# Transitional Equilibrium: Tension

• Cummings
In summary, the tightrope walker is walking on a wire with a mass of 90kg and each wire has a tension of 20239 Newtons.
Cummings
A 60 kg tight-rope walker carries a long beam with a mass of 30kg across a 10m long wire. When she is at the centre of the wire (i.e. 5 m across) each section of the wire makes an angle of 5 degrees to the horisontal. Calculate the tension in the wire.

This one is not that difficult but a lack a certain part of me to get the answer.

60+30 = 90 which is the combined weight Multiply this by 9.8 and we get the force the combined weight exerts on the wire. This is 882 Newtons. Now, from trigonometry i got the tension in the wire to be (2 * 882)/sin(5degrees) = 20239 Newtons of tension. This is 4 times the correct answer. So i though that maybe half the weight acts on half the wire to 822/sin(5degrees) might be the answer but it would leave you with double the correct answer. Argh.

I need help on this one :)

Each wire supports half of the 90 kg.

The forces acting on one of the wires must be balanced. So, equate the x and y components of the tension T with the gravitational force acting on the tightrope walker (for one wire, 441 N).

It will probably be something like 441 = T sin(5), so solving for T gives T = 5059 N.

futz is correct. Why in the world do you have that factor of 2 in
"(2 * 882)/sin(5degrees) "? The total weight is 882 Newtons and, since, each side supports 1/2 of that: you should have divided by 2, not multiplied by 2. That's why your answer is 4 times what it should be.

Ok, so my mistake was that i doubled the tension when i shouldn't have, and not divided the weight into halve for the 2 sides.

The main thing i did wrong was not knowing that once you find the tension for the side your working with, you don't double it to get the full tension of the wire.

So the tension on the side we found is the total tension :) if that makes sense to you.

## 1. What is transitional equilibrium?

Transitional equilibrium, also known as mechanical equilibrium, is a state in which all forces acting on an object are balanced, resulting in no net change in motion or position.

## 2. How is tension involved in transitional equilibrium?

Tension is one of the forces that can act on an object and contribute to transitional equilibrium. It is a pulling force that is exerted by a string, rope, or other flexible material and can help to balance out other forces acting on an object.

## 3. What are some examples of transitional equilibrium involving tension?

Examples of transitional equilibrium involving tension include a book hanging motionless from a string, a person sitting in a hammock, and a flag hanging vertically on a flagpole.

## 4. How does the direction of tension affect transitional equilibrium?

The direction of tension is important in transitional equilibrium because it must be opposite in direction to other forces acting on the object. This ensures that the net force is zero and the object remains in equilibrium.

## 5. What happens when the tension force is greater than the other forces in transitional equilibrium?

If the tension force is greater than the other forces acting on the object, the object will experience acceleration in the direction of the net force. This will result in a change in motion or position, breaking the state of transitional equilibrium.

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