Three strings and a weight, need tensions in strings

In summary, the question asks about the tension in three strings holding a 20kg weight suspended from a ceiling. The attempted solution includes equations for the tensions and mentions the need for a free body diagram to solve the problem. The person is unsure if their solution is correct and asks for help with drawing the diagram and setting up the equations.
  • #1
thedarkone80
8
0

Homework Statement


You have three strings holding a 20kg weight, all tied to a ceiling above the weight, one centered right above the weight, the other two tied to the string at equal angles. What is the tension in each of the cables

Homework Equations


Fnet=0


The Attempt at a Solution


Tension 1 (x)= T1 cos theta
Tension 1 (y)= -T1sin theta -n
Tension 2 (x)= 0
Tension 2 (y)=mg+T2-n
Tension 3 (x)= -T3cos theta
Tension 3 (y)= -T3sin theta -n
I really don't know if this is right, and what in the world the angle would be, i need help. Thanks
 
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  • #2
thedarkone80 said:

The Attempt at a Solution


Tension 1 (x)= T1 cos theta
Tension 1 (y)= -T1sin theta -n
Tension 2 (x)= 0
Tension 2 (y)=mg+T2-n
Tension 3 (x)= -T3cos theta
Tension 3 (y)= -T3sin theta -n
I really don't know if this is right, and what in the world the angle would be, i need help. Thanks

For a problem like this, you need to:

1. Draw a free body diagram , showing each force that acts on the weight.
2. Set up separate Fnet=0 equations for the horizontal and vertical directions.

Have you drawn the free body diagram ? If it's not easy to post the drawing, can you at least list all the forces acting on the weight?
 
  • #3


I can provide a response to this content by stating that in order to calculate the tension in each of the cables, we need to apply the principles of equilibrium. This means that the sum of all the forces acting on the weight must be equal to zero. In this case, we have three tensions acting on the weight - T1, T2, and T3. Since the weight is not moving, the net force must be zero. This leads to the equation T1 + T2 + T3 = mg, where m is the mass of the weight and g is the acceleration due to gravity.

Now, in order to find the individual tensions, we need to consider the components of each tension in the x and y directions. The x components of T1 and T3 will cancel each other out, leaving only the y components to contribute to the net force equation. This means that -T1sin theta - T3sin theta - n = 0. Similarly, the y components of T2 and T3 will add up to contribute to the net force equation, giving us mg + T2 - n = 0.

By solving these two equations simultaneously, we can find the individual tensions T1, T2, and T3. The angle theta can be calculated using trigonometric functions, such as tangent or cosine, depending on the given information.

In conclusion, the tension in each of the cables can be calculated by applying the principles of equilibrium and solving the resulting equations. Further information, such as the angle theta, is needed to determine the exact values of the tensions.
 

1. What is the concept of "three strings and a weight"?

The concept of "three strings and a weight" refers to a physical system consisting of three strings attached to a weight or object. The strings are typically attached at different points on the weight and pulled in different directions, creating tension in each string.

2. Why is it important to know the tensions in the strings?

Knowing the tensions in the strings allows us to understand the forces acting on the weight and how it will behave in the system. This information is crucial in determining the stability and equilibrium of the system.

3. How do you calculate the tensions in the strings?

The tensions in the strings can be calculated using Newton's laws of motion. By analyzing the forces acting on the weight in each direction, we can determine the tension in each string using equations such as F=ma and Fnet=0.

4. Does the length of the strings affect the tensions?

Yes, the length of the strings can affect the tensions. The longer the string, the greater the distance over which the tension is distributed, resulting in a lower tension. Conversely, a shorter string will have a higher tension due to the shorter distance over which the tension is distributed.

5. Can the tensions in the strings be equal?

Yes, it is possible for the tensions in the strings to be equal in certain cases. This occurs when the weight is in equilibrium, meaning the net force and torque acting on it is zero. In this case, the tensions in the strings will be equal and opposite.

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