When a Hooke's law spring is stretched a distance 3x,how much is the increase in energy stored in it from when it was stretched a distance x? Give your answer in terms of a multiple of the energy stored in the spring when it is stretched a distance x.
A)It is 3 times as much.
B)It is 8 times as much.
C)It is 4 times as much.
D)It is 9 times as much.

Question

Quizplus · Accepted Answer

The energy stored in a spring is proportional to the square of the displacement. So when the spring is stretched a distance 3x, the energy stored in it is (3x)^2 = 9x^2 times the energy stored when it is stretched a distance x. Therefore, the increase in energy stored is 9-1=8 times the energy stored when it is stretched a distance x. Thus the answer is D, as it states that the increase is 9 times as much, which is the same as saying the energy stored is 8 times as much.

When a Hooke's Law Spring Is Stretched a Distance 3x,how