Question

A wooden box of mass $20kg$ is kept on a rough horizontal surface. The co-efficient of static friction ${\mu }_s=0.41$ and co-efficient of kinetic friction ${\mu }_k=0.3$ exist between the box and the horizontal surface. A constant force $F$ of $70N$ is applied to the box at an angle of ${30}^o$ with the horizontal. Find the acceleration of the box on the surface and the frictional force on the box. Take $g=10m/s^2$.

Answer 1

On resolving the force $F$ along horizontal and vertical direction,

We get,

$N+35-200=0$

$f_{max}={\mu }_s\times N=0.41\times 165=67.75$

For atleast a motion,

The horizontal force is supposed to overcome the static friction,

But,

$F\cos {30}^0=60.62,f_{max}=67.75$

Hence the body won't come into Motion,

$a=0m/s^2$

And $f=F\cos {30}^0=60.72N$