Question

An object is kept at x = 0, force on the object is F(constant) from t = 0. Friction coefficient varies as $\mu =cx$. Find the ratio of the maximum value of friction force and magnitude of static friction just after the block stopped.

Answer 1

$x=2y$

When frictional force equal to $F$

$f_1=\mu Mg=cyMg=F$

$y=\frac{F}{cMg}$

Then when block stops then displacement is $2y$

force of friction is

$f_{max}=\mu Mg=2y\left(cMg\right)$

$f_{max}=2F$