Work done by quadratic air resistance.

[GS416492]

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

 

[darkSun]

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.

 

[nlightner]

every time I try to solve it.

I would suggest using the formula for work done by air resistance, which is W = Fd = 1/2 * p * Cd * A * v^2 * d, where p is the density of air, Cd is the drag coefficient, A is the cross-sectional area of the object, v is the velocity, and d is the distance traveled. This formula takes into account the quadratic relationship between air resistance and velocity, and will give you a more accurate estimate of the work done on the baseball as it falls from the tower. It is also important to note that the terminal velocity of the baseball will also change as it falls, so you may need to use the appropriate value for v in the equation at each point in time.