What Is the Tension in the String Connecting Two Blocks of Equal Mass?

[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?

 

[stevendaryl]

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.

 

[astrophysics12]

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

 

[stevendaryl]

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]

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