Question

A body of mass $60kg$ is dragged with just enough force to start moving on a rough surface with coefficients of static and kinetic frictions $0.5$ and $0.4$ respectively. On applying the same force, what is the acceleration?

• A. $0.98m{s}^{-2}$
• B. $9.8m{s}^{-2}$
• C. $0.54m{s}^{-2}$
• D. $5.292m{s}^{-2}$

Answer 1

The correct option is A

$0.98m{s}^{-2}$

Step 1. Given data

Mass of the body, $m=60kg$

Coefficient of kinetic friction, ${\mu }_k=0.4$

Coefficient of static friction, ${\mu }_s=0.5$

Step 2. Finding the acceleration, $a$

For the motion of the body, the applied force should be equal to or greater than the static friction. According to the question, the static force is equal to the applied force.

We equate the difference in the frictional force by the force of the object without friction.

Net force acting on the body,

$F=F_s-F_k$ [Where, $F_s$ is static frictional force, $F_k$ is kinetic frictional force]

$F={\mu }_{s}R-{\mu }_{k}R$ [Where, $R=mg$ is reaction]

$ma=\left({\mu }_s-{\mu }_k\right)mg$ [Where, $F=ma$]

$a=\left({\mu }_s-{\mu }_k\right)g$

$a=\left(0.5-0.4\right)\times 9.8$ [Where, $g=9.8m{s}^{-2}$]

$a=0.98m{s}^{-2}$

Hence, the correct option is $\left(A\right)$.