Question

A $20\,kg$ block is initially at rest on a rough horizontal surface. A horizontal force of $75\,N$ is required to set the block in motion. After it is in motion, a horizontal force of $60\,N$ is required to keep the block moving with constant speed. The coefficient of static friction is
(A) $0.60$
(B) $0.44$
(C) $0.52$
(D) $0.38$

Answer 1

Hint Since the question is asking about the coefficient of static friction, you need to consider the force which is required to change the state of the block from rest to motion. Maximum static friction is nothing but the maximum amount of friction that can act on a body while it is in rest. Hence, to change a body’s state from rest to motion, you need to apply at least the amount of force equal to the maximum static friction.

Complete step by step answer
As explained in the hint section of the solution to the asked question, we need to consider the force which is needed to set the block in motion since the question is only asking us about the coefficient of static friction. The coefficient of static friction is the deciding factor in the maximum amount of friction that can be applied on an object or body which is currently at rest and if someone wants to set the object or the body in motion, they have to apply the amount of force which is at least equal to or more than the maximum static friction that can be applied on the object.
Let us have a look at the relevant information given in the question:
Mass of the block, $m = 20\,kg$
Horizontal force required to set the block in motion, ${f_h} = 75\,N$
Now, since there is no motion in vertical direction, we can safely say that the normal reaction force balances the weight of the block, hence:
$
  N = W \\
  N = mg \\
  N = 20 \times 10 = 200\,N \\
 $
Friction is given as:
${f_s} = {\mu _s}N$
Since the force needed to set the block in motion is given, we can write:
${f_s} = {f_h}$
Substituting their values, we get:
$
  {\mu _s}\left( {200} \right) = 75 \\
   \Rightarrow {\mu _s} = 0.375 \\
   \Rightarrow {\mu _s} \approx 0.38 \\
 $

As we can see, this matches with the value given in the option (D). Hence, the correct answer is option (D).

Note The main confusion can be the deduction about which of the two given forces we need to use so as to find the value of coefficient of static friction. As we explained that to find the value of coefficient of static friction, we need to consider only the force which needs to set the block in motion from rest.