Question

Three identical blocks, each of mass $10kg$, are pulled as shown on the horizontal frictionless surface. If the tension (F) in the rope is $30N$. What is the acceleration of each block? And what are the tensions in the other ropes? (Neglect the masses of the ropes)

Answer 1

The surface is horizontal and frictionless.

All the blocks are moving together, thus the blocks have common acceleration.

Thus,

$F=ma$

$30=(10+10+10)\times a$

$a=1m/s^2-----\left(1\right)$

Force balance for the first block from right:

$F-ma=T_2-----\left(2\right)$

Force balance for middle block:

$T_2=T_1+ma-----\left(3\right)$

Force balance for left most block:

$T_1=ma-----\left(4\right)$

From $\left(1\right)\&\left(4\right)$

$T_1=10\times 1=10N$

From $\left(3\right)\&\left(4\right)$

$T_2=2ma$

$T_2=20N$

Therefore,

The block will accelerate with $1m/s^2$ and the tension in the ropes as represented in the figure will be $T_1=10N$ and $T_2=20N$.