Three identical blocks , each of mass 10 kg , if the tension in the rope is 30N . what is the acceleration of each block ? and what are the tensions in the ropes ? ( neglect the masses of the ropes )
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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)×a
a=1 m/s
2
−−−−− (1)
Force balance for the first block from right:
F−ma=T
2
−−−−− (2)
Force balance for middle block:
T
2
=T
1
+ma −−−−− (3)
Force balance for left most block:
T
1
=ma −−−−− (4)
From (1) & (4)
T
1
=10×1=10 N
From (3) & (4)
T
2
=2ma
T
2
=20 N
Therefore,
The block will accelerate with 1m/s
2
and the tension in the ropes as represented in the figure will be T
1
=10 N and T
2
=20 N
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