Question

A $20$ metal block is placed on a horizontal surface.The block just begins to slide when horizontal force of $100$ N is applied to it,Calculate the coefficient of static friction.

Answer 1

At the start the $100N$ force is just enough to overcome static friction so we can write:
$\text{Force}=\text{Static Friction}$

$F=\mu secN$
where ${\mu }_s$ is the coefficient of static friction and $N=$ Normal Reaction that in an horizontal case such this will be equal to the weight of the block, so $N=mg$.

We get:

$F=\mu sec\times mg$

in numbers:

$100=\mu sec\times 9.8\times 20$
$\mu s=100\times 20\times 9.8=0.51$
When the movement starts, kinetic friction kicks in and we have that to have uniform motion we need acceleration equal to zero (constant velocity).

We use Newton Second Law: $F=ma$:
or in our case:
$\text{Force}-\text{Kinetic Friction}=\text{mass}\cdot \text{acceleration}$

or

$F-\mu kN=0$ because acceleration has to be zero

$F-\mu k\times mg=0$

in number

$F-0.4\times 20\times 9.8=0$

$F=78.4N$