An object with a mass of #5 kg# is hanging from an axle with a radius of #18 m#. If the wheel attached to the axle has a radius of #8 m#, how much force must be applied to the wheel to keep the object from falling?
There is something wrong with the data in your question. You say the axle has a radius of 18 meters. So that means a diameter of 36 m. That would be about the length of 9 small cars (VW Beetles). And then the wheel is less, 8 m - only 2 small cars. I will work the problem with the data you provided.
Keeping it from falling requires establishing equilibrium. Equilibrium requires that the sum of torques equal zero. Another way to say that is that torques must have equal magnitude but opposite direction.
Clockwise torque = Counter-clockwise torque
The hanging mass has weight of
The force to be applied to the wheel creates torque through its 8 m lever arm according to:
So, using Clockwise torque = Counter-clockwise torque
That is the weight of
I hope this helps,