Question

A force of $3kgf$ is just sufficient to pull a block of $5kgf$ over a flat surface. Find the coefficient of friction and angle of friction.

Answer 1

Here in this question we have to find the coefficient of friction and the angle of friction. For this we will use the formula of coefficient of friction, $f = \mu N$ and the angle of friction will be calculated by using the formula $\tan \alpha = \mu$ . So by using these formulas we will be able to solve this question.

Formula used
Coefficient of friction,
$f = \mu N$
Here,
$f$ , will be the frictional force
$\mu$ , will be the coefficient of friction
$N$ , will be the normal force
Angle of friction,
$\tan \alpha = \mu$ .

Complete step by step answer
So we have the value of force given as $3kgf$ and in terms of newton it will be equal to $30N$ . Similarly we have the pulling force of $5kgf$ and in terms of newton it will be equal to $50N$ .
Now by using the formula of coefficient of friction, and substituting the values, we will get the equation as
$\Rightarrow 30 = \mu \times 50$
And on solving the above equation, we get
$\Rightarrow \mu = 0.6$
Therefore, the coefficient of friction will be equal to $0.6$
Now we will solve for the angle of friction, and as we know that $\tan \alpha = \mu$
So on substituting the values, we get
$\Rightarrow \tan \alpha = 0.6$
And from here the value of $\alpha = {\tan ^ - }0.6$
And it can be written as $\alpha = {\tan ^ - }\dfrac{3}{5}$ or $\alpha = {30.96^ \circ }$
Therefore, the angle of friction will be equal to $\alpha = {30.96^ \circ }$ .

Note:
Here while solving this question we can see that we had converted the units. As the units are given in terms of $kgf$ and we had converted them to Newton. So we should take care of the units always while solving such types of questions. As we should know $1kgf = 10N$ .