Question

A block of mass $M=5kg$ is resting on a rough horizontal surface for which the coefficient of friction is $0.2$. When a force $F=40N$ is applied, the acceleration of the block will be $(g=10m/s^2)$

• A. $5.73m/s^2$
• B. $8.0m/s^2$
• C. $10.0m/s^2$
• D. $3.17m/s^2$

Answer 1

The correct option is A $5.73m/s^2$

Formula Used: $a=\frac{F_{net}}{m}$
Given: $M=5kg,F=40N,\mu =0.2$
Force equation along $y$ axis
$R+F\sin {30}^{\circ }=mg$
$R+20=50$
$R=30N$
Kinetic friction $=\mu R=0.2\left(30\right)=6N$
Acceleration of block,
$a=\frac{F\cos {30}^{\circ }-6}{5}=\frac{20\sqrt{3}-6}{5}=5.73m/s^2$