Considering the situation presented in the figure where
a woman is pushing three blocks at the same time, what makes each of the
blocks move? For simplicity, let us assume that there is not friction
between the blocks and the floor.

The woman applies a total force F_{Ex}
to the three blocks. As a consequence of this force, the three blocks
accelerate in the horizontal direction with the acceleration

The previous equation is obtained by applying the FBD technique to a
single block of mass
.

What is accelerating the block of mass m_{3}?
This block is pushed by the block of mass m_{2} with the
force F_{32}; which, in this kind of problems, is called
the contact force
.
Since the acceleration of this block is known, the magnitude of the
force can be calculated,

From the previous results, the
magnitude of the force applied by the block of mass m_{1}
over the block m_{2} can be calculated. Thus, over the
mass m_{2} there are two forces acting on the horizontal
direction, F_{23} which is the reaction force to F_{32},
the push of block 2 on block 3, and the push of the block of mass m_{1}
on the mass m_{2}
.
The net force acting on the block of mass m_{2} is

The acceleration of this block is also the same acceleration as the
acceleration of the other blocks,

Equating the last two relations, an equation for F_{21}is obtained,

Thus,

The same analysis can be made for the block of mass
m_{1}.
In this case, the forces acting on the block are the external force and
the force exerted by the second block on the first block. This last
force is the reaction to the push of the block of mass m_{1}
on the block of mass m_{2}. The net force acting on the
mass m_{1} is

Newton's second law applied to the first block is

.

Thus,

The previous relation is the same equation as
Newton's second law applied to the three blocks when considered as a
single mass.