# A 20kg  metal block is place on a horizontal surface. The block just begins to slide when horizontal force of 100 N is applied to it. 1) Calculate the coefficient of static friction. 2) If coefficient of kinetic friction is 0.4 then find.......?

## A $20 k g$ metal block is place on a horizontal surface. The block just begins to slide when horizontal force of $100 N$ is applied to it. 1) Calculate the coefficient of static friction. 2) If coefficient of kinetic friction is $0.4$ then find minimum force to maintain its uniform motion?

Apr 8, 2017

I got:
${\mu}_{s} = 0.51$
$F = 78.4 N$

#### Explanation:

At the start the $100 N$ force is just enough to overcome static friction so we can write:
$\text{Force"="Static Friction}$
$F = {\mu}_{s} N$
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 $N = m g$.

We get:

$F = {\mu}_{s} \cdot m g$
in numbers:
$100 = {\mu}_{s} \cdot 20 \cdot 9.8$
${\mu}_{s} = \frac{100}{20 \cdot 9.8} = 0.51$

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's Second Law: $\Sigma \vec{F} = m \vec{a}$
or in our case:
$\text{Force"-"Kinetic Friction"="mass"*"acceleration}$

or

$F - {\mu}_{k} N = 0$ because acceleration has to be zero.
$F - {\mu}_{k} \cdot m g = 0$

in numbers:
$F - 0.4 \cdot 20 \cdot 9.8 = 0$
$F = 78.4 N$