Question

A single horizontal force F is applied to a block of mass M1 which is in contact with another block of mass M2. If the surfaces are frictionless, the force between the blocks is?

Ans M2F/M1+M2 but how?

Answer 1

Let “C” be the force between the two blocks. So m1 applies a force “C” on m2 and m2 inturn applies the same force “C” on m1 but in the opposite direction. Now consider the figure below:



F.B.D : Free Body Diagram. These diagrams represent the forces acting on the body.

N=W for both cases. No movement in the vertical.

Horizontal Motion:

As the question says the entire system undergoes an acceleration of “a”. So this means the acceleration of both m1 and m2 are the same.

So if we consider them as a combined mass then :

F = (m1+m2).a

a = F/(m1+m2) ………………Eqn 1

Now let us write down the force equations for both blocks.

Block m1:

F - C = m1.a ……………Eqn2

Block m2:

C = m2.a …………….Eqn3

We want to find “C”.

You can use Eqn 2 or Eqn 3 and substitute for “a” using Eqn 1.

Let us take Eqn 3 since it is simple.

C = m2.a = m2.(F/(m1+m2))

It can be more conveniently written as