Quote:
Originally Posted by redpoint5
Still doesn't explain the constant rate of acceleration due to gravity. Gravity can't input more force, and yet you fall at the same rate of acceleration.
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Force isn't the same as energy.
1. Force is mass times acceleration.
For a constant force and a fixed mass, acceleration will be constant. In the case of gravity, the force is proportional to the mass, so acceleration will always be 9.8 m/s/s regardless of the mass.
2. Energy is force times distance.
If you drop an object, it will accelerate at 9.8 m/s/s, and after one second, it will have traveled a total of 4.9m (since it's
average speed over that second will have been 4.9 m/s). After two seconds, it will have fallen 19.6m (two seconds times an average speed of 9.8 m/s). After three seconds, it will have fallen 44.1 meters (three seconds times 14.7 m/s), and so on.
Notice that in the above, speed is proportional to time (after N seconds, it is moving at N x 9.8 m/s), and distance is proportional to time squared (after N seconds, it has fallen N x N x 4.9m) Alternatively, you could say that the distance is proportional to speed squared, since speed is proportional to time.
Since energy is force times distance, the force is constant, and distance is proportional to speed squared, we can see that energy is proportional to speed squared.