A force applied to a spring compresses the spring 11 cm, storing a certain amount of elastic potential energy. Then a larger force is applied to compress the spring a total of 66 cm. How does the elastic potential energy stored in the spring after it is compressed 66 cm compare to the elastic potential energy stored in the spring after it was compressed 11 cm

Respuesta :

Let k be the spring constant.

• When the spring is compressed by 11 cm = 0.11 m, it stores

1/2 k (0.11 m)²

of potential energy.

• When it's compressed by 66 cm = 0.66 m, it stores

1/2 k (0.66 m)²

of potential energy.

Then the ratio of these potential energies is

(1/2 k (0.66 m)²) / (1/2 k (0.11 m)²) = 36

which is to say, the spring stores 36 times more energy when it's compressed by 66 cm compared to 11 cm.