Calculate the force required to pull a copper ball of radius 1.69 cm upward through a viscous fluid at a constant speed of 9.3 cm/s. Take the damping constant of the fluid to be 0.884 kg/s\.\*

Since we have an ball we can consider this like a sphere and the volume is given by

The density for the copper is approximately

So then the mass is :

And now we have everything in order to replace into the formula for F, like this:And that would be the final answer for this case.

Explanation:

For this case if we assume that we have a damping motion the force action on the vertical direction would be:

Where F represent the upward force on the copper ball

m represent the mass

g = 9.8 m/s^2 represent the gravity

b = 0.884 kg/s represent the proportionality constant

v = 9.3 cm/s = 0.093 m/s represent the velocity

We can solve for the mass from the following expression:

Since we have an ball we can consider this like a sphere and the volume is given by

The density for the copper is approximately

So then the mass is :

And now we have everything in order to replace into the formula for F, like this:And that would be the final answer for this case.

resonant frequency