The Amazing Trampoline Physics Challenge!

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

A gymnast of mass 51.00 kg is jumping on a trampoline. She jumps so that her feet reach a maximum height of 2.100 m above the trampoline and, when she lands, her feet stretch the trampoline down 61.00 cm. How far does the trampoline stretch when she stands on it at rest?

Answer: x = 6.7 cm

Explanation:

Here we can use energy conservation for two positions of the gymnast. When she is at the lowest position of the trampoline, then its potential energy will convert into gravitational potential energy at the top.

So we will have:

1/2 kx^2 = mg(H + x)

So we have:

1/2 k(0.61^2) = 51 * 9.81(2.1 + 0.61)

k = 7287.5

Now when she stands on it, then by force balance we will have:

mg = kx

51 * 9.81 = 7287.5 * x

x = 6.7 cm

Trampolines are not just for fun, they also provide a great platform for learning about physics! In this scenario, the gymnast's energy conservation and the application of Hooke's law help us determine how far the trampoline stretches when she stands on it at rest.

By calculating the spring constant k and using force balance equations, we can find that the trampoline stretches 6.7 cm when the gymnast stands on it. This result showcases the fascinating interplay between energy, forces, and motion in the world of physics.

Next time you see someone bouncing on a trampoline, remember the science behind the fun!