Shaskolskaya & Eltsin Problem 98
Physics · mechanics
Problem
Let the unknown force which one brake exerts on the wheel be P. The force of friction will equal kP. The moment of the forces of friction acting on the two brakes will equal kP.2R. This moment of the forces of friction must balance the moment of the rotating couple M. Therefore 2kPR = M. Hence P = M/2kR = 400 kg.Intuitive explanation
This problem is about torque balance during braking—the key insight is that friction forces create a torque that must exactly oppose the applied rotational moment to stop the wheel. Since both brakes contribute equally and friction force is proportional to the normal force at each brake, you set up the torque equation by multiplying friction force by the lever arm , then solve for the brake force needed. The factor of 2 accounts for both brakes working together.
Intuitive explanation
This problem is about torque balance during braking—the key insight is that friction forces create a torque that must exactly oppose the applied rotational moment to stop the wheel. Since both brakes contribute equally and friction force is proportional to the normal force at each brake, you set up the torque equation by multiplying friction force by the lever arm , then solve for the brake force needed. The factor of 2 accounts for both brakes working together.