A conveyor belt is moving with constant velocity (V). Sand is being dropped on the belt at the rate of M ~kg / s . The force necessary to keep the belt moving with a constant velocity V m / s will be

Step-by-step solution

The sand is deposited with zero initial horizontal velocity onto the belt moving at constant velocity V . The force needed to maintain constant belt velocity arises solely from accelerating each infinitesimal mass dm to speed V . The rate of mass deposition is M = dm dt , and the change in momentum for mass dm is dP = (dm) V . By Newton's second law, the required force equals the rate of momentum transfer: F = dP dt = V dm dt . Substituting the mass flow rate gives F = M V . The force necessary to maintain constant