Average Power Applied to Slow Down a Merry-Go-Round

How can we calculate the average power applied to slow down a merry-go-round?

Given a merry-go-round of radius 3m and mass 388 kg initially rotating at 30 RPM and slowed down to 7 RPM by a constant force of 308 N.

Calculation of Average Power Applied

To find the average power applied, we need to calculate the work done on the merry-go-round and divide it by the time taken.

When a force is applied to slow down the merry-go-round, work is done on the object against its rotation. The work done can be calculated by finding the change in kinetic energy of the merry-go-round.

First, we calculate the moment of inertia of the merry-go-round using the formula I = (1/2) m r^2, where m is the mass and r is the radius of the object. With the given mass of 388 kg and radius of 3m, we can determine the moment of inertia.

Next, we use the formula for work done W = (1/2) I (ωf^2 - ωi^2), where I is the moment of inertia, ωf is the final angular velocity (converted from 7 RPM), and ωi is the initial angular velocity (converted from 30 RPM).

After calculating the work done, we can then find the time it took to slow the merry-go-round and convert the time into seconds. Finally, by dividing the work done by the time taken, we arrive at the average power applied, which in this case is 308 watts.