Calculating tension in each of 3 strings

In summary, the question is about determining the tension in three strings of unequal lengths that are used to support a mass of 50g. Two of the strings cannot be in the same plane as the other string, and the third string is suggested to be placed in the k or k-j plane. There are potentially infinite solutions to this question and it is important to define the planes and angles accurately. Suggestions for placing the third string in a symmetric arrangement are made, with a freebody diagram and the need to calculate the tension using the chosen lengths and angles.
  • #1
mathsgeek
63
0
I have got a question i am having a lot of trouble with. The question is that three strings on unequal lengths are used to support a mass of 50g. All of these strings are used to support the weight. Two of these strings cannot be in the same plane as the other string. Determine the tension in each String.

Well, i have 2 strings in the i and j plane and was thinking to have a third string in the k or k and j plane. However i do not know if this is correct. Also, could someone show me the general steps on how to calculate the tension in each string as i am having trouble with calculating this.
 
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  • #2
It's going to depend exactly on how you define your planes and the angles that follow.
 
  • #3
well the planes are goin to be defined in terms of i, j and k.
 
  • #4
So you're putting the j plane parallel to the acceleration due to gravity?
There are potentially infinite solutions to this question, I must be interpreting it incorrectly. Is that the exact wording of the question? Could you not have 1 string hanging from a ceiling straight down parallel to gravity, then two strings of equal tensions opposing each other perpendicular to the acceleration due to gravity?
 
  • #5
The strings have to be of unequal length though. And yes the j component is the same as y. (vertical)
 
  • #6
It gives no definition of where they have to be fixed though? The end that is not fixed to the mass I mean.
 
  • #7
its basically fixed to a wall or sumthing, so it must be fixed at both ends.
 
  • #8
any1? Its urgent. Thanks
 
  • #9
Draw a freebody diagram.

Fnet = 0 for x, y, and z directions.

It depends on what angles the strings are oriented, which you know (hopefully) but we don't know.
 
  • #10
Heres a pic of 2 of the strings:
http://img124.imageshack.us/img124/7268/25255782he6.th.png http://g.imageshack.us/thpix.php

i just can't think of the length to place the third one in the k (or k and j) plane. Could u guys make sum suggestions and show me the process and calculations with ur sugeested length as i am having trouble calculating it. Thanks
 
Last edited by a moderator:
  • #11
Yes, placing the 3rd string in the k-j plane would make sense. Are you free to choose the string lengths and angles? Making the arrangement as symmetric as possible is probably the best way to approach this, so perhaps making all 3 string lengths equal.
 

FAQ: Calculating tension in each of 3 strings

How do you calculate the tension in each of 3 strings?

To calculate the tension in each of 3 strings, you will need to know the mass of the object being suspended by the strings, the angle at which the strings are being pulled, and the length of each string. You can then use the formula T = mg / cosθ, where T is the tension, m is the mass, g is the acceleration due to gravity, and θ is the angle at which the strings are being pulled. Repeat this calculation for each string to determine the tension in each one.

Why is it important to calculate the tension in each of 3 strings?

Calculating the tension in each of 3 strings is important because it allows you to understand the forces acting on an object being suspended by those strings. This can help you determine the stability and safety of the object, as well as the weight it can support without breaking the strings.

Can the tension in each of 3 strings be different?

Yes, the tension in each of 3 strings can be different. This is because the tension in a string is affected by the mass of the object being suspended, the angle at which the string is being pulled, and the length of the string. If any of these variables change, the tension in the string will also change.

What units are used to measure tension?

Tension is typically measured in units of force, such as Newtons (N) or pounds (lbs). This is because tension is a force that is exerted by a string or rope when it is pulled taut.

What factors can affect the tension in each of 3 strings?

The tension in each of 3 strings can be affected by several factors, including the mass of the object being suspended, the angle at which the strings are being pulled, the length of the strings, and any external forces acting on the object or strings. In addition, the elasticity and strength of the strings themselves can also affect the tension.

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