How is the tension of a rope calculated in a climber's FBD?

[BadSkittles]

A climber is hanging off a cliff with a rope tied to his waist. The rope is attached to a rock 10 meters from the edge of the rock. What is the tension of the rope? There is friction between the rock and the ground.

I am not sure if i got it right, but is it

m1= climber , m2= rock

τ - Frictional force of climber - m2 (g) = -m2(a) ?

or is it

T - frictional force - m2(g) = -m1+2 (a)?

Help is much appreciated!

 

[ModusPwnd]

Im a little confused by this... "The rope is attached to a rock 10 meters from the edge of the rock." Do you mean 10 meters from the edge of the cliff?

In any case, have you drawn a free body diagram? Draw one for the climber. He has two forces acting on him right? The rope tension and the force of gravity. After you draw the free body diagram you should sum up the forces and equate that to "ma" (Newton's second law). Does this process seem familiar?

 

[Tsunoyukami]

That same bit is confusing me as well.

Also, could someone explain how this is relevant? "There is friction between the rock and the ground.My interpretation is that there is a cliff with a rock on top jutting out over the edge of the cliff by 10 m to which the rope is attached. Is that correct?

 

[barryj]

I would interpret the problem this way. There is a rock back a distance from the edge of the cliff. The rope is tied to the rock and the rope extends over the edge of the cliff to the climber.

Also, there is friction between the rock and the ground, but there is no friction as the rope passes over the edge of the cliff.

 

[BadSkittles]

Im a little confused by this... "The rope is attached to a rock 10 meters from the edge of the rock." Do you mean 10 meters from the edge of the cliff?

In any case, have you drawn a free body diagram? Draw one for the climber. He has two forces acting on him right? The rope tension and the force of gravity. After you draw the free body diagram you should sum up the forces and equate that to "ma" (Newton's second law). Does this process seem familiar?

That same bit is confusing me as well.

Also, could someone explain how this is relevant? "There is friction between the rock and the ground.


My interpretation is that there is a cliff with a rock on top jutting out over the edge of the cliff by 10 m to which the rope is attached. Is that correct?

Opps, sorry I meant the rock is placed 10 meters from the edge of the cliff. I was wondering if I had the right equation with all the forces on it. I just don't know if the Force should be m1+m2(a) or just m2(a)

 

[BadSkittles]

I would interpret the problem this way. There is a rock back a distance from the edge of the cliff. The rope is tied to the rock and the rope extends over the edge of the cliff to the climber.

Also, there is friction between the rock and the ground, but there is no friction as the rope passes over the edge of the cliff.

Yeah there's no friction as the rope slides down.

 

[barryj]

Is the rock sliding? If sliding then there is one problem, if not sliding then its a different problem

 

[Tsunoyukami]

Is the rock sliding? If sliding then there is one problem, if not sliding then its a different problem

To make this more "obvious" you need to solve the problem for both cases (unless otherwise specified) for the problem to be complete.

If the rock is stationary what happens to the climber? What happens to the climber if it moves?

 

[BadSkittles]

To make this more "obvious" you need to solve the problem for both cases (unless otherwise specified) for the problem to be complete.

If the rock is stationary what happens to the climber? What happens to the climber if it moves?

Is the rock sliding? If sliding then there is one problem, if not sliding then its a different problem

Yeah the rock is sliding. The climber is being pulled down by gravity.

 

[barryj]

You should start by drawing a FBD of each mass. Get relationships ( determine the equation) between the tension, mass, cooeficient of friction and etc. You should have two equations that you can solve.

 

[Tsunoyukami]

Yeah the rock is sliding. The climber is being pulled down by gravity.

Does the problem state that the rock is sliding or are you assuming it is sliding? This is an important distinction - just because there's a person hanging onto a rope attached to the rock doesn't mean the rock will move: what if it's a very very large rock and the person's weight isn't enough to move it?

I'm just making sure that the problem explicitly states that the rock is moving, because if it doesn't state this you have to solve it for both cases.

 

[BadSkittles]

Does the problem state that the rock is sliding or are you assuming it is sliding? This is an important distinction - just because there's a person hanging onto a rope attached to the rock doesn't mean the rock will move: what if it's a very very large rock and the person's weight isn't enough to move it?

I'm just making sure that the problem explicitly states that the rock is moving, because if it doesn't state this you have to solve it for both cases.

yeah both the rock and the person is sliding. The acceleration is the same for both.

 

[Tsunoyukami]

Then, as suggested above, try drawing and FBD for each mass (ie. the rock and the climber). You should the. Have two equations, each with T in them. You should be able to solve this system using substitution or elimination.