Question

The blocks of masses 1 kg and 2 kg are connected by an upstretched spring of constant k = 10 N/m. If the block of mass 1 kg is pulled by a force of 3 N and the block of mass 2 kg is pushed by a force of 6 N. Then find the maximum elongation of the spring.

Answer 1

• We will consider the mass 1 kg, 2 kg and the unstretched spring as a system. Now we see that the net force on the system is 3+6=9 N towards left.
  

Now we can calculate the acceleration of the system,

as $a=\frac{F}{m}$

which comes $\frac{9}{3}$=3 meter per $s^2$

It simply denotes that the block 1 kg, the block 2 kg and the spring are moving with an acceleration of value 3 towards left.

now suppose at any instant the spring has an elongation x, then it will pull its both ends thus exerting a force=kx on the 1kg block in the rightward direction and a force kx on the 2 kg block in the leftward direction. Where k is spring constant of the spring.

Considering the block of 1 kg, it has net leftward force as

(3- kx) = mass$\times$ acceleration

but acceleration is 3 and mass is 1 so the above equation becomes

$3-kx=3$

$orx=0$

means no elongation at all

The similar result can be drawn from the free body diagram of the block of 2kg mass

By Newton's Second Law, the net leftward force on the block of mass 2 kg should be equal to mass multiplied by its acceleration towards left.

so we have,

6 + kx = 2$\times$3

or 6 = kx = 6 which leads to x=0

So the spring will remain unstretched throughout the motion.