1. Aim: How do we explain the potential energy of a system?

2. Review of Work-Energy Theorem
What does the work-energy theorem that we studied in class say? (W = ΔKE) Which statement is true? Wtot = ∆KE Wgrav= ∆KE

3. Potential Energy
What are the two types of potential energy that we studied last year in mechanics? Gravitational and Elastic

4. Potential Energy
The work done on a system does not always cause an increase in the kinetic energy. Often, it is stored as potential energy. Potential energy pertains to the configuration of a system, and not the speed.

5. Conservative Force
A force is conservative if it does the same amount of work on an object moving from A to B, regardless of the path taken.

6. Thought Question 1
Assume three of us in this class want to walk from room 153 to room 253. Person A walks to the elevator on the 1st floor and takes the elevator up to the second floor and then walks to room 253. Person B drills a hole through the ceiling and climbs a ladder to get to room 253. Person C takes the nearest staircase to walk to the 2nd floor and then walks to room 253. On which person, does gravity do the most work and least work? Same Work on Each On which person, does friction do the most work and least work? Friction does the most work on A and the least work on C

7. Conservative Forces and Non-Conservative Forces
Gravity is a conservative force. Friction is a non-conservative force.

9. Thought Question 2
The graph shows one direct path and four indirect paths from initial position i to final position f. A conservative force Fc acts along the direct path and three of the indirect paths. A nonconservative force Fnc acts along one of the indirect paths. The change in mechanical energy is indicated along each straight segment of the indirect paths.
What is the change in mechanical energy that occurs along the direct path?
12 J
b)What is the change in mechanical energy that occurs along the indirect path in which the nonconservative force Fnc acts?
10 J

10. Relationship between work and potential energy of a system.
When work is done on a particle by gravity, what happens to its gravitational potential energy? The gravitational potential energy decreases When work is done on an object attached to a spring, what happens to its elastic potential energy? The gravitational potential energy increases Wc =-ΔU (U is potential energy)

11. Deriving functions for gravitational and elastic potential energy
Using the definition of work, W = ʃF◦dr or -ΔU = ʃF◦dr Let us find the gravitational potential energy by substituting the gravitational force and substituting for dr = dx + dy

12. Potential Energy Functions
Ug = U0 + mgy Us = U0 + 1/2kx2 We usually set U0 equal to 0.

13. Potential Energy Problems
What is the gravitational potential energy, relative to the ground, associated with a 0.15 kg baseball at the top of a 100 m tall building? Ug=mgh=0.15(10)(100)= 150J

14. Potential Energy Problems
2. A 1000 kg roller coaster is initially at the top of a rise at point A. It then moves 41 m, at an angle of 40 degrees below the horizontal, to a lower point B. Assume that the rollercoaster has 0 potential energy at point B.
Find the potential energy of the rollercoaster at point A and B. Find the change in potential energy.
Find the height by using h=41sin40=26.35m
Ug = mgh=1000(10)(26.35)=263,500 J at point A and Ug = 0 at point B
So ∆Ug=Uf – Ui =-263,500 J
b) Repeat part A, setting point A as the zero level of potential energy.
Ug=0J at point A and Ug = -263,500 J at point B
a) 259,000 J , 0, -259,000 J b) 0, -259,000 J, - 259,000 J if you use g = 9.8

15. Potential Energy Problem 3
Assume Kobe Bryant’s center of mass is 2 m off the floor, Kobe Bryant has a mass of 100 kg, and he is bending the rim back 0.1 m while the rim has a spring constant of 8 N/m
How much total potential energy does Kobe Bryant have?
U=Ug+Us
U=mgh + 1/2kx2
U=100(10)(2) + ½ (8)(0.1)2
U= J