## Strings Tension on Blocks

- Category: Shortcuts
- Written by fisikastudycenter

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 m_{1} = 1 kg, m_{2} = 2 kg, m_{3} = 3 kg, m_{4} = 4 kg, m_{5} = 5 kg. You have to find the ratio of T_{1} and T_{2} . 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/s^{2}.

**Step 2** : Find the tensions T_{1} and T_{2}, use normal methods.

**T _{1}**

Σ F = ma

F−T

_{1}= m

_{1}a

30− T

_{1}= 1(2)

T

_{1}= 28 N

**T**

_{2}T

_{1}−T

_{2}= m

_{2}a

28−T2 = 2(2)

T2 = 24 N

The ratio

T

_{1}: T

_{2}= 28 : 24

T

_{1}: T

_{2}= 7 : 6

**Short-cut**

Now, quickly try to find the ratio of :

1) T_{1} : T_{3}

2) T_{3} : T_{4}