# Tension in a rope

## Homework Statement

I have a rope held by a hook, which is attached to the ceiling by a chain (with an angle theta), in one side, the rope (with an angle alpha) is attached to a a wall, in the other side, the rope is carrying an anvil of 110 Kg mass in vertical position. What is the tension in the rope? The system is static.

W=m.a

## The Attempt at a Solution

No matter the configuration of this system, the tension in a rope will be the same at any point, so if the rope is carrying an anvil 110 Kg mass: W=(110 Kg)(9.81m/s^2)=1079.1 N.
Which is equal to the tension but in different direction.

Am I right?

#### Attachments

• WhatsApp Image 2018-05-26 at 8.04.30 PM.jpeg
72.3 KB · Views: 484

Chestermiller
Mentor

## Homework Statement

I have a rope held by a hook, which is attached to the ceiling by a chain (with an angle theta), in one side, the rope (with an angle alpha) is attached to a a wall, in the other side, the rope is carrying an anvil of 110 Kg mass in vertical position. What is the tension in the rope? The system is static.

W=m.a

## The Attempt at a Solution

No matter the configuration of this system, the tension in a rope will be the same at any point, so if the rope is carrying an anvil 110 Kg mass: W=(110 Kg)(9.81m/s^2)=1079.1 N.
Which is equal to the tension but in different direction.

Am I right?
Any chance if your providing a sketch?

Chestermiller
Mentor
The anvil looks like it is sitting on the floor. Is that the case?

If the configuration is as shown in the photo and the anvil is hanging vertically from the rope, the tension in the rope is exactly that needed to counteract the gravitational force on the anvil. So the computation for tension is correct and will not change no matter what the angle of the chain is or the angle the rope makes with the fixed object.

• Chestermiller
The anvil looks like it is sitting on the floor. Is that the case?
The anvil is in the air, a little but it is, and is static.

If the configuration is as shown in the photo and the anvil is hanging vertically from the rope, the tension in the rope is exactly that needed to counteract the gravitational force on the anvil. So the computation for tension is correct and will not change no matter what the angle of the chain is or the angle the rope makes with the fixed object.
That´s what I was thinking, thanks for your opinion.

haruspex
Homework Helper
Gold Member
No matter the configuration of this system, the tension in a rope will be the same at any point, so if the rope is carrying an anvil 110 Kg mass: W=(110 Kg)(9.81m/s^2)=1079.1 N.
Which is equal to the tension but in different direction.
Am I right?
Yes, except for the possibility of some static friction where the rope runs through the chain link. Looks to me that the line of the chain does not bisect the angle in the rope.

Yes, except for the possibility of some static friction where the rope runs through the chain link. Looks to me that the line of the chain does not bisect the angle in the rope.
The problem does not consider any friction, but let's say the chain does not bisect the angle. The tension in the rope would be equal the weight generated for the anvil?

haruspex
Homework Helper
Gold Member
The problem does not consider any friction, but let's say the chain does not bisect the angle. The tension in the rope would be equal the weight generated for the anvil?
Consider the balance of forces normal to the chain on the link the rope passes through. If the two rope tensions are the same, what can you say about the angles the rope sections make to the chain?

Chestermiller
Mentor
Consider the balance of forces normal to the chain on the link the rope passes through. If the two rope tensions are the same, what can you say about the angles the rope sections make to the chain?
Are you saying that the rope tension changes across the chain link?

haruspex
Homework Helper
Gold Member
Are you saying that the rope tension changes across the chain link?
it looks that way to me. Do you agree that the line of the chain does not appear to bisect the angle of the rope? It is hard to be sure because we are not seeing it side on.
If I am right, though, is there another explanation for that?

Last edited:
Chestermiller
Mentor
Consider the balance of forces normal to the chain on the link the rope passes through. If the two rope tensions are the same, what can you say about the angles the rope sections make to the chain?
All that haruspex is saying is that there is a jump change in tension across the chain link that the rope passes through. Your answer (OP) for the tension below the chain link is correct.

haruspex