Question

A ring is attached at the center of the underside of a trampoline. A sneaky teenager crawls under the trampoline and uses the ring to pull the trampoline slowly down while his 67-kg mother is sleeping on it. When he releases the trampoline, she is launched upward. As she passes through the position at which she was before her son stretched the trampoline, her speed is 3.0m/s.

How much elastic potential energy did the son add to the trampoline by pulling it down? Assume the interaction is nondissipative.

Answer 1

E = 301.5 J

Step-by-step explanation:

We have,

Mass of mother, m = 67 kg

Here, a sneaky teenager crawls under the trampoline and uses the ring to pull the trampoline slowly down. As she passes through the position at which she was before her son stretched the trampoline, her speed is 3 m/s.

It is required to find the elastic potential energy the son add to the trampoline by pulling it down. It is based on the conservation of energy.

The elastic potential energy of the mother = the elastic potential energy the son add to the trampoline.

`(1)/(2)mv^2=(1)/(2)kx^2`

So, the elastic potential energy is :

`E=(1)/(2)mv^2\\\\E=(1)/(2)* 67* 3^2\\\\E=301.5\ J`

So, the elastic potential energy of 301.5 J the son add to the trampoline by pulling it down.