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

Hint: 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 $ .