These assumptions apply to the theoretical calculations to find \"calculated hei

Question

These assumptions apply to the theoretical calculations to find "calculated height," he All of the potential energy from the spring in the gun is converted to kinetic energy in the dart. No energy is converted to sound, heat, velocity of the gun, or anything else. All of the kinetic energy in the dart is converted to potential energy in a gravitational field in the dart. No energy is converted to sound, heat, or anything else 1. 2. 3. Assume that there is no air resistance. 4. Assume that the spring is linear and that the spring is unloaded when the gun is in the "un-cocked" position. Explain the reason for each of these assumptions: 1. 2. 3. 4.

Explanation / Answer

1. If no external force is acting on the gun, the total mechanical energy of the system is conserved. It merely gets converted from one form to another.

Now only internal forces do their work on the dart. The coils of the spring are initially compressed and on pulling the trigger the potential energy of spring gets converted into kinetic energy of the dart.

The energy converted to sound, heat and velocity of gun is small as compared to total energy, hence it is assumed as negligible.

2. When the dart reaches the highest point of its motion all of its kinetic energy gets converted to potential energy. Again all other energies are assumed negligible since they are small.

3. The effect of drag on dart is quite small, so it is not a bad approximation to neglect air resistance. It makes the problems a lot easier when you neglect air resistance.

4. The spring is assumed linear and unloaded when the gun is in uncocked position so that after cocking the spring gets compressed uniformly. Further if the spring is not unloaded before cocking it means there is an external force acting on the system and hence mechanical energy of the system does not remain conserved i.e the initial amount of mechanical energy will not be same as final.

THANK YOU.

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