Question 191: Laws of Motion

Question

A conveyor belt is moving with constant velocity (V). Sand is being dropped on the belt at the rate of $\mathrm{M} \mathrm{kg} / \mathrm{s}$. The force necessary to keep the belt moving with a constant velocity $\mathrm{V} \mathrm{m} / \mathrm{s}$ will be

Accepted Answer

We need to find the force needed to keep the conveyor belt moving at the same speed when sand is dropped on it.
Newton's second law says that force is the change in momentum per second:
$$ F = \frac{d\vec{p}}{dt} $$
Here, momentum ($\vec{p}$) is mass ($m$) times velocity ($\vec{v}$):
$$ F = \frac{d(m\vec{v})}{dt} $$
The velocity of the belt is constant ($V$), and sand is added at a rate of $M$ kg/s, so:
$$ F = \frac{dm}{dt} 	imes V $$
Since $\frac{dm}{dt} = M$, we get:
$$ F = M V $$

Answer

$\frac{M V}{2} \mathrm{~N}$

Answer

2 MV N

Answer

Zero N

Answer

MV N

Laws of Motion

A conveyor belt is moving with constant velocity (V). Sand is being dropped on the belt at the rate of \mathrm{M} \mathrm{kg} / \mathrm{s}. The force necessary to keep the belt moving with a constant velocity \mathrm{V} \mathrm{m} / \mathrm{s} will be

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