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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

Gravitational Potential Energy and Conservative vs. Nonconservative Forces

6.3 and 6.4

work done by gravity
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)
work done by gravity3
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
gravitational potential energy
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
conservative vs nonconservative forces
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
conservative vs nonconservative forces6
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.
conservative forces
Conservative Forces
  • Examples of conservative forces
    • Gravitational Potential Energy
    • Elastic Spring Force (Ch 10)
    • Electric Force (Ch 18 and 19)
nonconservative forces
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
both usually happen at once
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
slide10
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…
example 1
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
example 2
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
practice problems
Practice Problems
  • Spend some energy on these
  • 174 CQ 9 – 10, P 25, 27, 29 – 31
  • Total of 7 problems