Analyzing Forces in a Three-String Knot

In summary, the problem involves three strings meeting in a knot and being pulled with three forces while being held stationary. The tension in string 1 is given as 2.9 N and the angles between the strings are provided. The key to solving the problem is realizing that the knot is held stationary, meaning the net forces and the sum of the component forces in each direction are all equal to 0. By choosing a convenient coordinate system and developing equations for the x and y components of the tension in each string, the problem can be solved with two equations and two unknowns.
  • #1
CaptainSFS
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Homework Statement



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Three strings, in the horizontal plane, meet in a knot and are pulled with three forces such that the knot is held stationary. The tension in string 1 is T1 = 2.9 N. The angle between strings 1 and 2 is q12 = 130° and the angle between strings 1 and 3 is q13 = 120° with string 3 below string 1 as shown.

Homework Equations



F=ma

The Attempt at a Solution



I am unsure. I tried finding two equations with two unknowns and then tried solving for one, but I no idea what to do. my free body diagrams aren't helping either. Could someone explain how my FBD would look or at least explain what equations I should have come up with? Thanks for any help.
 
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  • #2
CaptainSFS said:

Homework Statement



Three strings, in the horizontal plane, meet in a knot and are pulled with three forces such that the knot is held stationary. The tension in string 1 is T1 = 2.9 N. The angle between strings 1 and 2 is q12 = 130° and the angle between strings 1 and 3 is q13 = 120° with string 3 below string 1 as shown.
I am unsure. I tried finding two equations with two unknowns and then tried solving for one, but I no idea what to do. my free body diagrams aren't helping either. Could someone explain how my FBD would look or at least explain what equations I should have come up with? Thanks for any help.

The key phrase is the "knot is held stationary". That means that the net forces are = 0. It also means that the sum of the component forces in each direction is also 0 or it would move along that direction.

Now you can choose any coordinate system, but being lazy I like to choose at least one axis that makes things easier. Since the angles are given in terms of the relationship with T1, that would be my choice for x-axis.

Now develop equations for T1_x and T2_x and their angles and T3_x and since there is no Y component of T1 then another equation expressing T1_y and T2_y as a function of their angles.

2 equations. 2 unknowns. You don't need any more than that.
 
  • #3
hey thanks! I worked out the rest of it just fine. :)
 

Related to Analyzing Forces in a Three-String Knot

What is tension?

Tension is a force that is exerted by a string or other object when it is pulled tight. It is a measure of how much force is being applied to an object in order to keep it in place or maintain its shape.

What causes tension between 3 strings?

The tension between 3 strings is caused by the force applied to each string. When an object is suspended by 3 strings, the weight of the object is distributed among the strings, creating a balanced tension.

How is tension between 3 strings calculated?

Tension between 3 strings can be calculated using the formula T = F/l, where T is tension, F is the force applied, and l is the length of the string. This formula takes into account the amount of force being applied and the length of the string to determine the tension.

What is the relationship between tension and the length of the strings?

The longer the string, the higher the tension will be. This is because longer strings have a larger surface area and can support more weight, resulting in a higher tension. Additionally, shorter strings will have less tension because there is less surface area to distribute the weight.

How does the angle of the strings affect tension?

The angle of the strings also affects tension. The greater the angle between the strings and the vertical, the higher the tension will be. This is because the angle increases the effective length of the string, resulting in a higher tension.

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