Question: The momentum of the person increases during free fall. Explain whether or not this is a violation of the principle of conservation of momentum. (H1 2008)
Answer: The momentum of the person increases during free fall because of an “external” gravitational force. The principle of conservation of linear momentum holds if there is no external force acting on the person. However, there is an external gravitational force acting on the person in this case.
Further details: Alternatively, we can consider the person and the earth to be a system. In this case, the increase in the downward momentum of the person equals to the upward momentum of the earth. However, the mass of the person is relatively very small as compared to the mass of the earth. Thus, the upward velocity of the earth is negligible. More importantly, we can consider the gravitational force to be an internal force for the person-earth system.
Question: Explain why it would be extremely dangerous to have a bungee rope that is much stiffer. (H1 2008)
Answer: If the rope is more elastic, the person would be stopped in a longer period of time. This implies a lower resistive force and a longer extension of the rope for the person to decelerate. On the contrary, a much stiffer bungee rope will cause a much higher resistive force and a very shorter extension of the rope to stop the person. The larger force can result in serious injury, and thus, it is extremely dangerous.
Further details: By using v2 = u2 + 2ax, we can rewrite the equation as a = (v2 – u2)/2x. If the rope is much stiffer, it means the extension will be very short. Thus, the magnitude of acceleration will be very large based on the equation. By using Newton’s second law of motion, F = ma, higher acceleration means greater force. However, the elasticity of bungee rope can also cause more energy to be stored in the rope. As a result, the person will oscillate for a while before the motion is finally stopped.
Note:
1. For a fatal accident relating to bungee jumping, please refer to this website:
2. For a demonstration of bungee jumping, you can visit the following youtube video:
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