Solve Mechanics Question: Hanging Thread, Gravity, Angle @

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In summary, the conversation discusses a mechanics question about finding the tension at the lowermost point of a rope hanging between two hinges. The solution involves using trigonometry and Newton's laws to calculate the tension at both points A and B. The final solution is t2=(mg cot@)/2.
  • #1
twinklealices
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mechanics question..please help!

Homework Statement


a thread hangs between 2 hinges A and B. gravity is acting. The angle(acute) made by tangent to rope at point A and the line AB is @. find the tension at the lower most point..i.e the mid point of the rope?


Homework Equations



don know!

The Attempt at a Solution

 
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  • #2


You need to know the mass of the rope in order to calculate the tension. Assume the mass is M. Then you must realize that the vertical force and tension at A are related by basic trig. You must show some attempt at a solution for further assistance.
 
  • #3


ok ...i take the tension to be t1 at point A...and t2 at bottom most point then
t1sin@=mg...then how to proceed??
 
  • #4


EDIT: [strike]Yes, that's OK. [/strike]Sorry, I was half asleep this morning, that is not OK. The weight of the rope is divided equally amongst points A and B. Sorry about that :yuck:. Now the direction of the tension t2 at the bottom most point is in the horizontal direction, right? So try taking a free body diagram of the left half of the rope and then what does Newton 1 tell you when looking in the x direction at point A?
 
Last edited:
  • #5


oh ...okkkk...so i do this
for left half of the rope ...
in x direction ...
its ... t1cos@=t2..(1
then t1sin@=mg/2...(2

so i divide 1/2 and
cot@=2*t2/mg..
so t2=(mg cot@)/2...!
right??!
 
  • #6


twinklealices said:
oh ...okkkk...so i do this
for left half of the rope ...
in x direction ...
its ... t1cos@=t2..(1
then t1sin@=mg/2...(2

so i divide 1/2 and
cot@=2*t2/mg..
so t2=(mg cot@)/2...!
right??!
Oh yes, right you are! :smile:
And welcome to PF!:smile::smile:
 
  • #7


oh ..thank you!...this is an awesome site for doubt clarification!
 

What is the formula for calculating tension in a hanging thread?

The formula for calculating tension in a hanging thread is T = (mg)/(cosθ), where T is the tension, m is the mass of the object, g is the acceleration due to gravity, and θ is the angle at which the thread is hanging.

How does the angle at which a thread is hanging affect the tension?

The tension in a hanging thread is directly proportional to the angle at which it is hanging. As the angle increases, the tension also increases. This is because a larger angle means that more of the weight of the object is pulling down on the thread, resulting in a higher tension.

What is the relation between the weight of an object and the tension in the hanging thread?

The weight of an object is equal to the tension in the hanging thread when the thread is at an angle of 90 degrees. As the angle decreases, the tension decreases and the weight becomes greater than the tension. This is because at an angle of 90 degrees, the entire weight of the object is pulling down on the thread, resulting in an equal tension.

How does gravity affect the tension in a hanging thread?

Gravity plays a major role in determining the tension in a hanging thread. As the acceleration due to gravity, g, increases, the tension also increases. This is because a higher g means that there is a stronger downward force acting on the object, resulting in a higher tension in the thread holding it up.

Can the angle at which a thread is hanging ever be greater than 90 degrees?

No, the angle at which a thread is hanging cannot be greater than 90 degrees. This would result in a negative tension, which is not physically possible. In order for an object to be held up by a thread, the angle must be less than or equal to 90 degrees.

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