# Fisika Study Center

## Strings Tension on Blocks

physics.fisikastudycenter.com - How to find the ratio of strings tensions on a couple of blocks travel at frictionless surface. Given 5 blocks being pulled by a force F = 30 N along x direction. The masses are m1 = 1 kg, m2 = 2 kg, m3 = 3 kg, m4 = 4 kg, m5 = 5 kg. You have to find the ratio of T1 and T2 . See the figure below and the following steps both normally and the short-cut.

Step 1 : Find the acceleration of the system (5 blocks), the force F divided by the sum of all block masses, it's a simple step even you don't need to use your pen to finish this. We have the system acceleration a = 30 : (1 + 2 + 3 + 4 + 5) = 2 m/s2.

Step 2 : Find the tensions T1 and T2, use normal methods.
T1
Σ F = ma
F−T1 = m1a
30− T1 = 1(2)
T1 = 28 N

T2
T1−T2 = m2a
28−T2 = 2(2)
T2 = 24 N

The ratio
T1 : T2 = 28 : 24
T1 : T2 = 7 : 6

Short-cut

All masses pulled by T1 = 2 + 3 + 4 + 5 = 14 kg
All masses pulled by T2 = 3 + 4 + 5 = 12 kg
T1 : T2 = 14 : 12 = 7 : 6

Now, quickly try to find the ratio of :
1) T1 : T3
2) T3 : T4

1) T1 : T3 = 14 : 9
2) T3 : T4 = 14 : 5
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