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We can now apply this to the example of the suitcase on the cupboard. Consider the mechanical energy of the suitcase at the top and at the bottom. We can say:
The suitcase will strike the ground with a velocity of .
From this we see that when an object is lifted, like the suitcase in our example, it gains potential energy. As it falls back to the ground, it will lose this potential energy, but gain kinetic energy. We know that energy cannot be created or destroyed, but only changed from one form into another. In our example, the potential energy that the suitcase loses is changed to kinetic energy.
The suitcase will have maximum potential energy at the top of the cupboard and maximum kinetic energy at the bottom of the cupboard. Halfway down it will have half kinetic energy and half potential energy. As it moves down, the potential energy will be converted (changed) into kinetic energy until all the potential energy is gone and only kinetic energy is left. The of potential energy at the top will become of kinetic energy at the bottom.
During a flood a tree truck of mass falls down a waterfall. The waterfall is high. If air resistance is ignored, calculate
The kinetic energy of the tree trunk at the bottom of the waterfall is equal to the potential energy it had at the top of the waterfall. Therefore .
To calculate the velocity of the tree trunk we need to use the equation for kinetic energy.
A metal ball is suspended from a rope. If it is released from point and swings down to the point (the bottom of its arc):
All quantities are in SI units.
As there is no friction, mechanical energy is conserved. Therefore:
As the mass of the ball appears on both sides of the equation, it can be eliminated so that the equation becomes:
This proves that the velocity of the ball is independent of its mass. It does not matter what its mass is, it will always have the same velocity when it falls through this height.
We can use the equation above, or do the calculation from 'first principles':
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