Trampoline Stretch Calculation with Hooke's Law

How far does the trampoline stretch when the gymnast stands on it at rest?

Given that the trampoline stretches 67.0 cm when the gymnast lands.

Answer:

The trampoline stretches by approximately 0.67 meters when the gymnast stands on it at rest.

In order to calculate the stretch of the trampoline when the gymnast is standing on it at rest, we can utilize Hooke’s law. Hooke’s law states that the force applied to stretch (or compress) a spring is directly proportional to the distance that it is stretched (or compressed). Mathematically, it is represented as F = kx, where F is the force applied, x is the distance stretched, and k is the spring constant.

Given that the trampoline stretches by 67.0 cm when the gymnast lands, we can use the equation F = kx to determine the spring constant k. The force applied in this case is the weight of the gymnast, which is 52 kg x 9.8 m/s^2 = 508 N. Therefore, k can be calculated as follows:

k = F/x = 508 N / 0.67 m = 757 N/m

Now that we have found the spring constant k, we can proceed to find the stretch of the trampoline when the gymnast is standing on it at rest. By using the equation F = kx, where F is the weight of the gymnast and x is the stretch of the trampoline when she is standing on it at rest, we can calculate the stretch:

x = F/k = 508 N / 757 N/m = 0.67 m

Therefore, the trampoline stretches by approximately 0.67 meters when the gymnast stands on it at rest.