Question

in the game of pinball, you put the ball into play by pulling a plunger that compresses a spring; when the spring is released, it launches the ball. in one case, you compress the spring a distance d. if instead you were to compress it a distance 3d, how many times more spring potential energy would the spring have?

Answer 1

The potential energy stored in a spring is directly proportional to the square of the displacement (compression or extension) of the spring. Therefore, by compressing the spring a distance 3d instead of d, the potential energy stored in the spring would be:

(3d)^2 / d^2 = 9.

This suggests that by compressing the spring a distance 3d, the spring would have 9 times more potential energy compared to compressing it a distance d.

In other words, compressing the spring 3 times further results in a potential energy increase of 9 times.