Question

An object of mass $100\,kg$ is accelerated uniformly from a velocity of $5\,m{s^{ - 1}}$ to $8\,m{s^{ - 1}}$ in $6\,s$ . Calculate the initial and the final momentum of the object. Also, find the magnitude of the force exerted on the object.

Answer 1

Hint
In order to calculate the value of the initial and the final momentum of the object, substitute the required values of mass and velocity in the below given formulae. Use these answers in the formula of force and also substitute the time taken to know the magnitude of the force.
(1) The momentum of the object is given by
Initial momentum= $mu$
Where $m$ is the mass of the object and $u$ is the initial velocity of the object.
(2) Final momentum= $mv$
Where $m$ is the mass of the object and $v$ is the initial velocity of the object.
(3) The magnitude of the force is given by
$\Rightarrow F = \dfrac{{{\text{Final momentum - initial momentum}}}}{t}$
Where $t$ is the time taken for the movement and $F$ is the magnitude of the force exerted.

Complete step by step answer
The given data are
Mass of the object, $m = 100\,Kg$
Initial velocity of the object, $u = 5\,m{s^{ - 1}}$
Final velocity of the object, $v = 8\,m{s^{ - 1}}$
Time taken, $t = 6\,s$
By using the formula of initial momentum,
Initial momentum= $mu$
Substituting the values,
Initial momentum= $100 \times 5$
By doing the multiplication,
Initial momentum= $500\,Kgm{s^{ - 1}}$.
Similarly the final momentum is calculated by the formula.
Final momentum= $100 \times 8$
Hence the final momentum of the object is $800\,Kgm{s^{ - 1}}$.
In order to calculate the magnitude of the force, substitute the value of the initial momentum, final momentum and the time taken in its formula.
$\Rightarrow F = \dfrac{{{\text{800 - 500}}}}{6}$
$\Rightarrow F = \dfrac{{300}}{6}$
By performing division in the above step,
$\Rightarrow F = 50\,N$.

Hence the initial and the final momentum are $500\,Ns$ and $800\,Ns$ respectively. The magnitude of the force exerted by the object taken is $50\,N$

Note
The momentum at the initial and the final condition differs, since the velocity of the object in those conditions changes. When the object begins to move, there is some force required to overcome the frictional force and to pick up the normal force, so the velocity at the starting is always less.