# Free-hanging string with 4 attached masses

• Nikitin
In summary, the student attempted to solve a problem that was written in Norwegian, and was having difficulty understanding the notation. After a second look, he realized that he needed to simplify the notation and found that two equations existed from vertical equilibrium and one from horizontal equilibrium, if he did not use the third tension. He also found that the unknown, G, would not disappear if he inserted the equations into the one for D.

## Homework Statement

http://home.phys.ntnu.no/brukdef/undervisning/tfy4145/ovinger/Ov03.pdf
look at "oppgave 5".

In the problem, you have a massless string with 4 uniform masses attached symmetrically, and you are supposed to show that the implicit equation for x (and x = cos(alpha)) is correct. Each of the masses are L/5 apart and the distance between the two ends of the string is D.

## The Attempt at a Solution

I should be getting 5 equations for the 5 unkowns, but I am only getting 4 (the last 4 equations written on the paper)..

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-prn2/1234158_10201385459335100_1607600845_n.jpg

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This problem would make a lot more sense if I read Norwegian.

Look at the picture in the pdf: You see a massless string weighed down by 4 attached point-masses. Each of the mass is a distance L/5 apart from each-other, where L = total length of the string. D= distance between the two ends of the string.

Next you can see two angles: alpha and beta. The point with this problem is to show that the implicit equation for cosine of alpha written in the assignment,where x = cos(a), is correct.

Please tell me if there is something more you do not understand! I really need help with this

It is more convenient to simplify your notation by calling the tensions T and S.

Then use your D equation to get cosβ in terms of x where x = cosα.

I think that you do not need to use S$_{3}$.

You are probably right, but if I removed $$S_3$$ I would have 4 unkowns and 3 equations.. I don't understand how I can get my last equation?

Also sorry about the notation, but I took it from the assignment.

You have FOUR equations.

Two from vertical equilibrium and one from horizontal equilibirum if you do not use the third tension. But you have also your D equation from which to get cosβ in terms of x where x = cosα.

You mean those involving G? But G is also an unknown, because I don't know the mass. Do you think G would disappear if I inserted the equations into the one for D?

thanks for all help :)

OK after a fresh look at the problem I see you were completely right. thanks !