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

• A. Mv newton
• B. 2Mv newton
• C. Mv/2 newton
• D. Zero

To determine the force required to keep the conveyor belt moving at a constant velocity while sand is being dropped onto it, we can apply Newton's second law of motion. When sand is added to the belt, it increases the mass of the system, but since the velocity is constant, the net force acting on the system must be zero.

Analyzing the Situation

The force needed to maintain constant velocity is related to the rate of change of momentum. The momentum of the sand being added is given by:

• Momentum = mass × velocity
• Rate of momentum change = M × v

Understanding the Force

Since the conveyor belt is moving at a constant speed, the force required to keep it moving is equal to the rate of momentum change of the sand being added. Thus, the force necessary to keep the belt moving is:

Force = Mv newton

Final Answer

The correct answer is A. Mv newton.