Springs

To determine how the potential energy of a spring changes when the stretching is increased, we can use Hooke's Law and the formula for the potential energy of the spring. The potential energy stored in a spring is given by:

where:

• is the spring constant.
• is the amount of stretch or compression from the spring's equilibrium position.

Given that initially the spring is stretched by a distance and the potential energy is :

If the stretching is increased to times, then the new stretching distance will be . The new potential energy is given by:

Which simplifies to:

Comparing the original and new potential energies:

Thus, the potential energy of the spring when stretched to times the original distance is .

Therefore, the correct answer is: