How Much Work Does a Gymnast Do While Jumping on a Trampoline?
What is the work done by the gymnast during the jump on a trampoline?
If a gymnast with a mass of 55.0kg is jumping on a trampoline with an effective spring constant of 1300 N/m, and compresses the trampoline a distance of 0.60m to reach a height of 2.3m above the surface within 0.50s, how much work does the gymnast do during the jump?
Answer:
The work done by the gymnast while jumping on a trampoline is 234 Joules.
When a gymnast jumps on a trampoline, they exert a certain amount of work to compress the trampoline and achieve a certain height. In this scenario, the work done by the gymnast can be calculated by considering the principles of elastic potential energy and gravitational potential energy.
The work done by the gymnast during the jump is determined by the elastic potential energy stored in the trampoline's spring during compression. This can be calculated using the formula:
Work = ½kx²
Where 'k' is the spring constant and 'x' is the compression distance. Substituting the given values:
Work = ½(1300 N/m)(0.6 m)²
Work = 234 Joules
This indicates that the energy used by the gymnast is 234 Joules, and this energy is transferred to lifting the gymnast to a height of 2.3m above the trampoline surface, against Earth's gravity. Therefore, all the energy transferred is related to the gymnast's gravitational potential energy during the jump.