# Why Is Calculating Rope Tension with Angles Confusing?

• druidwoody
In summary, the conversation discusses a problem involving finding the tension on a rope suspended between two points with a 20 Newton force hanging in the center. The textbook example shows how to find the tension using the formula 2TCos65=20N, but the individual is confused about where this formula comes from and uses a simultaneous equation to solve for T2. However, the person realizes that their equations are incorrect and that the correct equation should be 2TCos25=20. They seek clarification and explanation for their mistake.
druidwoody
This homework problem was originally posted in another forum so there is no template
Hi,

I have a revision book that has an example in it for the tension on a rope
if a 20 Newton force is hanging on the centre of a rope suspended between two points.

The rope dips 25 Degrees either side. So effectively an upside down pair of right angled triangles is formed.
The Hypoteneuse being 25 Degrees down.

http://d:\Rope-example.png

The Revision textbook Example shows how to find the Tension
2TCos65(Degrees)=20N
and shows T works out to be 24 Newtons.

I can not see where the 2TCos65=20 comes from, at least its not intuitive to me.
So I figured it out with a simultaneous equation. T1 = left T2 = right
Where the forces are worked out, asuming everything is static.

1) T1Cos25 + T2Cos65=0
2) T1Sin65 + T2Sin25=20N

From 1)
3) T1=T2x0.466

From 2)
T1x0.966 + T2x0.422 = 20

Substitute for T1 from 3)
T2x0.466x0.906 + T2x0.422 = 20
=> T2 x 0.844 = 20
Therfore T2 = 23.69N which is close enough to 24 Newtons in the example. I assume this is correct? (Maybe the book is wrong too?)

I was pleased with myself, until I checked by substituting T2 back fot T1 to check T1 was the same. I assume T1 and T2 are equal tensions.
But it is not, which I found very puzzling. I get about 11 Newtons. i.e put 23.69 in place of T2 in 3) above.

Can anyone explain what I have done wrong? Signs perhaps?, unfortunately my math is not the greatest.

Regards,

#### Attachments

• Rope-example.png
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Your Eqns. 1 and 2 are incorrect. Check the geometry more carefully. All the angles in both these equations should be 25. Also, in Eqn. 1, there should be a minus sign, not a plus sign.

druidwoody said:
I can not see where the 2TCos65=20 comes from, at least its not intuitive to me.

It should be.

Step by step...
Its a static problem so the vertical forces sum to zero.
I assume you know where the 65 degree angle is.
The tension each side is T.
The vertical component of each T is TCos65.
There are two of them so the total upward force is 2TCos65.
The downward force is 20N.
Sum the forces to zero...
2TCos65 - 20 = 0
Rearrange to give
2TCos65 = 20

## 1. What causes tension in a rope?

Tension in a rope is caused by a force applied to both ends of the rope in opposite directions. This force creates a pulling or stretching effect on the rope, resulting in tension.

## 2. How does tension affect the rope?

Tension can have different effects on a rope depending on its strength and elasticity. In some cases, tension can cause the rope to stretch or deform, while in others it can cause the rope to break or snap if the tension is too great.

## 3. How can I measure tension in a rope?

Tension can be measured using a device called a tension meter, which measures the force being applied to the rope. Alternatively, tension can also be calculated using the formula T = F/A, where T is tension, F is force, and A is the cross-sectional area of the rope.

## 4. What are some common causes of confusion about tension in a rope?

One common cause of confusion is the difference between tension and weight. While weight is a measure of the force of gravity on an object, tension is the force applied to a rope. Another source of confusion is the difference between tension and compression, which is a pushing or squeezing force applied to an object.

## 5. How can I reduce tension in a rope?

The best way to reduce tension in a rope is to reduce the force being applied to it. This can be done by either decreasing the weight or load being supported by the rope, or by increasing the strength or thickness of the rope to better withstand the tension. Proper maintenance of the rope, such as regular inspection and replacement of worn or damaged sections, can also help to reduce tension.

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