lecture14

# lecture14 - 6.3 Gravitational Potential Energy We've...

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6.3 Gravitational Potential Energy We’ve discussed Kinetic Energy (KE) , which is energy due to motion. But, an object can also have energy due solely to its position. This is called Potential Energy (PE). In this chapter we will be focused on the PE you can get due to gravity. First, consider a tennis ball in a vertical free-fall from some initial height, h o , to some final height, h f . What would be the work done by gravity on the tennis ball in moving it from h o to h f ? d F d = W h f h o ) ( ) ( o f h h ma - = ) ( ) ( o f h h mg - - = y ) ( f o h h mg - = Work done by gravity: ) ( W Grav f o h h mg - = Notice, that if the ball is moving downward, then h o is greater than h f , and W is positive, which it needs to be. But what if the ball doesn’t fall straight down? What if it follows a curved path?

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Let’s flick the tennis ball off the edge of the table with some speed v , so that it follows the curved path shown. Now what is the work done by gravity in moving the ball from h o to h f ? v h f h o The only force that acts on the ball after it is pushed is, again, just gravity, and gravity only acts in the vertical direction. Thus, to calculate the work I need the displacement that’s along the direction of the force. In other words, the vertical displacement. ) ( W h h mg - = This again is just the difference in height, h o – h f . Grav f o The work done is the same in either case. Thus, the work done by gravity on an object only depends on the initial and final heights and not the path taken. Now let’s go back to the vertical case and say the tennis ball is resting on the surface of the table. I reach down and pick the tennis ball up and raise it to some height, h . If I apply a force equal to the weight of the tennis ball, then I can raise it at constant speed. Now I just hold the tennis ball at rest at this height above the table. The tennis ball is not moving, therefore its KE = 0, but does the ball still have energy???!!! I do positive work on the ball: W = F d ·d = mgh
Yes! Where does the energy come from? It comes from the work I put into the ball in raising it to the height h. Thus, the energy it now has is just equal to the work I put in . This is called Gravitational Potential Energy : mgh = G PE Units? Still [force x distance] [J] (Joules) h in the equation for PE G is relative to some arbitrary zero. Huh? Let’s say I hold a tennis ball 2 m above the floor, but a 1-m high table is nearby. 1 m 2 m If I put y = 0 at the ground, then relative to the ground the ball’s PE G = mg (2 m).

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