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Gravitational Potential Energy and Conservative vs. Nonconservative Forces

Gravitational Potential Energy and Conservative vs. Nonconservative Forces. 6.3 and 6.4. 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(h 0 – h f ). Work Done by Gravity.

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Gravitational Potential Energy and Conservative vs. Nonconservative Forces

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  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

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