Question

Gravels are dropped on a conveyor belt at the rate of \[0.5kg/s\]. The extra force required in Newton to keep the belt moving at \[2m/s\] is:
A. 1
B. 2
C. 4
D. 0.5

Answer 1

Hint: Here given quantities are the rate of change of mass and asked to find the extra force required to maintain a particular velocity that is here the given velocity is constant. By using this particular data we can find the required force with the help of Newton’s second law of motion.

Formula used:
 \[\begin{align}
  & p=mv \\
 & F=\dfrac{dp}{dt} \\
\end{align}\]

Complete answer:
According to Newton’s second law of motion, the rate of change of momentum is directly proportional to the force applied and the direction in which rate of change of momentum takes place in the direction of force applied.
\[\begin{align}
  & F=\dfrac{dp}{dt} \\
 & \Rightarrow F=\dfrac{d(mv)}{dt} \\
 & \Rightarrow F=v\dfrac{dm}{dt} \\
\end{align}\]
As here the rate of change of mass with respect to time is given \[\dfrac{dm}{dt}=0.5kg/s\] and the velocity is kept constant therefore we have taken the velocity parameter out of the bracket \[v=2m/s\]
Substituting the values in the above equation the required force to keep the belt moving at \[2m/s\] can be determined
\[\begin{align}
  & \Rightarrow F=2m/s\times 0.5kg/s \\
 & \Rightarrow F=1N \\
\end{align}\]
Hence the extra force required is 1N.

So, the correct answer is “Option A”.

Additional Information:
Newton’s first law of Motion- A body in rest will remain in rest or a body in motion will remain in motion until and unless some external force is applied on it.
Newton’s third law of motion- Every action has an equal and opposite reaction. In other words, if one body applies force on the second body, say F, then the force applied on the first body by second will be –F that is equal force and opposite in magnitude.

Note:
Newton’s second law of motion can also be given in terms of acceleration, which is force is the product of mass and the acceleration of the body. Here acceleration is not given and the rate of change of mass is given therefore we used Newton's second law of motion in terms of momentum.