Question

A number of discs each of momentum M $kgm/s$ are striking a wall at the rate of $n$ discs per minute. The force associated with these discs in newtons would be:
A) $\dfrac{{Mn}}{{60}}$
B) $60Mn$
C) $\dfrac{M}{{60n}}$
D) $\dfrac{n}{{60M}}$

Answer 1

Any object of mass m that is in motion, is said to be in momentum. Therefore, momentum means the property of an object due to its mass and motion. Here the concept of how the force is affected due to the momentum associated with a body will be used. Recall the principle that momentum is always constant.

Step-by-Step Explanation:
Step I:
Momentum associated with a body can be calculated as $p = mv$ ---(i)
Where $p$ is the momentum of the system
$m$ is the mass of the object
$v$ is the velocity with which the object is moving

Step II:
Given that the discs have a momentum$= M$
The rate at which they are colliding is$= n/\min$
Suppose that each disc is travelling with velocity$v$ $m/s$, then the rate at which they strike will be$= \dfrac{n}{{60}}$

Step III:
It is clear from the law of conservation of momentum, that momentum can be transferred from one form to another but can not be destroyed or created.
Therefore in this case,
Force $F = \dfrac{{dp}}{{dt}}$
Where p is the momentum
Substituting value of ‘p’ from equation (i),
$F = \dfrac{{M.dv}}{{dt}}$
$F = M \times \dfrac{n}{{60}}$
Or $F = \dfrac{{Mn}}{{60}}$

Step IV:
Force associated with these momentums is $= \dfrac{{Mn}}{{60}}$

Hence, option A is the right answer.

Note: The momentum not only helps in the motion of objects, but it is also responsible for stopping the objects. This can be done by decreasing the velocity of the object and transferring its energy to the object with which it will be colliding. Also the objects that are at rest, they do not have any momentum. They have zero momentum.