What does the middle of a chain on a pulley mean?

[misu]

Homework Statement

A chain of length 16 meters and a mass of 8 kilograms is suspended on a pulley. What is the tension in the middle of the chain when on a side of the pulley are 10 meters of the chain ( see the image attached )?

Relevant Equations

A side is 10 meters and the other side is 6 meters

 

[kuruman]

According to our rules, to receive help, you need to show some credible effort towards answering the question. How about telling us what you do know and how you would approach this problem?

Please read, understand and follow our homework guidelines, especially item 4, here
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

 

[misu]

hello ! I tried diving the chain into 2 separate parts based on the length and the mass of the chain . The first part is the one on the right and has a mass of 10*8/16 which is 5 kg and the other being 3 kg , being linked by a wire with no mass . The tension resulted is negative now ..

 

[kuruman]

OK, so you figured the mass of each hanging piece. How did you proceed to find your negative answer for the tension?

Please note that we prefer that you post any relevant equations in LaTeX. To learn how to do that, click "LaTeX Guide", lower left, above "Attach files".

 

[misu]

I did some calculations wrong but I figured out that using the ecuation F= m*a it resulted that the tension is 37.5 Newtons . My teacher told us that the result is 30 Newtons , equal to the lower mass object but I can’t figure out why ..

 

[kuruman]

Your answer of 37.5 Newtons is just a number. If it is wrong, it must be because you don't understand how to get the correct number. How can we help you improve your understanding if you don't tell us what reasoning you followed, what equations you worked with and how you used them to get your answer? Here, at PF, we help students get on the right path to the answer. We do not give answer away.

 

[berkeman]

Thread paused for Moderation...

 

[berkeman]

Okay, thread is reopened provisionally.

@misu -- Please check your messages. You need to show more work before we can offer tutorial assistance. Please draw a Free Body Diagram (FBD) of the chain and upload it using the "Attach files" link below the Edit window. It should show the forces on the chain, and any imbalance of those forces will cause an acceleration that you should be able to calculate.

I will also send you a message about how to use LaTeX going forward to post math at PF, but for now, please just show us your calculations as best as you can. Thank you.

 

[Lnewqban]

A side is 10 meters and the other side is 6 meters

Welcome, @misu !

If that statement is true, and the total lenght of that chain is 16 meters; then, the radius of that pulley must be zero.

What is the meaning of “the middle of the chain”?

 

[kuruman]

Welcome, @misu !

If that statement is true, and the total lenght of that chain is 16 meters; then, the radius of that pulley must be zero.

What is the meaning of “the middle of the chain”?

My interpretation is that, yes, the "pulley" has zero diameter and can be modeled as a thin wire with no friction at the point of contact. Then you have 6 m of chain on the left and 10 m of chain on the right. The "middle" of the chain is at 8 m from the tip of the 10 m segment, i.e. 2 m below the "pulley."