Question

Kate, a bungee jumper, wants to jump off the edge of a bridge thatspans a river below. Kate has a mass m, and the surface of thebridge is a height h above the water. The bungee cord, which haslength L when unstretched, will first straighten and then stretchas Kate falls.

Assume the following:
? The bungee cord behaves as an ideal spring once it begins tostretch, with spring constant k.
? Kate doesn't actually jump but simply steps off the edge of thebridge and falls straight downward.
? Kate's height is negligible compared to the length of the bungeecord. Hence, she can be treated as a point particle.
Use g for the magnitude of the acceleration due to gravity(don’t put numbers in - give both answers in terms of thealgebraic quantities in the statement).
(a) How far below the bridge will Kate eventually be hanging, onceshe stops oscillating and comes finally to rest? Assume that shedoesn't touch the water.
(b) If Kate just touches the surface of the river on her firstdownward trip (i.e. before the first bounce), what is the springconstant k?

Answer 1

(i) 140 N/m

(ii) 28 m/s²

Step-by-step explanation:

(i)

At the top of the jump, the bungee jumper has gravitational potential energy.

At the bottom of the jump, the bungee jumper has elastic potential energy.

mgh = ½ kx²

(60 kg) (9.8 m/s²) (31 m) = ½ k (31 m − 15 m)²

k = 140 N/m

(ii)

At the bottom of the jump:

∑F = ma

kx - mg = ma

(140 N/m) (31 m − 15 m) − (60 kg) (9.8 m/s²) = (60 kg) a

a = 28 m/s²