Question

A force of 12 N acts on a block P and block Q of masses of 2kg and 4kg respectively as shown. Given that the floor is smooth, find the force acting on the string between the blocks P and Q.

Answer 1

Hint: In this question we have to apply the concept of the second law of motion given by Newton. We have to apply the concept of force being equal to the product of mass and acceleration of a body, with this we can calculate the tension between the two blocks acting on the string.

Complete step by step answer:
The second law of motion states that when a force is applied in a body it provides some acceleration to the body in the direction of the force. The mathematical representation of the above law is given as:
$F = ma$, Where F is the force acting on a body m is the mass of the body and a is the acceleration produced in the body.
This is equally true for a system of bodies. If we consider the two blocks given in the question to be a system, we can consider the mass of the complete system and calculate the acceleration produced in the whole system due to the force applied.
Therefore, the acceleration of the system will be calculated as:
$
F = {m_{net}}a\\
\implies a = \dfrac{F}{{{m_{net}}}}\\
\implies a = \dfrac{{12}}{{(4 + 2)}}\\
\implies a = 2\,m{s^{ - 2}}
$
When we considered the two blocks as a system, we calculated the net mass of the system by adding the mass of the two blocks and after applying the second law of motion we have calculated the acceleration produced in the system. Since the two blocks are connected by a string the acceleration of the whole system will be equal to the acceleration of the individual blocks.
Now we can calculate the force acting on the string between the two blocks. Since the block Q is only connected to block P via string and no other forces acting on Q, we can say that the force acting on Q is equal to the force being exerted on the string. Therefore, we calculate the force acting on the body Q, it will be equal to the force acting on the string.
The force acting on the body Q will be calculated by using the same formula which we used above.
This time we will put only the mass of the body Q in the formula:
$
F = {m_Q} \times a\\
\implies F = 4 \times 2\\
\implies F = 8N
$.

As the force acting on the body Q is only by the string, the force acting on the string is equal to 8N.

Note:
These kinds of problems can also be solved by using the free body diagrams. Making a free body diagram helps us to understand the number of forces and the direction of the forces acting on a body. Since this was a fairly simple question, the free body diagram was not necessary, but for a more complicated setup, the free body diagrams help a lot.