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

2. I. Work Depends on: Force Distance/Displacement 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 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 object that is being moved to find the amount of work done in lifting the object
How much work is done lifting a 3 kg backpack a distance of 1.25 m?
How many calories is this? (1 cal = 4184 J)
force due to gravity
cal 5

6. II. Power
rate
Definition: _________ of doing ________ (how quickly work is done)
By doing work on an object, you transfer ________ from one object to another.
work
energy
Equations (see Reference Tables):
Units: 6

7. 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? 7

8. 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? 8

9. III. Kinetic Energy Definition: “Energy of motion”
Equation (see ref. tabs.)
KE = ½ mv2 KE
Units:
Joule (J) v 9

10. 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?

11. A. Gravitational Potential Energy (GPE)
IV. Types of Potential Energy
Definition: Stored energy (based on position)
A. Gravitational Potential Energy (GPE)
Definition: stored energy due to position in gravitational field 11

12. 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 12

13. 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? 13

14. B. Elastic Potential Energy
Restoring Force: force required to return spring to its original position
Spring Constant: (k) (Phet Sim) “stiffness” of spring
Larger the spring constant, larger the force 14

15. 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) 15

16. B. Elastic Potential Energy
Factors that affect how much elastic PE an object has:
1) Displacement of spring
2) Spring constant 16

17. B. Elastic Potential Energy
Equation (see ref. tables)
PEs = ½ k x2
PEs (J)
Units: Joules (J)
x (m) 17

18. 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? 18

19. V. Conservation of Energy
Energy cannot be created nor destroyed
Therefore, total energy before = total energy after
Equation:
MEbefore = MEafter (Mechanical E = KE + PE)
KEi + PEi = KEf + PEf
Larger Pendulum Version Video 19

20. V. Conservation of Energy
More conservation of Energy Animations 20

21. V. Conservation of Energy
More conservation of Energy Animations 21

22. 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 amount of KE and speed at position C. 22

23. 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. 23

24. B) The amount of KE and speed at position C.
Example:
If the cart has a mass of 100 kg and assuming no friction, find the following:
B) The amount of KE and speed at position C. 24

25. 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)
Energy is conserved 25

26. 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 26

27. Energy vs. Horizontal Position Graph27