# Equilibrium - The physics of a clothesline.

• L_0611
In summary, a problem involving finding the tension in each half of a clothesline with a pulley hanging in the middle and a sag of 0.20m between two fixed ends 10.0m apart was discussed. The solution involved making a drawing to find the angle θ, using the formula 2Tcosθ=mg to solve for T, and using five steps to find the x and y components of the forces. These steps included selecting the object, drawing a free-body diagram, choosing axes, resolving the diagram into components, and setting up and solving equations for the unknown quantities. The conversation also included clarifications and steps for finding the equation 2Tcosθ=mg.
L_0611

## Homework Statement

A clothesline is attached to two fixed ends which are 10.0m apart. A pulley of mass 40.0kg hangs freely in the middle of the line. The sag at the centre is 0.20m. Find the tension in each half of the clothesline.

## The Attempt at a Solution

not sure how to tackle this problem since I don't have the values for the angle θ that is formed at the centre. Please point me towards the right direction with this problem. Thank you.

Make a drawing and you will find the angle.

ehild

ok so I made a drawing like ehild recommended and I think I figured out angle θ. This is what I got for an answer.

tanθ = 5/0.2 = 25
θ = tan-1*25 = 87.7

then then formula I used to solve the problem would be 2Tcos87.7=mg

2Tcos87.7=40*9.8
then i rearranged the formula to read:
T=40*9.8/2cos87.7
T=392/2cos87.7
T= 4884N

Therefore the tension on each half of the clothesline is 4884N.

please correct me if I'm wrong on this problem. Thank you.

ok perfect, thank you. As part of my solution I'm asked to find the x and y components but I'm not sure how to do so, can anyone help me? they want me to use these five steps to solve the problem, the steps are as follows:
Step 1: select the object to be studied.
Step 2: draw a "free-body diagram" for each object chosen.
Step 3: choose a set of x and y axes for each of the objects being analyzed, and resolve the free-body diagram into components that point along these axes. (this is the step I'm having issues with).
Step 4: set up the equations in such a way that the sum of the x-components of the forces is zero, and the sum of the y-components is also equal to zero.
Step 5: solve the equations for the unknown quantities you are looking for.

How did you get the equation 2Tcos87.7=mg before? Describe this in steps for them.

ok so that's basically all I have to do? put it into words...?

Yeah man!

Alright then, funny how sometimes I can miss the simplest things, thanks a lot.

## 1. What is equilibrium and how does it apply to a clothesline?

In physics, equilibrium refers to a state in which all forces acting on an object cancel each other out, resulting in a stable and balanced system. In the case of a clothesline, equilibrium is achieved when the tension in the clothesline is equal on both sides, allowing the clothes to hang without falling.

## 2. Why is it important to understand the physics of a clothesline?

Understanding the physics of a clothesline can help us make more efficient use of it. By understanding the concept of equilibrium, we can ensure that the clothesline is set up properly and can hold the weight of the clothes without breaking. This can also help us save energy and time by maximizing the use of the clothesline.

## 3. How does the weight of the clothes affect the equilibrium of a clothesline?

The weight of the clothes plays a significant role in the equilibrium of a clothesline. If the weight on one side of the clothesline is heavier than the other, it will cause an imbalance and the clothesline will not be in equilibrium. This is why it is important to distribute the weight evenly when hanging clothes on a clothesline.

## 4. Can other factors, such as wind, affect the equilibrium of a clothesline?

Yes, other factors such as wind can affect the equilibrium of a clothesline. Wind can create an additional force on the clothesline, causing it to sway and potentially disrupt the balance of tension. This is why it is important to consider wind direction and strength when setting up a clothesline.

## 5. How can we use the concept of equilibrium to make a clothesline more efficient?

By understanding the concept of equilibrium, we can make a clothesline more efficient by adjusting the tension on each side to achieve a balanced system. This can help prevent the clothesline from breaking or clothes from falling off. Additionally, we can strategically place heavier items closer to the center of the clothesline to maintain balance and prevent the clothesline from sagging.

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