Question

An amusement park ride is designed such that one end of an elastic cord is fixed to a platform that is a distance D above the ground. The other end of the cord is attached to a person of mass M. The cord has an unstretched length of L. To begin the ride, the person jumps up from the platform with an initial speed, V0, as shown in figure 1. As the person falls, the elastic cord stretches and can be modeled much like a spring of negligible mass. After the cord can no longer be stretched, the person is a distance H above the ground and is no longer in motion, as shown in figure 2. The reference position for zero gravitational potential energy of the person cord Earth system is a distance H above the ground. All frictional forces are considered to be negligible. A) The initial state of the system is shown in Figure 1, and the final state of the system is shown in figure 2. i. Describe the energy transformations that take place from the initial state to the final state of the system. For each form of energy, identify the object or system that has that form of energy.

Answer 1

The energy transformations involve conversions between kinetic energy, gravitational potential energy, and elastic potential energy as the person jumps, ascends, descends, and comes to rest.

Initially, the person has kinetic energy that is gradually converted into gravitational potential energy and elastic potential energy during the ascent. At the peak of the jump, when the person is momentarily at rest before descending, all the initial kinetic energy is now in the form of gravitational potential energy and elastic potential energy.

As the person descends, the elastic potential energy in the cord is converted back into kinetic energy of the person. Upon reaching the final state, the person is at rest again, and all the initial kinetic energy is now stored as elastic potential energy in the stretched cord, and the person has gravitational potential energy.