Question

A 90 kg circus performer jumps from a 5.9 m height onto a trampoline and stretches it downward 0.40 m. Assume that the trampoline obeys Hooke's law. (a) How far will it stretch if the performer jumps from a height of 8.7 m? m

(b) How far will the trampoline stretch if the performer stands still on it while taking a bow? m

Answer 1

Here,

m = 90 Kg

h = 5.9 m

x = 0.40 m

a) let the spring constant is k

Using conservation of energy

0.50 * k * x^2 = m * g * (h + x )

0.50 * k * 0.40^2 = 90 * (9.8) * (5.9 + 0.40)

solving for k

k = 69500 N/m

Now, for 8.7 m

Using conservation of energy

0.50 * k * x^2 = m * g * (h + x )

0.50 * 69500 * x^2 = 90 * (9.8) * (8.7 + x)

solving for x

x = 0.48 m

the stretch is 0.48 m

part b)

let the distance is x

k * x = m * g

69500 * x = 90 * 9.8

x = 0.013 m

the stretch is 0.013 m