Question

Suppose a block of mass 1 kg is placed over a rough surface and a horizontal force F is applied on the block as shown in figure. Now, let us see what are the values of force of friction f and acceleration of the block a if the force F is gradually increased. Given that ${\mu }_s=0.5,{\mu }_k=0.4$ and (g= $10m/s^2$).

Answer 1

From the graph it is clear that the maximum frictional force we can get is maximum static friction
$f_s={\mu }_{s}N$

$f_s=0.5\times 1\times 10$

$f_s=5N$

After this if we increase the force the block will start moving and there is a constant frictional force will act on the block that force is call kinetic frictional force and the value of kinetic frictional force is
$f_k={\mu }_{k}N$

$f_s=0.4\times 1\times 10$

$f_s=4N$

now the acceleration the block will be
$a=\frac{F-{\mu }_{k}N}{M}$

$⟹a=\frac{F-4}{1}$

$acceleration\left(a\right)=F-4$