First slide

Law of conservation of momentum and it's applications

Question

When a belt moves horizontally at a constant speed of 1.5 m/s, gravel is falling on it at 5kg/s, then the extra power needed to drive the belt is :

Easy

A

11.25 W
B

37.5 W
C

7.5 W
D

0.75 W

Solution

Given
Constant speed $v = 1.5 m / s$
$\frac{d m}{d t} = 5 kg / s$
From Newton’s law $F = \frac{d p}{d t} (∵ p = m v)$
$\Rightarrow F = \frac{d m v}{d t} = v . \frac{d m}{d t}$
$F = v \frac{d m}{d t} = 1.5 \times 5 = 7.5 N$
Power $P = F \times v = 7.5 \times 1.5 = 11.25 W$

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