# Tension in string with rollers

1. Oct 15, 2008

### stringtension

I have read at many places that tension in the string remains same throught the string.

I have a string which is held tight at two ends. It is passing around different rollers. Now, I have small weight hanging on the string at one place. Does this mean that I have same tension throught the string in the amount equivalent to the weight?

I have drawn a free body diagram and attached it here.

Thanks everyone,

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• ###### string tension.JPG
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2. Oct 15, 2008

### stewartcs

Provided that the string is massless, then yes, the tension is the same throughout.

CS

3. Oct 15, 2008

### stringtension

And that will be equivalent to the mass hanging. ( T = mg ) Am I right?

4. Oct 15, 2008

### stewartcs

Yes.

CS

5. Oct 15, 2008

### stringtension

Thanks,

Now, instead of string held at both places, if I have some acceleration on one side, does that change the tension in the string?

I have attached a new picture which shows the acceleration. The mass will be lifted because of the string motion. I am not sure whether this will change the tension.

#### Attached Files:

• ###### string tension 2.jpg
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6. Oct 15, 2008

### stewartcs

As long as the string is massless, the acceleration will not matter. The tension is still constant.

BTW I can't see your pictures since they have not been approved yet.

CS

Last edited: Oct 15, 2008
7. Oct 15, 2008

### stewartcs

Also I'm assuming the pulleys are ideal.

CS

8. Oct 15, 2008

### stringtension

Yes. Pulleys are ideal.

String held tight at one end all the time. On the other end, there is a block attached. In the beginning, block is steady. So, only tension in the string is because of the weight hanging there in the middle of the string.

Now, we are moving the block. This will lift the weight. So, you are saying that movement of the block will not add any tension in the string.

It will be much easier once you see the picture.

Thanks,

9. Oct 15, 2008

### stewartcs

What I've said so far is that the tension will be constant throughout the string assuming an ideal pulley and a massless string. The magnitude of the tension, however, will depend on the acceleration.

Once I can see your picture I may be able to reply more directly to your case. In the mean time, perhaps this site will help:

http://hyperphysics.phy-astr.gsu.edu/Hbase/atwd.html#c1

CS

10. Oct 16, 2008

### stringtension

I got to make sure here is that tension in the spring does not go beyond equal to 200 gms at any point.
I believe I already have a tension of 125 gms.
Direction of the tension of acceleration is different than tension because of weight. Does that make dieerence or should I just add the two tensions together.
Any help will be apreciated,

11. Oct 17, 2008

### stewartcs

It seems reasonable that if you accelerate the string (and thus lift the weight), you'll be accelerating the weight which will cause its apparent weight to increase, thus increasing the tension in the string. The weight and thus tension increase will be negligible for a 0.02 m/s^2 acceleration.

Hope this helps.

CS