Solve Tension in Rope: 110 Kg Anvil & 9.81m/s^2 Force

In summary: 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?In summary, a rope is attached to a hook on the ceiling and a wall, with an anvil of 110 Kg mass hanging vertically from the rope. The system is static and the tension in the rope is equal to the weight of the anvil, which is 1079.1 N. This tension will remain the same regardless of the angle of the chain or the rope's angle with the fixed objects, unless there is static friction in the chain. The line of the chain does not bisect the angle
  • #1
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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.

Homework Equations


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?
 

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  • #2
Favio said:

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.

Homework Equations


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?
 
  • #4
The anvil looks like it is sitting on the floor. Is that the case?
 
  • #5
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.
 
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  • #6
Chestermiller said:
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.
 
  • #7
j amann said:
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.
 
  • #8
Favio said:
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.
 
  • #9
haruspex said:
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?
 
  • #10
Favio said:
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?
 
  • #11
haruspex said:
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?
 
  • #12
Chestermiller said:
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:
  • #13
haruspex said:
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.
 
  • #14
Chestermiller said:
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.
It is not clear, but it seemed to me post #1 was asking about the tension in the angled section of rope.
If I am reading the image correctly, it will be a bit less than in the vertical section.
 

1. How do you calculate tension in a rope?

To calculate tension in a rope, you need to know the mass of the object (110 kg in this case), the acceleration due to gravity (9.81 m/s^2), and the angle of the rope. You can use the formula T = mg + ma, where T is the tension, m is the mass, g is the acceleration due to gravity, and a is the angle of the rope.

2. What is the force acting on the 110 kg anvil?

The force acting on the 110 kg anvil is its weight, which is equal to its mass (110 kg) multiplied by the acceleration due to gravity (9.81 m/s^2). This gives a force of 1079.1 N.

3. How does the angle of the rope affect the tension?

The angle of the rope affects the tension because it changes the direction of the force applied to the rope. The greater the angle, the more the force is directed horizontally, resulting in a higher tension in the rope.

4. What happens to the tension if the mass of the anvil is increased?

If the mass of the anvil is increased, the tension in the rope will also increase. This is because the weight of the anvil (and therefore the force acting on the rope) will be greater, resulting in a higher tension in the rope.

5. How can tension in a rope be reduced?

Tension in a rope can be reduced by either decreasing the force acting on the rope or increasing the angle of the rope. This can be achieved by either decreasing the mass of the object or changing the direction of the force.

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