Question

1. Using the symbols in the problem described above, write an expression for the total mechanical energy of the jumper-rope-Earth system when the jumper is standing at rest on the bridge.
2. What is the height of the jumper above the river when they've fallen the full length of the unstretched rope?

When bungee jumping from a high bridge over Victoria Falls, an operator first attaches an elastic rope to the jumper. The jumper then jumps off the bridge, falling freely until they reach the unstretched length of the rope. Then, the rope begins to stretch and slows the jumper to a stop. The rope pulls the jumper back up, and they oscillate up and down for a while until the operator pulls the jumper back up to the bridge. The rope is essentially a long spring. Let's label the jumper's mass m, the unstretched length of the rope Lo, the height of the bridge above the water H, the elastic (spring) constant of the rope k, and the gravitational field strength g. The jumper's speed at the point where they've fallen the full length of the unstretched rope is a maximum, Vmax. For simplicity, we will neglect resistive forces like air drag.

3. Write an expression for the total mechanical energy of the jumper-rope-Earth system when they've fallen the full length of the unstretched rope. Your expression should include the maximum speed, v_max.

4. After falling the full length of the unstretched rope, the rope begins to stretch as the jumper continues falling. The jumper comes to a stop at the bottom when the rope has stretched its maximum distance, d. What is the height of the jumper above the river when they've come to a stop and the rope has stretched its maximum distance?

5. Write an expression for the total mechanical energy of the jumper-rope-Earth system when the jumper comes to a stop after the rope has stretched its maximum distance. Your expression should include the maximum distance the rope has stretched, d.

6. We are neglecting resistive forces like air drag in this problem. Using A, B, and C to represent the total mechanical energies that you have written in parts A, B, and C above, what is the correct relationship between these energies?

7. The jumper has a mass of 55 kg, and the bridge's height above the river is 150 m. The rope has an unstretched length of 11 m and stretches a distance of 6 m before bringing the jumper to a stop. Determine the maximum speed of the jumper and the spring constant of the rope. In your calculation, use g = 10 N/kg.

8. Now suppose the jumper has a mass of 80 kg. Do you think the maximum speed of the jumper will increase, decrease, or stay the same? Will the rope need a larger, smaller, or the same spring constant to bring the jumper to a stop in the same distance as part D? (Your answers to these questions are not graded for correctness.)

9. The maximum speed of the jumper will _______

10. The rope will need a spring constant that is _________

11. Now calculate the maximum speed of this more massive jumper and the spring constant of the rope needed to bring the jumper to a stop after the rope stretches 6 m. (Again, use g = 10 N/kg for your calculations.) Were your predictions correct?

Answer 1

use concepts of work and energy

Etot n mgh F Gm Me RetH) Me = mass of earth Re = radius of earth acceleration due to B.) height = HEL son Ett = mg (H-Lo) + Im Vimaxe c.) height , H-(Lord) H-Load. Etot = mg (H-Lord) t TolPie). o TKIE) can