A Question I Need Answered Badly

Question

The horsepower that can be safely transmitted to a shaft varies jointly as the shaft's angular speed of rotation (in revolutions per minute) and the cube of its radius. A 2-inch radius shaft making 120 revolutions per minute safely transmits 40 horsepower. Find how much horsepower can be safely transmitted by a 3-inch radius shaft making 80 revolutions per minute.

Answer 1

P = horsepower, k = constant we are solving for, w = angular speed, r = radius

From the problem we can say P = kwr^3 however we don't know what k is

We can solve by setting up this equation, 40 = k * 120 * (2)^3 which becomes 40 = 720k, which gives k = 40/720

We can then go to solve the question as a whole for the new radius

The new conditions state r = 3, w = 80 and k remains as 40/720

So the new power is P = (40/720) * 80 * (3)^3 = 40