Question

A sledge of mass $25\,kg$ is pulled across level ground with a horizontal force of $60\,N$. The constant force of friction is $20\,N$. Then what is the acceleration of the sledge?
A. $0.63\,m/{s^2}$
B. $1.6\,\,m/{s^2}$
C. $2.4\,m/{s^2}$
D. $3.2\,m/{s^2}$

Answer 1

Hint: In order to find the acceleration, we need to find the net force acting on this sledge. We will get the net force by subtracting the frictional force from the horizontal force. From Newton's second law force is the rate of change of momentum. Using this we can find the acceleration.

Complete step by step answer:
It is given that a sledge has a mass
$m = 25\,kg$
It is being pulled with a horizontal force across a level ground.
${F_h} = 60\,N$
The force due to friction acting on it is given as
${F_r} = 20\,N$
We need to find the acceleration of the sledge.
Let us find the net force acting on the sledge.
The forces acting on the sledge are horizontal force and force due to friction.
Hence net force will be the resultant of these two forces. The force due to friction tries to resist the motion. Hence, we should subtract frictional force from the horizontal force to get the net force.
$ \Rightarrow F = {F_h} - {F_r}$
$ \Rightarrow F = 60 - 20$
$ \Rightarrow F = 40\,N$
This is the net force on the sledge.
We know that according to Newton's second law force is the rate of change of momentum.
$ \Rightarrow F = \dfrac{{dP}}{{dt}}$
$ \Rightarrow F = \dfrac{{d\left( {mv} \right)}}{{dt}}$
$ \Rightarrow F = m\dfrac{{d\left( v \right)}}{{dt}}$
$ \Rightarrow F = ma$
From this acceleration can be found out as
$ \Rightarrow a = \dfrac{F}{m}$
Now let us substitute the value of force and mass of sledge. Then we get
$ \Rightarrow a = \dfrac{{40}}{{25}}$
$ \Rightarrow a = 1.6\,m/{s^2}$
This is the acceleration of the sledge.
So, the correct answer is option B.

Note: Remember that the force due to friction will be always acting in a direction to resist the motion. Hence it will be acting opposite to the direction of the horizontal force which is used to pull the sledge. So, while calculating the net force we should subtract this effect of frictional force from the force applied to move the sledge.