of energy are lost due to air resistance. (a) What is the ball’s kinetic energy as it strikes the ground? (b) What is the final velocity as the ball strikes the ground?
A) 392 J, B) 8.85 m/s, C) 8.51 m/s (8.27 m/s)
m/s
283,000 J
A) 481 J, B) 13.9 m/s 49