In order to use common symbols, let’s call the jumper’s mass, m , the unstretche

Question

In order to use common symbols, let’s call the jumper’s mass, m, the unstretched length of the rope, L0, the height of the bridge above the water, H, the elastic constant of the rope, k, and the gravitational field strength, g.

a) Write an expression for the energy of the jumper-rope system in terms of symbols that can be used to describe her descent.

b) How fast is she falling when she reaches the length of the unstretched rope?

c) The approximate values of the symbols for this case are: m = 50 kg, L0 = 8 m, H = 150 m, and g = 10 N/kg. If the elastic rope stretches an extra 4 m to bring her to a stop, what is its spring constant, k?

physic hw 4

I was inspired to think about bungee jumping as I watched a video of a friend bungee jumping from a high bridge over Victoria Falls. In this activity, an operator attaches an elastic rope to the jumper. The jumper then jumps off the bridge. She falls freely until she reaches the unstretched length of the rope. Then, the rope begins to stretch and slow her to a stop. It yanks her back up and she oscillates up and down for a while. When she is nearly stopped, the operator of the jump pulls on the elastic rope and hauls her back up to the bridge.

In order to use common symbols, let’s call the jumper’s mass, m, the unstretched length of the rope, L0, the height of the bridge above the water, H, the elastic constant of the rope, k, and the gravitational field strength, g.

Explanation / Answer

a)

By Conservation of energy

mgH =mg(H-Lo)+(1/2)mv2

mgLo=(1/2)mV2

b)

V=sqrt(2gLo)

c)

By Conservation of energy

mg(Lo+x)=(1/2)Kx2

50*10*(8+4)=(1/2)*K*42

K=750N/m

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