Gravitational Potential Energy and Conservative vs. Nonconservative Forces

1. Gravitational Potential Energy and Conservative vs. Nonconservative Forces 6.3 and 6.4

2. Work Done by Gravity • Force of gravity near the earth is weight • Weight = mg (direction is down) • Work = Fs (direction of s must be down) • Work = mg(h0 – hf)

3. Work Done by Gravity • Since the force of gravity is down • We only worry about the vertical distance • The path the object takes doesn’t matter, just the vertical distance • Wgravity = mgh0 – mghf

4. Gravitational Potential Energy • PE = mgh • h is measured from any chosen point. Just be consistent • Potential Energy is not absolute • It is a difference as we saw with Wgravity = mgh0 – mghf • Only we are making hf = 0

5. Conservative vs Nonconservative Forces • Gravitational Potential Energy has property • It’s value does not depend on the path taken • It only depends on the difference of heights • The object could do many loops and sideways moves • The object could go up and down like a roller coaster, BUT • PE only depends on the initial and final heights

6. Conservative vs Nonconservative Forces • Conservative Forces • A force where the work it does is independent of the path • Only thing that matters is starting and stopping point • A force when it does no net work on an object on a closed path (starting and stopping at same point) • Like a roller coaster starts and stops at same point.

7. Conservative Forces • Examples of conservative forces • Gravitational Potential Energy • Elastic Spring Force (Ch 10) • Electric Force (Ch 18 and 19)

8. Nonconservative Forces • Examples of Nonconservative forces • Friction • Air resistance • Tension • Normal force • Propulsion force of things like rocket engine • Each of these forces depends on the path

9. Both usually happen at once • Often both conservative and nonconservative forces act on an object at once. • We can write Work done by net external force as • W = Wc + Wnc

10. W = Wc + Wnc • W = KEf – KEi • If the only conservative force is gravity • ½ mvf2 – ½ mvi2 = mgh0 – mghf + Wnc • Wnc = ½ mvf2 – ½ mvi2 + mghf - mgh0 • Wnc = KE + PE • To be continued…

11. Example 1 • A 70-kg man rides in a chair lift up a mountain. The lift is 1000 m long and makes an angle of 20° with the horizontal. What is the change in the potential energy of the man? • PE = 2.35 x 105 J

12. Example 2 • A rocket starts on the ground at rest. Its final speed is 500 m/s and height is 5000 m. If the mass of the rocket stays approximately 200 kg. Find the work done by the rocket engine. • W = 3.48 x 107 J

13. Practice Problems • Spend some energy on these • 174 CQ 9 – 10, P 25, 27, 29 – 31 • Total of 7 problems