Question

A spring stores potential energy U0 when it is compressed a distance x0 from its uncompressed length In terms of U0, how much energy does it store when it is compressed twice as much?

Answer 1

The potential energy stored in a spring when it is compressed twice as much as its original compression is four times the original potential energy.

Step-by-step explanation:

The potential energy stored in a spring when it is compressed twice as much as its original compression can be calculated using the formula for potential energy of a spring, which is given by U = kx². Here, U0 represents the potential energy when the spring is compressed a distance x0 from its uncompressed length.

So, if the spring is compressed twice as much, the new displacement would be 2x0. Therefore, the energy stored in the spring would be U = k(2x0)² = 4U0.

Therefore, when the spring is compressed twice as much, it stores four times the amount of potential energy as it did originally.