Rankers Physics
Topic: Laws of Motion
Subtopic: Linear Momentum and Second Law of Motion

Sand is poured on a conveyor belt at the rate of 2 kg/s. If belt is moving horizontally with velocity 4 m/s, then additional force required by engine to keep the belt moving with same constant velocity
8 N
10 N
12 N
14 N

Solution:

The force required to keep the conveyor belt moving at a constant velocity is given by the rate of change of momentum.

Momentum of sand per second:

Force=dPdt=dmdt×v\text{Force} = \frac{\text{dP}}{\text{dt}} = \frac{\text{dm}}{\text{dt}} \times v

Given dmdt=2\frac{dm}{dt} = 2 kg/s and v=4v = 4 m/s,

F=2×4=8 NF = 2 \times 4 = 8 \text{ N}

Thus, the additional force required is 8 N.

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