Statics, friction of a rope around a post

[J-dizzal]

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.

Homework Equations

T₂=T₁e^μβ
where T₂ is in the direction of impending motion.

The Attempt at a Solution

Not sure what i am missing here, it looks right to me.

 

[Nathanael]

T₂=T₁e^μβ

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.

 

[J-dizzal]

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.

 

[Nathanael]

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.