Question

A horizontal force just sufficient to move a body of mass $4kg$ lying on a rough horizontal surface is applied on it. The coefficient of static and kinetic friction between the body and the surface are $0.8$ and $0.6$, respectively. If the force continues to act even after the block has started moving, the acceleration of the block in $m{{s}^{-2}}$is ( $g=10m{{s}^{-2}}$)
$\begin{aligned} & A.\dfrac{1}{4} \\\ & B.\dfrac{1}{2} \\\ & C.2 \\\ & D.4 \\\ \end{aligned}$

Answer 1

Here the friction is acting on the body. Firstly static friction is in action and after that when the body starts to move, kinetic friction is happening. Find out the maximum static frictional force acting on the body and then the acceleration can be found from that of kinetic friction. These all help us to find out the answer for this question.

Complete step by step answer:

Here the force sufficient to make a movement is given as,
$F=f$
The force balances out the friction.
$F=f$
Therefore the frictional force is given as,
${{f}_{s\max }}={{\mu }_{s}}mg$
Where
${{\mu }_{s}}=0.8$
Substituting this in the equation,
$\begin{aligned} & {{f}_{s\max }}=0.8\times 4\times 10 \\\ & {{f}_{s\max }}=32N \\\ \end{aligned}$
Now, we can write that,
$F-{{f}_{k}}={{\mu }_{k}}mg=ma$
We know that the coefficient of kinetic friction is less than the coefficient of static friction.
$F-{{f}_{k}}=32-\left( 0.6\times 4\times 10 \right)=ma$
Substituting this in equation will give,
$\begin{aligned} & 32-24=4a \\\ & a=\dfrac{8}{4}=2m{{s}^{-2}} \\\ \end{aligned}$
Therefore the correct answer is option C.

Note:
The Force of Static Friction helps to keep a stationary material at rest. Once the Force of Static Friction is crossed and then the force of Kinetic friction is what opposes a moving body. Static friction is greater than kinetic friction since there are more other forces at work in order to keep an object stationary than the forces working to oppose an object once it is in motion. Static friction is a result of adhesion, light chemical attraction between two surfaces. And friction is commonly caused by imperfections or the ridges on the surface making a grip for the body.