For each of the following situations identify what energy transformation is taking place.
(a) A child jumps out of a tree and lands on a trampoline. Consider “initial” to be the moment when they have left the tree and “final” to be the moment when they are brought to rest the first time by the trampoline (i.e. before the first bounce).
(b) An airplane is landing on a short landing strip in the wilderness. It touches down and a hook on its tail catches an “arrestor cable”. The arrestor cable is basically a big spring. The plane’s brakes have failed but it is still brought to rest by the arrestor cable. Consider “initial” to be the moment when the plane touches down and “final” to be the moment when it is brought to rest.
(c) A model rocket is at rest on its launch pad. Its engine ignites and it zooms off into the sky.
Consider “initial” to be when the rocket is stationary on the launch pad and “final” to be the moment when the rocket is at maximum height.
(a) In this situation, the energy transformation that is taking place can be explained as follows:
Initially, when the child jumps out of the tree, the energy transformation involves potential energy being converted into kinetic energy. As the child falls towards the trampoline, potential energy (due to the height from the ground) is being converted into kinetic energy (the energy of motion).
At the moment when the child first comes to rest on the trampoline, the energy transformation involves kinetic energy being transformed into elastic potential energy. The kinetic energy of the child's motion is transferred to the trampoline, causing it to compress.
(b) For the airplane landing on a short landing strip with its brakes failed and being brought to rest by the arrestor cable, the energy transformation can be explained as follows:
During the touchdown, the energy transformation involves the conversion of kinetic energy (due to the motion of the airplane) into thermal energy (due to friction between the airplane's wheels and the landing strip).
When the hook on the airplane's tail catches the arrestor cable, the energy transformation involves kinetic energy being converted into elastic potential energy. The kinetic energy of the airplane's motion is transferred to the arrestor cable, causing it to stretch or compress like a spring.
As the arrestor cable brings the airplane to rest, the energy transformation involves the conversion of the elastic potential energy stored in the cable into thermal energy. The energy is dissipated as heat due to the deformation and friction in the cable.
(c) In the case of a model rocket launching from rest on its launch pad and reaching maximum height, the energy transformation can be described as follows:
Initially, before the rocket ignites, the energy transformation involves potential energy (due to the rocket's height above the ground) and chemical potential energy (stored in the rocket's fuel) being converted into thermal energy when the rocket's engine ignites.
As the engine burns and propels the rocket upwards, the energy transformation involves the conversion of the chemical potential energy stored in the rocket's fuel into kinetic energy. The thrust generated by the engine propels the rocket upwards, causing its kinetic energy to increase.
At the moment when the rocket reaches its maximum height, the energy transformation involves the conversion of the rocket's kinetic energy into potential energy. The rocket's upward motion slows down until it eventually stops, and the kinetic energy is transformed into potential energy (due to the rocket's height above the ground).
These are the energy transformations taking place in each of the given situations.