A conveyor belt at a quarry lifts 1,800 kg of sand per minute up a vertical distance of 9.5 meters. The sand is initially at rest, then moves at a speed of 0.28 m/s along the conveyor belt. What is the instantaneous power generated by this machine?

2.8 kW

1.0 kW

3.9 kW

890 W

The power of the quarry belt is, P = 2.8 kW

Explanation:

Given data,

The mass of the sand, m = 1800 kg

The displacement of the quarry belt, s = 9.5 m

The initial velocity of the sand, u = 0

The final velocity of the sand, v = 0.28 m/s

The acceleration of the belt, a = (v-u) / t

= 0.28/10

= 0.028 m/s²

The net force acting on the quarry belt is,

F = mg + ma

= m (g + a)

= 1800 (9.8 + 0.028)

= 17690 N

The work done by the quarry belt,

W = F S

= 17690 x 9.5

= 168058 N

The power of the quarry belt,

P = W / t

= 168058 / 60

= 2800 W

= 2.8 kW

Hence, the power of the quarry belt is, P = 2.8 kW