Question

A child (32 kg) jumps up and down on a trampoline. The trampoline exerts a spring restoring force on the child with a constant of 5000 N/m. At the highest point of the bounce, the child is 1.0 m above the level surface of the trampoline. What is the compression distance of the trampoline? Neglect the bending of the legs or any transfer of energy of the child into the trampoline while jumping.

a) 0.20 m
b) 0.25 m
c) 0.30 m
d) 0.35 m

Answer 1

The compression distance of the trampoline is approximately 0.20 m.

Step-by-step explanation:

The compression distance of the trampoline can be determined using Hooke's Law, which states that the force exerted by a spring is proportional to the distance it is compressed or stretched.

In this case, the child's weight is balanced by the restoring force of the trampoline, so we can set up the equation:

mg = kx

where m is the mass of the child (32 kg), g is the acceleration due to gravity (9.8 m/s^2), k is the spring constant (5000 N/m), and x is the compression distance.

Substituting the given values, we have:

32 * 9.8 = 5000 * x

Simplifying, we find that the compression distance of the trampoline is approximately 0.20 m.