Calculating Tension in a 3kg Block at 10cm from Left Side - 12N Force on Right

[PhysicsKid703]

Homework Statement

What is the tension in a 3kg block at a point 10cm from its left side, when pulled by a string from its right side with a force of 12N

The block is 30cm.

Homework Equations

The Attempt at a Solution

So it's pretty obvious the acceleration of the block is 4 ms^-2
Now, how do I find tension? And will the 10cm part affect it anyhow? I know that if there was another block, then we could find net force of each individual block and thereby calculate the tension in the strings connecting the blocks, but since there's only one block, how would I get the tension? It's rather the concept I want to understand, and the answer in the book is 24N

 

[HallsofIvy]

Imagine the block being cut into two blocks at the point 10 cm from its left side and the two blocks connected by a short string.

 

[PhysicsKid703]

Thank you so very much. That's exactly what I needed. This is a great forum :)
One more conceptual thing. What would be the tension in the string, not in the block? Can it even be calculated without knowing how much of a reaction force the block can give? Also, what would be the tension of the extreme leftmost side of the block?

 

[Doc Al]

What would be the tension in the string, not in the block? Can it even be calculated without knowing how much of a reaction force the block can give?

You are told that the string is pulling with 12 N of force. So what must be its tension?

Also, what would be the tension of the extreme leftmost side of the block?

What do you think? Imagine a very thin slice of the block on the leftmost side. How much force is needed to pull it along?

 

[PhysicsKid703]

Tension in the string is 12N. Tell me if I'm wrong.
I'm not understanding the tension of the leftmost side, could you please explain? Thanks though, you guys are really very helpful.

 

[Doc Al]

Tension in the string is 12N. Tell me if I'm wrong.

I'll even tell if you're right. You're right!

I'm not understanding the tension of the leftmost side, could you please explain?

Use the same logic you used when considering the tension pulling the 10 cm chunk. Just imagine now that you take leftmost chunks to be 5 cm from the end, then 1 cm, then just a tiny sliver. What happens to the force pulling the chunks as the chunks get smaller?

 

[PhysicsKid703]

Ahh thank you so much sir. You've been a great help. It's zero. I've understood the concept.

 

[Doc Al]

Ahh thank you so much sir. You've been a great help. It's zero. I've understood the concept.

Excellent. The tension in the block varies from the full 12 N at the leading end to zero at the trailing end.