Question

A time varying horizontal force (in Newton) $F=8|\sin \left(4\pi t\right)|$ is acting on a stationary block of mass $2kg$ as shown. Friction coefficient between the block and ground is $\mu =0.5$ and $g=10m/s^2$. Then resulting motion of the block will be:

• A. It will oscillate
• B. It remains stationary
• C. It moves towards left
• D. It moves towards right

Answer 1

Answer: (B)

It remains stationary

Given,
Applied variable horizontal force $F=8|\sin \left(4\pi t\right)|N$
Mass of block $\left(m\right)=2kg$
Friction coefficient between block and ground $\mu =0.5$
and $g=10m/s^2$
We know that,
maximum possible friction force, $F_{frictionmax}=\mu mg$
$=0.5\times 2\times 10$
$=10N....\left(i\right)$
Maximum applied force $\left(F_{appliedmax}\right)=8\times 1$
$=8N....\left(ii\right)$
$[\because$ maximum value of $\sin \theta$ is $1$]
From equation (i) and (ii), we get
$f_{frictionmax}>f_{appliedmax}$
So, the block will remain stationary.