Physics Power Question

Question

10. Sand falls on a conveyor belt at the rate of 20kg/s. The conveyor belt moves at 7.0m/s. Ignore the effects of friction.

(a) How much power must be supplied to the conveyor belt to keep it moving at 7.0m/s?

(b) The power that must be supplied to the conveyor belt is proportional to what power of conveyor belt speed v

Answer 1

(a)

Each second, it must transport an additional 20 kg of mass.

m/t = 20 kg/s

v = 7.0 m/s

P = power = ?

KE = kinetic energy

P = KE/t = (mv²/2)/t = (m/t)v²/2

m/t = 20 kg/s

P = (20 kg/s)(7.0 m/s)² / 2 = ? joules/s = ? watts

(b)

The power is proportional to the square of the belt speed.