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Q: If you had 70 joule of potential energy and converted it into 55 joule of kinetic energy what happens for the missing 15 joule?
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What happens to potential energy when rock falls?

When the rock is high up but has not been dropped yet, it has a lot of gravitational potential energy because of its position. PE = (mass) x (G) x (height) After it is dropped, the lower it goes, the less potential energy it has. That bit of missing potential energy has become the kinetic energy that it now has on account of its speed of descent. KE = 1/2 (mass) x (speed)2


If the work output of a machine is always less then the work input where does the missing work go?

The energy, lost to friction, is converted to heat and sound.


In a machine is work output is less than work input because some energy is converted into thermal energy?

The missing energy is converted into some form of unusable energy. It may be heat (thermal energy), but it may be other types of energy as well.


How is mass converted into energy in nuclar fusion?

It isn't. This is a popular statement, but it is complete incorrect. Both mass and energy are conserved. Energy: The energy was already available previously, but in another form (nuclear energy, which is a type of potential energy). Mass: The heat or light that is produced is energy; it has an associated mass. For example, the photons (light) that leave the Sun not only take energy, but also mass, away from the Sun. This mass is exactly equal to the "missing" mass.


What kind of potential energy are there?

Here are a few:Gravitational potential energy, defined by the height of an objectElastic energy, e.g. the energy stored in a stretched rubber bandChemical energyElectric energy stored in a capacitorNuclear energyThere are probably a few more, which I am missing. I suggest checking the Wikipedia article on potential energy for more information.