Potential Energy Formula

Potential Energy Formula

If you lift a stone up by a height h, you have to do work against the weight mg. You have to apply enough force F to just overcome this weight.

The work you have to do is W = Fd, where d is the height in this case. So the work done is W = mgh.

This work is converted into potential energy of the stone. So potential energy E_p = mgh.

Exercise. I lifted a stone to a height of 1 m. If the mass is 0.5 kg, what is the potential energy? Assume that the acceleration due to gravity is 10 m/s². Answer. The potential energy is E_p = mgh = 0.5 x 10 x 1 = 5 J.

Exercise. After walking along a hill slope for 100 m, I find that I am 10 m higher than where I have started. If I am 50 kg, find my potential energy. Assume that g is 10 m/s². Answer. The horizontal distance makes no difference to the potential energy. It only depends on the vertical distance. So the potential energy is E_p = mgh = 50 x 10 x 10 = 5000 J.

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