Question

In: Physics

When bungee jumping from a high bridge over Victoria Falls, an operator first attaches an elastic...

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. A. The rope is essentially a long spring. Let's label the jumper's mass m, the unstretched length of the rope L0, 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.

A. 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 9 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.

1) vmax = _____ m/s ?

2) k = _________ N/m ?

B. 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?

1) The maximum speed of the jumper will?

2) The rope will need a spring constant that is?

C. 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?

1) vmax = _____ m/s ?

2) k = _____ N/m?

Solutions

Expert Solution


Related Solutions

A person is bungee jumping. The bungee cord is attached to a bridge over a river....
A person is bungee jumping. The bungee cord is attached to a bridge over a river. At time t0, before the person jumps (and while she is at rest), the bungee cord is unstretched. At time t1, the cord is stretched and the person is moving downward at her maximum speed. At time t2, the person has fallen her maximum distance and the cord is stretched by its maximum amount. At t3, the person is moving back up toward the...
Design a "bungee jump" apparatus for adults . A bungee jumper falls from a high platform...
Design a "bungee jump" apparatus for adults . A bungee jumper falls from a high platform with two elastic cords tied to the ankles. The jumper falls freely for a while, with the cords slack. Then the jumper falls an additional distance with the cords increasingly tense. Assume that you have cords that are 11 m long, and that the cords stretch in the jump an additional 23 m for a jumper whose mass is 140 kg, the heaviest adult...
Design a "bungee jump" apparatus for adults. A bungee jumper falls from a high platform with...
Design a "bungee jump" apparatus for adults. A bungee jumper falls from a high platform with two elastic cords tied to the ankles. The jumper falls freely for a while, with the cords slack. Then the jumper falls an additional distance with the cords increasingly tense. Assume that you have cords that are 12 m long, and that the cords stretch in the jump an additional 19 m for a jumper whose mass is 120 kg, the heaviest adult you...
Design a "bungee jump" apparatus for adults. A bungee jumper falls from a high platform with...
Design a "bungee jump" apparatus for adults. A bungee jumper falls from a high platform with two elastic cords tied to the ankles. The jumper falls freely for a while, with the cords slack. Then the jumper falls an additional distance with the cords increasingly tense. Assume that you have cords that are 11 m long, and that the cords stretch in the jump an additional 23 m for a jumper whose mass is 140 kg, the heaviest adult you...
Design a "bungee jump" apparatus for adults. A bungee jumper falls from a high platform with...
Design a "bungee jump" apparatus for adults. A bungee jumper falls from a high platform with two elastic cords tied to the ankles. The jumper falls freely for a while, with the cords slack. Then the jumper falls an additional distance with the cords increasingly tense. Assume that you have cords that are 14 m long, and that the cords stretch in the jump an additional 20 m for a jumper whose mass is 80 kg, the heaviest adult you...
A bungee jumper with mass 64.5 kg jumps from a high bridge. After arriving at his...
A bungee jumper with mass 64.5 kg jumps from a high bridge. After arriving at his lowest point, he oscillates up and down, reaching a low point seven more times in 44.0 s . He finally comes to rest 20.5 m below the level of the bridge. Part A Estimate the spring stiffness constant of the bungee cord assuming SHM. Part B Estimate the unstretched length of the bungee cord assuming SHM.
A bungee jumper with mass 58.5 kg jumps from a high bridge. After arriving at his...
A bungee jumper with mass 58.5 kg jumps from a high bridge. After arriving at his lowest point, he oscillates up and down, reaching a low point seven more times in 41.0 s . He finally comes to rest 20.0 m below the level of the bridge. Part A Estimate the spring stiffness constant of the bungee cord assuming SHM. Part B Estimate the unstretched length of the bungee cord assuming SHM.
A 61 kg bungee jumper jumps from a bridge. At the point when she is travelling...
A 61 kg bungee jumper jumps from a bridge. At the point when she is travelling 20 m/s, the cord starts to stretch. The cord stretches 25 m before causing her to stop completely for a moment. How fast is she travelling when the cord is stretched 12 m?
A 61 kg bungee jumper jumps from a bridge. At the point when she is travelling...
A 61 kg bungee jumper jumps from a bridge. At the point when she is travelling 22 m/s, the cord starts to stretch. The cord stretches 28 m before causing her to stop completely for a moment. How fast is she travelling when the cord is stretched 12 m? Please show all of your work.
A bungee jumper plans to bungee jump from a bridge 74.0 m above the ground. He...
A bungee jumper plans to bungee jump from a bridge 74.0 m above the ground. He plans to use a uniform elastic cord, tied to a harness around his body, to stop his fall at a point 6.00 m above the water. Model his body as a particle and the cord as having negligible mass and obeying Hooke's law. In a preliminary test he finds that when hanging at rest from a 5.00 m length of the cord, his body...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT