You sign up for a bungee jump off a tall bridge. A thick rope with a fixed lengt

Question

You sign up for a bungee jump off a tall bridge. A thick rope with a fixed length of 24.0 m is tied to the bridge, and a bungee cord with an unstretched length of 9.00 m is then connected to the rope. The other end of the bungee cord is attached to your legs.

You step off the bridge, falling from rest. The bungee cord does not start exerting any force on you until you have fallen a distance of 33 m (the sum of the rope's length and the unstretched length of the bungee cord). After that, it exerts an upward force on you that eventually brings you to rest, for an instant. Assume the bungee cord, when stretched, acts like an ideal spring, and take g = 10 N/m, to make the calculations easier. Your mass is 40.0 kg.

(a) You fall a total distance of 52.0 m before coming instantaneously to rest. Determine the spring constant of the bungee cord.
N/m

(b) How far below the bridge are you when you reach maximum speed?
m

(c) Determine your maximum speed.
m/s

Explanation / Answer

(a) Energy at bridge height = Energy at 52 m down to bridge = Energy stored in spring/rope

1/2 kx^2 = mgh

here x = 52 - 33 = 19 m
h = 52 m

.5 x k x (19)^2 = 40 x 10 x 52

k = 115.23 N/m

(b) Maximum speed is where that from when the rope starts stretching because the stretch starts to decraese the velocity.

So,
at 33 m the speed is maximum.

(c) energy conservation

mgh = 1/2 mv^2

10 x 33 = .5 x v^2

v^2 = 660

v = 25.69 m/s

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