A 22cm diameter bowling ball has a terminal speed of 77 m/s. What is the balls mass. I need to get the answer in kg. I can`t figure this one out for some reason. Thanks!!

Answer 1

Is it being dropped from an airplane or thrown down a bowling alley?

For the dropped-from-airplane situation, you need to know the density of the air and the value of the drag coefficient, which is usually called Cd.

For more about the drag coefficient, see
http://en.wikipedia.org/wiki/Drag_coefficient

The value of Cd for a sphere is approximately 0.47 (dimensionless) , but it is not a true constant. It varies with Mach and Reynolds' number. That's a long story.

So set the weight (M g) equal to
(1/2)*Cd*(air density)*(frontal area)*V^2
and solve for M.
The frontal "projected" area is
A = pi*(0.22)^2/4 = 0.038 m^2

The density of air depends upon the temperature and altitde. The bowling ball will decelerate as it falls into denser atmosphere. Assume
1 atm and 10 C temperature.

If the answer is not about 7 kg, something is wrong with the question's assumptions.

Answer 2

Thanks