Free-hanging string with 4 attached masses

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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.
  • #1
Nikitin
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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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  • #2
This problem would make a lot more sense if I read Norwegian.
 
  • #3
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
 
  • #4
It is more convenient to simplify your notation by calling the tensions T and S.
 
  • #5
Then use your D equation to get cosβ in terms of x where x = cosα.
 
  • #6
I think that you do not need to use S[itex]_{3}[/itex].
 
  • #7
You are probably right, but if I removed [tex]S_3[/tex] 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.
 
  • #8
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.
 
  • #9
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 :)
 
  • #10
OK after a fresh look at the problem I see you were completely right. thanks !
 

1. What is a free-hanging string with 4 attached masses?

A free-hanging string with 4 attached masses refers to a physical system in which a string is suspended vertically from a fixed point and has 4 masses attached to it at different positions along its length. The masses are allowed to hang freely under the influence of gravity and the tension in the string.

2. How is the motion of a free-hanging string with 4 attached masses described?

The motion of a free-hanging string with 4 attached masses can be described using the principles of mechanics, such as Newton's laws of motion and Hooke's law. The motion of each mass is influenced by the tension in the string and the gravitational force acting on it.

3. What affects the motion of a free-hanging string with 4 attached masses?

The motion of a free-hanging string with 4 attached masses is affected by various factors, including the masses of the objects, the length of the string, the tension in the string, and the gravitational force. These factors determine the acceleration and velocity of each mass, as well as the overall motion of the system.

4. What types of oscillatory motion can occur in a free-hanging string with 4 attached masses?

A free-hanging string with 4 attached masses can exhibit various types of oscillatory motion, such as simple harmonic motion, where the masses move back and forth along the string with a constant frequency and amplitude. It can also exhibit complex oscillatory motion, where the masses move with varying frequencies and amplitudes due to the non-uniform distribution of masses along the string.

5. What are the practical applications of studying a free-hanging string with 4 attached masses?

The study of free-hanging strings with 4 attached masses has practical applications in various fields, such as engineering, physics, and mathematics. It can help in understanding the principles of mechanics and oscillatory motion, as well as in designing and analyzing structures and systems that involve suspended masses, such as bridges, cranes, and musical instruments.

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