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

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Homework Help Overview

The discussion revolves around determining the tension in a string connecting two blocks of equal mass, where one block is subjected to a constant pulling force. Participants explore the dynamics of the system, including the forces acting on each block and the resulting equations of motion.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of free-body diagrams to analyze the forces acting on each block. There are attempts to derive equations based on the forces involved, with some questioning the setup and assumptions made in their calculations.

Discussion Status

Some participants have provided guidance on how to approach the problem by suggesting the use of separate equations for each block. There is a recognition of the need to clarify the forces acting on the blocks and the relationship between them. Multiple interpretations of the problem are being explored, particularly regarding the application of Newton's second law.

Contextual Notes

Participants express uncertainty about how to represent their diagrams and calculations, indicating a potential barrier to fully articulating their reasoning. There is also mention of a discrepancy between their results and the answer provided in the textbook.

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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?
 
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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.
 
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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
 

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