# Will the Rope Hold the Archaeologist Safely?

• Eeroygirl
In summary, an archaeologist with a mass of 93.8 slowly crosses between two rock cliffs using a rope with a tension limit of 2.95EE4. The tension in the rope is 2408.796 N when the angle between the rope and the horizontal is 11.0 degrees. To prevent the rope from breaking, the smallest angle possible is 0.89 degrees.
Eeroygirl
An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope . The rope will break if the tension in it exceeds 2.95EE4 (2.95 x 10^4) , and our hero's mass is 93.8 .

<img src=http://session.masteringphysics.com/problemAsset/1041292/5/YF-05-42.jpg>

A. If the angle between the rope and the horizontal is = 11.0, find the tension in the rope.
B. What is the smallest value the angle can have if the rope is not to break?

A. 4817.6 N
B. 1.78 degrees

Last edited by a moderator:
Do you have your calculations at all?

Also the link you have posted is broken.

You did what many people get wrong. You forget to evenly distrubute the weight of the person to both sides of the rope. Since he is in the exact middle then you will divide his weight in half and put them on both the "y" dimension.

From this I got a) 2408.796 N
b) .89 degrees

Notice these are exactly half of your answer this is because I halved the weight of each side.

## 1. How do I determine the necessary tension for a rope?

The tension required for a rope depends on several factors such as the weight being supported, the angle of the rope, and the material and thickness of the rope. To determine the necessary tension, you can use the formula T = (W/sinθ) + (F x cosθ), where T is the tension, W is the weight, θ is the angle, and F is the friction force. You may also consult a tension chart specific to the type of rope you are using.

## 2. How do I measure the tension of a rope?

There are several methods for measuring the tension of a rope, including using a tension gauge, a spring scale, or a load cell. You can also use the formula T = F x L, where T is the tension, F is the force applied to one end of the rope, and L is the length of the rope.

## 3. What happens if the tension in a rope is too high or too low?

If the tension in a rope is too high, it can cause the rope to stretch, deform, or even break. This can also lead to excessive wear and tear on the rope, reducing its overall lifespan. On the other hand, if the tension is too low, the rope may not be able to support the required weight, leading to safety hazards and potential failure.

## 4. How can I adjust the tension in a rope?

To adjust the tension in a rope, you can either increase or decrease the force applied to one end of the rope, or change the angle of the rope. If using a tension gauge or load cell, you can also use the readings to adjust the tension accordingly.

## 5. What are some common causes of rope tension problems?

Some common causes of rope tension problems include incorrect calculations, improper installation, overloading, and wear and tear. It is important to regularly inspect and maintain ropes to ensure they are in good condition and have the appropriate tension for their intended use.

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