1. Honors Physics Chapter 11
Energy and Its Conservation

2. Chapter 11 Turn in Chapter 10 homework, worksheet, and Lab Report
Take Quiz 11
Lecture
Q&A

3. NGSS
HS-PS3-1.
Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.

4. Forms of Energy Kinetic energy: energy due to motion
Linear kinetic energy: translational motion
Rotational kinetic energy: rotation
Potential energy: energy stored in a system due to state, position, or configuration
Gravitational potential energy: due to height of object
Spring (elastic) potential energy: due to compression or stretch of spring
Chemical, nuclear, …
Work: energy transfer by means of force

5. Kinetic Energy, KE
m: mass
v: velocity
Unit:

6. Work-Kinetic Energy Theorem
Work and energy are related by
Wnet: net work done on an object
KE: kinetic energy of that object

7. Example: Pg287pp3 A comet with a mass of 7
Example: Pg287pp3 A comet with a mass of 7.85  1011 kg strikes Earth at a speed of 25.0 km/s. Find the kinetic energy of the comet in joules, and compare the work that is done by Earth in stopping the comet to the 4.2  1015 J of energy that was released by the largest nuclear weapon ever built.

8. Practice: A rifle can shoot a 4. 20-g bullet at a speed of 965 m/s
Practice: A rifle can shoot a 4.20-g bullet at a speed of 965 m/s. a) Find the kinetic energy of the bullet. b) What work is done on the bullet if it starts from rest? c) If the work is done over a distance of 0.75 m, what is the average force on the bullet? d) If the bullet comes to rest by pushing 1.5 cm into metal, what is the magnitude and direction of the average force it exerts?

9. Gravitational Potential Energy (PE, U, or Ug)
m: mass
g = 9.8 m/s2
h = height
Unit:

10. Frame of Reference
In the formula PE = mgh, upward has been defined as the positive direction for h.
We are still free to choose where h = 0.
Reference level, height, or point: h = 0
PE has no physical significance, only ΔPE has physical significance, and ΔPE does not depend on the choice of Reference level.

11. Example:
Is it possible for a system to have negative potential energy?
a) No, because the kinetic energy of a system must equal its potential energy.
b) Yes, since the choice of the zero of potential energy is arbitrary.
c) No, because this would have no physical meaning.
d) Yes, as long as the total energy is positive.

12. Practice:
An acorn falls from a tree. Compare its kinetic energy K, to its potential energy U.
a) K decreases and U decreases.
b) K increases and U decreases.
c) K increases and U increases.
d) K decreases and U increases.

13. Let h = 0 at initial position.
Example A 90-kg rock climber first climbs 45 m upward to the top edge of a quarry, then, from the top, descends 85 m to the bottom. Find the potential energy of the climber at the edge and at the bottom, using the initial height as the reference level.
Let h = 0 at initial position. 1
h1 = 45 m
h = 0
h2 = ? 2

14. Practice Pg291pp7
If a 1.8-kg brick falls to the ground from a chimney that is 6.7 m high, what is the change in its potential energy?

15. c) From person (food or fat).
Example A person weighing 630 N climbs up a ladder to a height of 5.0 m. a) What work does the person do? b) What is the increase in the gravitational potential energy of the person from the ground to this height? c) Where does the energy come from to cause this increase in the gravitational potential energy?
c) From person (food or fat).

16. Spring (Elastic) Potential Energy (PEs, PEsp, or Us)
x: compression or stretch of spring. (x is more exact.)
Displacement of spring from relaxed position
k: spring constant: Stiffness of spring
, unit: N/m
Hooke’s Law: Force by spring:
F is opposite to x.
Large k 
stiff spring
Small k 
soft spring
Unit:

17. Example:
Calculate the work required to compress an initially uncompressed spring with a spring constant of 25 N/m by 10 cm.
a) 0.25 J
b) 0.17 J
c) 0.10 J
d) 0.13 J

18. Practice:
What work is required to stretch a spring of spring constant 40 N/m from x = 0.20 m to 0.25 m? (Assume the unstretched position is at x = 0.)
a) 0.80 J
b) J
c) 0.45 J
d) 1.3 J

19. (Total) Mechanical Energy, Emec or E

20. Conservation of Energy
When the only forces doing work are gravitational forces and/or spring force during a process, the total mechanical energy is conserved.

21. Example: Pg297pp15 A bike rider approaches a hill with a speed of 8
Example: Pg297pp15 A bike rider approaches a hill with a speed of 8.5 m/s. The combined mass of the bike and rider is 85 kg. Choose a suitable system. a) Find the initial kinetic energy of the system. b) The rider coasts up the hill. Assuming there is no friction, at what height will the bike come to rest? c) Does your answer depend on the mass of the bike and rider? Explain.
Let system include bike, rider, and Earth.
b) Let h = 0 at initial height, then hi = 0, vf = 0, hf = ?
c) No. Mass canceled out in part b).

22. Practice Tarzan, mass 85 kg, swings down from a tree limb on the end of a 20-m vine. His feet touch the ground 4.0 m below the limb. a) How fast is Tarzan moving when he reaches the ground? b) Does your answer depend on Tarzan’s mass?
Let h = 0 at lowest point. i
h = 0 f
b) No, the mass canceled out.

23. Practice:
A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill. Which rises to a greater height?
a) The lightweight object, because it weighs less.
b) The heavy object, because it has greater kinetic energy.
c) They both slide to the same height.
d) cannot be determined from the information given

24. Practice:
A skier, of mass 40 kg, pushes off the top of a hill with an initial speed of 4.0 m/s. Neglecting friction, how fast will she be moving after dropping 10 m in elevation?
a) 7.3 m/s
b) 49 m/s
c) 15 m/s
d) 196 m/s

25. Collision Momentum is conserved Kinetic Energy is Pi = Pf Conserved
 KEi = KEf
 Elastic Collision
Not conserved
 KEi  KEf
 Inelastic Collision
If the two bodies stick together after collision
 v1f = v2f
 Completely Inelastic Collision
During completely Inelastic Collision, there is most possible loss (but usually not all) of kinetic energy.

26. Elastic Collision Consider only collisions with v2i = 0,
Only when v2i = 0
When using these formula, make sure we choose m1 and m2 such that v2i = 0.

27. Example
A 2.00-g bullet, moving at 538 m/s, strikes a kg piece of wood at rest on a frictionless table. The bullet sticks in the wood, and the combined mass moves slowly down the table.
Find the speed of the combination after the collision.
Find the kinetic energy of the bullet before the collision.
Find the kinetic energy of the combination after the collision.
How much (percent) kinetic energy was lost?

28. Solution

29. Solution
Where did the kinetic energy go?
 Heat (and sound)

30. Practice As everyone knows, bullets bounce from Superman’s chest
Practice As everyone knows, bullets bounce from Superman’s chest. Suppose Superman, mass 104 kg, while not moving, is struck by a 4.2-g bullet moving with a speed of 835 m/s. If the collision is elastic, find the speed that Superman had after the collision. (Assume the bottoms of his superfeet are frictionless.)
Must choose m1 and m2 this way to use formulas.

31. Practice: Pg300pp21
A 91.0-kg hockey player is skating on ice at 5.50 m/s. Another hockey player of equal mass, moving at 8.10 m/s in the same direction, hits him from behind. They slide off together.
What are the total energy and momentum in the system before the collision?
What is the velocity of the two hockey players after the collision?
How much energy was lost in the collision?

32. Solution: Pg300pp21

33. Solution