Equilibrium - The physics of a clothesline.

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Homework Help Overview

The problem involves a clothesline with a pulley hanging in the middle, requiring the calculation of tension in the line given specific measurements and conditions. The subject area pertains to equilibrium and forces in physics.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to approach the problem due to the lack of angle information. Some participants suggest creating a drawing to find the angle, while others discuss the process of calculating tension using trigonometric relationships.

Discussion Status

Participants have engaged in a back-and-forth regarding the calculations and the reasoning behind the equations used. Some guidance has been offered, particularly in the form of suggestions to visualize the problem through diagrams. There is an ongoing exploration of how to resolve forces into components.

Contextual Notes

The original poster mentions specific steps they are required to follow for their solution, indicating a structured approach to problem-solving that includes free-body diagrams and component analysis.

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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.


Homework Equations




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.
 
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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.
 
Your solution is ok.
 
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.

Again, thanks for your help.
 
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.
 

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