Question

Gravel is dropped into a conveyor belt at the rate of $0.5kg/s$. Find the extra force required to keep the belt moving at $2m/s$.

• A. $1N$
• B. $2N$
• C. $4N$
• D. $5N$

Answer 1

Answer: (A)

Step 1: Given

Extra force needs to be applied because the belt needs to carry more gravel. The mass of gravel which is added each second is accelerated from $0m/s$ to the velocity of the belt i.e $2m/s$.
Initial velocity(u) = 0 $m/s$

Finial velocity(v) = 2 $m/s$

Time(t) = 1 sec

Let F, p are force and momentum.

Step 2: Formula used

$F=\frac{\Delta p}{\Delta t}$

$\Delta p=m(v-u)$ (Change in momentum)

Step 3: Finding the force
$F=\frac{\Delta p}{\Delta t}$
$=\frac{m(v-u)}{t}=\frac{0.5(2-0)}{1}=1N$

Hence, the force required to keep the belt moving at $2m/s$ is $1N$.