Question

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

Answer 1

Step (1) Given:

The initial velocity of the object, $u=5m/s$

The final velocity of the object, $v=8m/s$

Mass of the object, $m=100kg$

Time taken by the object to accelerate, $t=6s$

Step (2) Finding the initial momentum of the object:

We know that momentum, $p=mv$ where $m$ is the mass of the object and $v$ is the velocity of the object.

Initial momentum $=mu=100\times 5$

$\Rightarrow mu=500kgm/s$

Step (3) Finding the final momentum of the object:

Final momentum $=mv=100\times 8$

$\Rightarrow mv=800kgm/s$

Step (4) Finding the force exerted on the object:

Let us calculate the Force exerted on the object (F)

We know that the force applied to an object is equal to the rate of change of its momentum.

$$\begin{gathered} F=\frac{(mv–mu)}{t} \\ F=\frac{(800–500)}{6} \\ F=\frac{300}{6} \\ F=50N \end{gathered}$$

Initial momentum of the object is 500 kg m s^-1.

The final momentum of the object is 800 kg m s^-1.

Force exerted on the object is 50 N