A body of mass 2kg is placed on another body of mass 4kg which is on top of a table. coefficient of friction between the body 2kg and 4kg is 0.2 and that of bod

Question

A body of mass 2kg is placed on another body of mass 4kg which is on top of a table. coefficient of friction between the body 2kg and 4kg is 0.2 and that of body 4kg and  surface of table  is 0.1 Find the Magnitude of friction force on 4kg body and also its acceleration if any? 

Answer 1

When you have frictional force acting on an object, you have an upward force that is perpendicular to the surface that the object is in contact with.  This force that limits the motion of the object is called the normal force.  The normal force is equal to that of weight because those two forces keep the object in equilibrium.  We denote the friction force as 

 

F_f = μN 

 

where:

F_f = friction force

μ = coefficient of friction

N = normal force = mass times acceleration due to gravity.

 

Before we can find friction force on the 4kg block, we need to find the normal force first.

 

N = (2kg + 4kg)*(9.81 m/s²)

N = 58.86 kg m/s²

 

Since the coefficient of friction between the table and 4kg block is less than the coefficient of friction between the 4kg block and 2kg block, we add the coefficients because the 2kg block seems to be attached to the 4kg block. 

 

F_f = N(μ_2kg + μ_4kg)

F_f = (58.86 kg m/s²)(0.3)

F_f = 17.66 kg m/s²