# A force of 3kgf is just sufficient to pull a block of 5kgf .Find the coefficient of friction and angle of Friction?

${\mu}_{s} = 0.6$
Yes, the value of $\phi$ is wrong.
$\phi$ is tan^-1(0.6)= 30.96376
->31 degrees approx

#### Explanation:

Coefficient of friction ${\mu}_{s}$is the ratio of friction force to the normal thrust.
Here, the pulling force need to be little more than the friction force beneath the block.
The limiting static friction shall be 3 kgf.
The normal thrust is due to the weight of the block itself.
The normal reaction shall be 5 kgf.
Thus, coefficient of friction ${\mu}_{s} = \frac{3}{5} = 0.6$
Angle of friction $\phi$and the coefficient of friction ${\mu}_{s}$ are related by the expression ${\mu}_{s} = \tan \phi$
Then,
$0.6 = \tan \phi$
$\phi = {\tan}^{-} 1 0.6 = {36.}^{0} 870$

${\mu}_{s} = 0.6$
$\phi = {36.}^{0} 870$