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Say you have a piston falling in a cylinder filled with water. The water is plumbed from the bottom of the cylinder to the top, so as the piston falls, the water is free to flow through the plumbing, from beneath the piston to the top. The piston weighs 100kg, but only weighs 1kg under water. What would the kinetic energy be at the end of a 20m descent?
The total decrease in gravitational potential energy would just be mgh,
*20m=196 J. (Only the 1 kg difference in weight between the piston and the dispaced water matters.) That energy will not all go into kinetic energy of the piston. In fact, since the water is forced to move with the piston, a lot of the energy will go into kinetic energy of the water. I canít give you what fraction, because you donít give the various masses and also the dimensions of the pipes, which would be needed to compute the speed of the water in the various bits of plumbing. In practice in this situation, most of the energy will not be in any large-scale motions but instead will flow via friction into thermal forms, heating the piston, the water, and the walls. This thermal energy is about half kinetic and about half potential, in loosening the bonds between the atoms.
(published on 10/22/2007)
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