Statics, friction of a rope around a post

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Homework Help Overview

The discussion revolves around a statics problem involving the friction of a rope wrapped around a mooring bit, specifically focusing on the forces acting on the rope as a dockworker adjusts it to prevent a ship from drifting. The problem includes parameters such as the force exerted by the dockworker, the number of turns of the rope, and the coefficient of friction.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are examining the equation T2=T1eμβ and questioning which variable corresponds to the 190 N force. There is discussion about the interpretation of T1 and T2 in the context of the problem, particularly regarding the direction of impending motion and the implications for the unknown tension.

Discussion Status

The conversation is ongoing, with participants providing insights into the relationship between the forces and the assumptions made about T1 and T2. There is an acknowledgment of the need to clarify the roles of these variables and the implications for the calculations involved.

Contextual Notes

Participants note the importance of understanding the direction of forces and the conditions under which the rope may slip, as well as the need to reassess the problem statement in light of the forces acting on the system.

J-dizzal
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Homework Statement


A dockworker adjusts a spring line (rope) which keeps a ship from drifting alongside a wharf. If he exerts a pull of 190 N on the rope, which has 1.25 turns around the mooring bit, what force T can he support? The coefficient of friction between the rope and the cast-steel mooring bit is 0.35.
20150722_171921_zpszgrymvcs.jpg

Homework Equations


T2=T1eμβ
where T2 is in the direction of impending motion.

The Attempt at a Solution


20150722_171849_zpsf7gup5ud.jpg

Not sure what i am missing here, it looks right to me.
 
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J-dizzal said:
T2=T1eμβ
In this equation, which is the 190N, T1 or T2? Which did you try to solve for?

You should also run through the algebra again.
 
Nathanael said:
In this equation, which is the 190N, T1 or T2? Which did you try to solve for?

You should also run through the algebra again.
T2 is in the direction of impending motion, so i assumed it was 190N. Re reading the problem statement the ship is pulling on the rope with a much greater force, so then T2 would be T, the unknown.
Thank you Nathanael.
 
Last edited:
J-dizzal said:
T2 is in the direction of impending motion, so i assumed it was 190N. Re reading the problem statement the ship is pulling on the rope with a much greater force, so then T2 would be T, the unknown.
If the unknown force of tension were too large, it would cause the rope to slip towards it. We are asked for the maximum force of this unknown tension, so that means the unknown tension is the 'direction of impending motion.'

If you took T2 to be the 190N tension and solved it for T1 then what you would be calculating is the minimum force of tension the other side needs in order for the rope to not slip towards the dockworker.
 
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