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 bridge and she is at her maximum speed (which is the same as her speed at time t1). Assume that the bungee cord is massless and has a resilience of 1. Ignore air resistance.

b. Define the system to include the person, bungee cord, and Earth. Between t1 and t3, is the absolute value of the change in the system’s gravitational potential energy greater than, less than, or equal to the absolute value of the change in the system’s elastic potential energy? Explain your reasoning

Solutions

Expert Solution

Applying work energy theorem:

Work done by all the forces = change in kinetic energy

At times t1 and t3 speed is same, therefore change in kinetic energy is zero. The forces that are working are gravitational force and elastic forces.

Wg , We are the works done by gravitational forces and elastic forces respectively.

Both gravitational and elastic forces are conservative forces. Work done by a conservative force is equal to decrease in corresponding potential energy.

Therefore, Decrease in systems gravitational potential energy = -(decrease in systems elastic potential energy)

Absolute value of change in system's gravitational energy = absolute value of change in system's eleastic potential energy.

genius_generous answered 1 year ago

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