Question

A block P of mass m is placed on a horizontal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring constant k, the two blocks are pulled by a distance A. Block Q oscillates without slipping. What is the maximum value of frictional force between the two blocks?
A. $\dfrac{{kA}}{2}$
B. Ak
C. Mgk
D. Zero

Answer 1

Hint: Here, we first know about the basics of frictional force. Further we use the second equation of motion to deduce the formula to find the maximum value of frictional force between the two blocks. This relation gives us the required answer.

Formula used: $F = ma$

Complete step by step answer:
As we know that the Frictional force can be defined as the force generated by two surfaces that come in contact with each other and slide against each other.
Frictional force is F, having mass m and acceleration of its SHM f is given by:
$\eqalign{
  & F = ma \cr
  & F = mf \cr
  & F = m{\omega ^2}A \cr
  & \because \omega = \sqrt {\dfrac{k}{{m + m}}} = \sqrt {\dfrac{k}{{2m}}} \cr
  & \Rightarrow F = m\dfrac{k}{{2m}}A \cr
  & \therefore F = \dfrac{k}{2}A \cr} $

So, the correct answer is “Option A”.

Additional Information: Force experienced by a particle or an object can be defined as the product of mass m and the acceleration a. The SI unit of force is Newton and it is represented as N. the mass of an object is defined as both a property of a physical body and also a measure of its resistance to acceleration or a change in its state of motion, when a net force is applied.
Also it can be said that an object's mass also tells about the strength of its gravitational attraction to other bodies. The SI unit of mass is kilogram or it can be represented as kg.
Pressure applied on an object is defined as the force exerted on the object per unit area.

Note: Here, we should also know that there are three equations of motion and from second equation motion we get the relation between force F, mass m and acceleration a. Also, we can get the relation between force and momentum from this equation of motion.