Tension in Cord: Same or Different?

[peripatein]

Hi,
Will the tension in the cord attaching all masses (see diagram) be the same (one tension T for the entire system) or will there be different tensions? It is stated that the cord has no mass and the masses are all the same. Furthermore, may I consider the 3 masses lying on the horizontal surface as one mass of 3m?

 

[Doc Al]

Hi,
Will the tension in the cord attaching all masses (see diagram) be the same (one tension T for the entire system) or will there be different tensions?

What do you think? Since the masses are connect by the cord, what must be the same for each?

It is stated that the cord has no mass and the masses are all the same. Furthermore, may I consider the 3 masses lying on the horizontal surface as one mass of 3m?

Depending up what you are trying to find, you can treat any grouping of the masses as a single system. For some purposes you may want to consider the three masses as a single mass of 3m; for other purposes you may want to consider each mass separately. Up to you and what you need to solve for.

 

[haruspex]

Will the tension in the cord attaching all masses (see diagram) be the same (one tension T for the entire system) or will there be different tensions?

Do the free body diagram for each mass. Look at the one for the mass on the table nearest the pulley. What does that tell you about the tensions?

may I consider the 3 masses lying on the horizontal surface as one mass of 3m?

It depends what you do with it. For some equations it would be valid.

 

[peripatein]

I think the tension would be similar throughout the cord as it is a massless cord and one and the same. Am I wrong?

 

[Doc Al]

I think the tension would be similar throughout the cord as it is a massless cord and one and the same. Am I wrong?

Yes, you are wrong. If the cord were not broken up by those masses and was one continuous piece, then you'd be correct. Since the segments are divided by masses, you must treat them as independent cords, each with its own tension.

Imagine you had to pull that chain of masses with some given acceleration. Would pulling three masses require the same force as pulling one?

 

[peripatein]

But the masses are equal. Why can't I just regard it as a uniform mass of 3m?

 

[Doc Al]

But the masses are equal. Why can't I just regard it as a uniform mass of 3m?

For some purposes, you can. (As I said earlier.) But that doesn't mean the tension in the cord segments are all the same.

What are you trying to determine?

 

[peripatein]

The tension in the cord

 

[Doc Al]

The tension in the cord

Which piece? All of them? They each will have a different tension.

 

[Chestermiller]

How many masses is the cord furthest to the left pulling? How many masses is the cord second furthest from the left pulling? How many masses is the cord third furthest from the left pulling?