Question

A 45 kg gymnast is bouncing on a trampoline. model the gymnast as a particle and the trampoline as a spring with a spring constant of 15,000 n/m . the spring is compressed by 30 cm when the gymnast is at her lowest point. we want to determine how high she goes above the trampoline.

The trampholine pushes the qymnast 30 cm upward. Unit the trampholine surface is flat. At which point she is launched into the air . how much work does the trampholine do on the qymnast?

Answer 1

The trampoline does 675 joules of work on the 45 kg gymnast when it compresses by 30 cm and applies a force governed by its spring constant of 15,000 N/m.

Step-by-step explanation:

To solve the mathematical problem completely, we first model the gymnast as a particle and the trampoline as a spring with a spring constant of 15,000 N/m. When the gymnast is at her lowest point, the spring (trampoline) is compressed by 30 cm (0.3 m).

To find out how much work the trampoline does on the gymnast, we can use the work-energy principle. The work done on the gymnast by the trampoline is equal to the change in her mechanical energy.

Given that the trampoline does work on the gymnast to push her up 30 cm, we can calculate this using the formula for the work done by a spring: W = (1/2)kx^2, where 'k' is the spring constant and 'x' is the compression distance. Substituting the given values, we get W = (1/2) * 15000 N/m * (0.3 m)^2, which equals 675 J.

Therefore, the trampoline does 675 joules of work on the gymnast.