Q.270. Acceleration of two blocks connected by a spring to which a force is applied.

Question 270.
Two blocks (one having mass m and the other having mass M) are connected by a massless spring and placed on a smooth horizontal surface.
(Please draw the figure such that the block with mass m is on the left of the spring to which it is attached and the one with mass M is on the right).
A force F acts on the block with mass M towards right.The blocks are initially at rest and the spring is unstressed.
Find the acceleration of centre of mass of the system at the instant of maximum elongation of the spring.

Answer 270.
At the maximum elongation of the spring, the mass m, M and the center of mass will all have the same acceleration.

Let T = tension in the spring
and a = common acceleration of the masses and the center of mass

Net force on mass M = F - T
=> F - T = Ma ... (1)

Net force on mass m = T
=> T = ma ... (2)

Adding (1) and (2),
F = (M + m)a
=> acceleration of the center of masses,
a = F / (M + m).

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