5 part question here. "Sand from a stationary hopper falls on a moving conveyor belt at a rate of 5.81 kg/s. The belt is supported by frictionless rollers and moves at .645 m/s under the action of a horizontal external force supplied by the motor that drives the belt."
1. Find the sand's rate of change of momentum in the horizontal direction (answer in units of N)
2. Find the frictional force exerted by the belt on the sand (in units N)
3. Find the magnitude of the external force supplied by the motor
4. Find the work done by the external force each second
5. Find the kinetic energy acquired by the falling sand each second due to the change in its horizontal motion.
I know I have to derivate momentum with respect to time, use conservation of momentum, and force equations. Work-energy theorm seems to be needed too.
The Attempt at a Solution
For one, would I just multiply the velocity of the sand on the belt by the changing mass? I would get v(dm/dt), which is a dP/dt. Seems too easy. I'm not quite sure how to get frictional force without the coefficient. It is acting against the external force in the positive horizontal direction on my free-body diagram, but I cant figure out how to solve it. I'm pretty lost on the next two, and especiallt the last one. There is no change in horizontal motion until the sand hits the belt, so why would it acquire KE while falling from it?