Calculating Tension in Connecting String of Two Blocks

[Jwill]

Homework Statement

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?

Homework Equations

F = ma

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.

 

[learningphysics]

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

 

[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?

 

[learningphysics]

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?

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...

 

[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?

 

[learningphysics]

They are acting in the same direction. So would that mean 24N - 16N = 8N as the net force?

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

 

[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.

 

[learningphysics]

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.

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.

 

[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.

 

[learningphysics]

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.

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

 

[learningphysics]

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.

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

 

[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?

 

[Saladsamurai]

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?

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

 

[Jwill]

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

 

[learningphysics]

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

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

 

[Jwill]

16Ni and gravity i guess

 

[learningphysics]

16Ni and gravity i guess

You also have tension.

 

[Jwill]

And that would add to 16N force right?

 

[learningphysics]

And that would add to 16N force right?

yes.

 

[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

 

[learningphysics]

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

Yes, that's right... you picked the right direction for tension since it comes out positive... T = 2.564... where are you getting -2.58? Is that for mass B?

EDIT: The numbers are slightly off because we rounded a to 3.57m/s^2... if we use the exact number, the tension will come out the same for both A and B

Remember the tension on B is in the opposite direction as the tension on A.

 

[Jwill]

Yes A is the lagging mass... for A i used T = 3.57(5.2) - 16

 

[learningphysics]

Yes A is the lagging mass... for A i used T = 3.57(5.2) - 16

So the tension acts in the forward direction for A, and the backwards direction for B (which makes sense because the tensions in a rope are in opposite directions at the opposite ends...)

 

[Jwill]

So would that make the tension on the rope be 5.144N by adding the magnitudes?

 

[learningphysics]

So would that make the tension on the rope be 5.144N by adding the magnitudes?

No... the tension just refers to the 2.564N...

 

[learningphysics]

So would that make the tension on the rope be 5.144N by adding the magnitudes?

The tension acting on A and B are the same magnitude(opposite directions)... it's just not coming out exactly the same because we rounded acceleration to 3.57m/s^2... if we kept the exact number... the tensions would come out the same.

 

[Jwill]

Why does T = 3.57(5.2) - 16 for A
and T = 3.57(6) - 24 for B
produce different results?

 

[Jwill]

Nevermind, it was because 3.57 is rounded... thank you very much... you've helped me better understand tension

 

[learningphysics]

Why does T = 3.57(5.2) - 16 for A
and T = 3.57(6) - 24 for B
produce different results?

If you draw tension in one direction acting on A... you should draw it in the opposite direction acting on B...

T = 3.57(5.2) - 16

T = 24 - 3.57(6)

If we used the exact a instead of 3.57... the two calculations would come out exactly the same...

 

[learningphysics]

Nevermind, it was because 3.57 is rounded... thank you very much... you've helped me better understand tension

cool. no prob.