Gravitational Potential Energy and Conservative vs. Nonconservative Forces

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# Gravitational Potential Energy and Conservative vs. Nonconservative Forces - PowerPoint PPT Presentation

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

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(h0 – hf)
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
• 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
• 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 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
• Examples of conservative forces
• Gravitational Potential Energy
• Elastic Spring Force (Ch 10)
• Electric Force (Ch 18 and 19)
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
• 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
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
• 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
• 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
• Spend some energy on these
• 174 CQ 9 – 10, P 25, 27, 29 – 31
• Total of 7 problems