Question

A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is $\mu$. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define $N=10\mu$, then N is

Answer 1

$F_1=mg(\sin \theta -\mu \cos \theta )$

$F_2=mg(\sin \theta +\mu \cos \theta )=3F_1$

$\Rightarrow \mu =\frac{1}{2}\tan \theta$

$\Rightarrow 10\mu =N=5$