Work done by quadratic air resistance.

AI Thread Summary
The discussion focuses on calculating the work done by quadratic air resistance on a baseball dropped from a height of 381 meters. The user attempts to derive the work using an integral involving terminal velocity and hyperbolic tangent functions, but encounters unexpected results. It is noted that the energy of the baseball upon impact differs when considering air resistance compared to free fall. The difference in energy is attributed to the work done by the air resistance force. Understanding these concepts is crucial for accurately analyzing the effects of air resistance on falling objects.
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Homework Statement



A baseball of mass 0.145kg and radius 0.0366m is dropped from a tower 381m high.

Homework Equations





The Attempt at a Solution



Work=integral(from 0 to 381): c(2) (terminal velocity)^3*(tanh(t/(characteristic time)))^3 with respect to time.

Gets me really strange (incorrect) numbers
 
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You could also look at it this way: the object would have a certain energy when it hits the ground if it was freefalling with no air resistance. It has less energy when it hits the ground if it falls with the air resistance. The difference is due to the work of the air resistance force.
 
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