# String Tension

1. Sep 14, 2007

### Jwill

1. The problem statement, all variables and given/known data
Two forces acting on two blocks A and B are connected with a string between them. Force FA = (16 N) acts on block A, with mass 5.2 kg. Force FB = (24 N) i acts on block B, with mass 6.0 kg. What is the tension in the string?

2. Relevant equations
F = ma

3. The attempt at a solution
At first I thought maybe the answer is the product of the difference between the accelerations and forces but I don't think that's right.

2. Sep 14, 2007

### learningphysics

First calculate the acceleration of the system... then you can find the tension... Use freebody diagrams.

3. Sep 14, 2007

### Jwill

I understand that I need to find acceleration but I don't understand what to do about the acceleration of blocks being different. I come up with 3.0769m/s^2 for A and 4m/s^2 for B. How do I use this to find the tension?

4. Sep 14, 2007

### learningphysics

That's not right... because the net force acting on A and B aren't just those forces given...

Are the 16N and 24N in opposite directions or the same direction?

Take the system as a whole(A and B and the string)... what is the net force acting on this system... what is the acceleration of this system....

5. Sep 14, 2007

### Jwill

They are acting in the same direction. So would that mean 24N - 16N = 8N as the net force? And the 8N force is acting on the 11.2kg blocks for an acceleration of 0.7142857 m/2^2?

6. Sep 14, 2007

### learningphysics

Why did you subtract instead of add (since the two forces are in the same direction)? What is the mass of the entire system?

7. Sep 14, 2007

### Jwill

I guess there's no reason to subtract... the sum would be 40 and the mass of the system is 11.2kg... so that'd make the acceleration 3.57m/s^2.

8. Sep 14, 2007

### learningphysics

Yeah, that's exactly right. Now you can examine the freebody diagram of either mass A alone or mass B alone to get the tension... use the knowledge that acceleration is 3.57m/s^2.

9. Sep 14, 2007

### Jwill

It would be the one lagging behind right? The thing that kind of confuses me is the outcome is 18.564N and I'm supprised that even though they're both moving in the same direction with forces how there is still so much tension between the two blocks. Thank you for your help by the way.

10. Sep 14, 2007

### learningphysics

can you show how you got 18.564N? I'm not getting that.

11. Sep 14, 2007

### learningphysics

Your intuition is correct I believe. I get a much smaller tension... you can use either mass to find the tension.

Last edited: Sep 14, 2007
12. Sep 14, 2007

### Jwill

I used f=ma ... 5.6 * 3.57m/s^2 = 18.564N. Is that not the correct formula for tension? or did i apply it incorrectly?

13. Sep 14, 2007

You need to take into acount that Tension is not the only force acting on each of these blocks.

Draw a freebody of Block A. What Forces are acting on it? Then Calculate Tension.

Draw a freebody of Block B. What Forces are acting on it? Caculate Tension again.

Is it the same? Hint: it should be.

Casey

14. Sep 14, 2007

### Jwill

Still have no idea what to do... shouldn't be that hard of a problem.. just missing something

15. Sep 14, 2007

### learningphysics

Let's use mass A... what are the forces acting on mass A?

16. Sep 14, 2007

### Jwill

16Ni and gravity i guess

17. Sep 14, 2007

### learningphysics

You also have tension.

18. Sep 14, 2007

### Jwill

And that would add to 16N force right?

19. Sep 14, 2007

### learningphysics

yes.

20. Sep 14, 2007

### Jwill

So that makes me think 16N + T = 3.57(5.2) which isn't right i don't think is it?

Well that would make the force from tension on A be -2.58 and B 2.564

Last edited: Sep 14, 2007