Calculating tension in a wire?

In summary, The wing on a light aircraft experiences an upward thrust of 10 kN which is counteracted by two steel wires each set at an angle of 30 degrees from the horizontal and a length of 4 meters. The diameter of the wire is 10 mm and Young's modulus for steel is 2.05*10^11 N/m^2. The tension in each wire cannot be determined using statics, but it is reasonable to assume that it is distributed equally. However, the stretch of the wires due to tension may cause a change in geometry and therefore affect the forces acting on the wing. The exact amount of tension and stress in each wire cannot be calculated without further information.
  • #1
BlueCB
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0

Homework Statement


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A wing on a light aircraft experiences an upward thrust of 10 kN.
This is counteracted by two steel wires each set at an angle of 30 degrees from the horizontal and of length of 4 meters.
The diameter or the wire is 10 mm, and Young's modulus for steel is 2.05*10^11 N/m^2.

What is the tension in each wire?

The Attempt at a Solution



10,000 / sin(30 = 20,000
Tension = 20 kN?

Apparently this is wrong according to my teacher?
 
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  • #2
The entire force of tension is 20 kN, that is correct. But you have two wires. Using ordinary statics, you cannot determine how much tension each wire experiences, but it is reasonable to assume that it is distributed equally.
 
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  • #3
So am I right in saying that the answer is 10 kN of tension in each tie, if the total is 20 kN?
 
  • #4
BlueCB said:
So am I right in saying that the answer is 10 kN of tension in each tie, if the total is 20 kN?

I think so.
 
  • #5
Yup..10 kN in each wire.
 
  • #6
Since the modulus is given, it is conceivable that the wires stretch enough to change the geometry. Not sure how difficult the question is supposed to be. However, seems to me the stretch is only about 0.05%. Or maybe there are more parts to the question.
 
  • #7
Tension and tensile stress are two different things. If tensile stress is to be calculated, then yes, E needs to be used.
 
  • #8
siddharth23 said:
Tension and tensile stress are two different things. If tensile stress is to be calculated, then yes, E needs to be used.
If the stretch were 10%, say, then it would change the geometry sufficiently to affect the tension.
 
  • #9
Tension will depend on the force, won't it? Stretch will change the cross sectional are, which will change the Tension/Area ratio (Stress), not the tension.
 
  • #10
haruspex said:
Since the modulus is given, it is conceivable that the wires stretch enough to change the geometry. Not sure how difficult the question is supposed to be. However, seems to me the stretch is only about 0.05%. Or maybe there are more parts to the question.

Yes, this is a good point. I thought that the modulus was given for a next step, but its is definitely true that as the wires stretch due to tension, the geometry changes.

However, the change in the geometry affects the wing and probably the force acting on it, and there is no information in the problem on that.
 
  • #11
siddharth23 said:
Tension will depend on the force, won't it? Stretch will change the cross sectional are, which will change the Tension/Area ratio (Stress), not the tension.
If it stretches enough to change the angle significantly then it will also change the forces.
 
  • #12
To change the angle, the position of the wing or other pivot would have to change.
 
  • #13
siddharth23 said:
To change the angle, the position of the wing or other pivot would have to change.
If the cable stretches, something else must change. Maybe the wing flexes, or maybe it stays straight and pivots freely at the point of attachment. Either way, the angle will change.
 
  • #14
If the wing flexes, who purpose of using cable is being lost.
 

Related to Calculating tension in a wire?

1. How do you calculate tension in a wire?

To calculate tension in a wire, you need to know the force acting on the wire and its length. Then, you can use the formula T = F * L, where T is the tension, F is the force, and L is the length of the wire.

2. What is the unit of measurement for tension?

The unit of measurement for tension is Newtons (N). This is the same unit used for force.

3. What factors affect the tension in a wire?

The tension in a wire can be affected by the force acting on the wire, the length of the wire, and the material properties of the wire such as its elasticity and thickness.

4. Can tension in a wire be negative?

No, tension in a wire cannot be negative. Tension is a force that acts in a specific direction, and negative values do not make sense in this context.

5. How does temperature affect tension in a wire?

As temperature increases, the tension in a wire can also increase due to thermal expansion. This is because the wire's length increases as it heats up, resulting in a higher tension. However, the material properties of the wire can also affect how it responds to temperature changes.

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