# To find tenstion in the string

• astrophysics12
In summary, when two blocks of equal mass m are tied together with a light string and one block is pulled with a constant force F, the tension in the string joining the blocks is equal to half of the force applied, or T=F/2. This can be determined by creating a free-body diagram for each block and applying the equation F=ma to each separately.
astrophysics12

## Homework Statement

Two blocks of equal mass m are tied to each other through a light string. One of the blocks is pulled along the line joining them with a constant force F. Find the tension in the string joining the blocks.

## Homework Equations

I tried doing this by this method.
(I don't know how to draw free body diagram here. It is just two bodies connected by string)
I got
F+T=ma
F-T=2ma

Hence, F=3ma/2
I got T=F/3
But the answer given at the back is F/2

Can someone help me with this?
Where am I going wrong?

astrophysics12 said:

## Homework Statement

Two blocks of equal mass m are tied to each other through a light string. One of the blocks is pulled along the line joining them with a constant force F. Find the tension in the string joining the blocks.

## Homework Equations

I tried doing this by this method.
(I don't know how to draw free body diagram here. It is just two bodies connected by string)
I got
F+T=ma
F-T=2ma

Hence, F=3ma/2
I got T=F/3
But the answer given at the back is F/2

Can someone help me with this?
Where am I going wrong?

You really need to draw a free-body diagram. You have the "front" block that has a force $F$ pulling it in one direction and a force $T$ pulling it in the opposite direction. You have the "rear" block that only has a force $T$ pulling it. The accelerations are the same. So just apply $F_{total} = m a$ for each block separately.

stevendaryl said:
You really need to draw a free-body diagram. You have the "front" block that has a force $F$ pulling it in one direction and a force $T$ pulling it in the opposite direction. You have the "rear" block that only has a force $T$ pulling it. The accelerations are the same. So just apply $F_{total} = m a$ for each block separately.
I did draw a free body diagram. I don't know how to draw it here. Is there some way where I can upload it?
I will do it again.
Thanks

astrophysics12 said:
I did draw a free body diagram. I don't know how to draw it here. Is there some way where I can upload it?
I will do it again.
Thanks

No, that's okay. Just write down "F = ma" for each block. Remember that the front block has two forces acting on it--whatever is pulling the blocks (force "F") and the tension ("T", acting in the opposite direction) The second block only has "T" acting on it. So write down your two F=ma equations and post them.

astrophysics12
stevendaryl said:
No, that's okay. Just write down "F = ma" for each block. Remember that the front block has two forces acting on it--whatever is pulling the blocks (force "F") and the tension ("T", acting in the opposite direction) The second block only has "T" acting on it. So write down your two F=ma equations and post them.
I got it.
Thank you.
I made the mistake of including F even for the second blockSystem: Second Block(behind)
T=ma
System: First Block(Front)
F-T=ma
F=ma+T
F=2ma
F/2=ma
Hence, T=F/2

Thanks, again

## 1. What is tension in a string?

Tension in a string is a force that is exerted on the string, pulling it tight. It is caused by the weight of an object that is attached to the string or by forces acting on either end of the string.

## 2. How is tension measured?

Tension can be measured in units of force, such as Newtons or pounds. It can also be measured using a tension meter, which uses a spring or weight to determine the force being exerted on the string.

## 3. What factors affect tension in a string?

The tension in a string can be affected by several factors, including the weight of the object attached to the string, the length and thickness of the string, and the force applied to the ends of the string.

## 4. Why is it important to know the tension in a string?

Knowing the tension in a string is important for various reasons. It can help in determining the strength and stability of structures that use strings, such as bridges or musical instruments. It is also important in industries such as construction, where the tension in cables and ropes is crucial for safety and efficiency.

## 5. How can tension in a string be calculated?

Tension in a string can be calculated using the formula T = F * L, where T is tension, F is the force applied to the string, and L is the length of the string. The force can be calculated using the weight of the object attached to the string and the acceleration due to gravity.

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