Question

Julia and Cate want to go bungee jumping. Julia goes first. She has a mass of m and uses a bungee cord with the length of L and unknown springiness. However, Cate is very hesitant to go and wants to calculate how far she will drop before she is pulled back up. She has a mass 0.8 times Julia's mass. How far will Cate go down?

Answer 1

The magnitude of force (F) from the spring is given as,

F = kx              (1)

where k is spring constant (springiness) and x is the amount of stretch in spring.

In the case of bungee jumping the force from spring to pull back will be equal to the weight of the person. This gives,

F = W = mg

where W is weight, m is mass and g is acceleration due to gravity.

If we let k be the springiness of bungee cord and the amount of stretch in cord. In the case of Julia,

               (2)

in the case of Cate,

mass = 0.8 times the mass of Julia

M = 0.8*m

The stretch of cord in case of Julia,

This means that the stretch of cord in case of Cate is 0.8 times that of Julia. Thus Cate will go down 0.8 times as much as Julia.