Tension in rope wrapped around pole

In summary, tension in a rope wrapped around a pole is the force exerted by the rope on the pole to keep it in place. It can be calculated using the formula T = F * d and can be affected by factors such as the weight of the object, the thickness and material of the rope, the angle of the rope, and the strength of the pole. A higher angle can result in increased tension, which can lead to damage or instability if not kept within a safe range.
  • #1
Jzhang27143
38
1
A rope is wrapped around a pole with one end attached to a large object and the other end pulled with a tension T. The rope does not slip. I am confused why the tension varies within the rope. How would I know that the static friction force is non-zero?
 
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  • #2
What would the rope do without that static friction force? Is your situation is equilibrium? Is the rope doing what it would do without friction? If not, then there must be friction. :tongue:
 
  • #3
Have you been taught about Eytelwein's formula?
 
  • #5


I can provide an explanation for the varying tension in the rope wrapped around the pole. This phenomenon is due to the distribution of forces within the system. When an external force, such as the tension from the pulling end, is applied to the rope, it creates a force on the pole in the opposite direction. This force is known as the normal force.

As the tension increases, the normal force also increases, resulting in a higher friction force between the rope and the pole. This friction force acts in the opposite direction of the tension force and helps to keep the rope from slipping.

The varying tension in the rope can also be attributed to the changing angle at which the rope is wrapped around the pole. As the angle increases, the effective force exerted by the rope decreases, leading to a decrease in tension.

To determine if the static friction force is non-zero, you can use the equation Ff = μN, where Ff is the friction force, μ is the coefficient of friction, and N is the normal force. If the tension force is greater than the maximum static friction force, the rope will start to slip. However, if the tension force is less than the maximum static friction force, the rope will remain in place and the static friction force will be non-zero.

In conclusion, the varying tension in the rope wrapped around the pole is a result of the distribution of forces within the system. The normal force and friction force play crucial roles in keeping the rope in place and preventing it from slipping. By understanding these principles, we can better understand and predict the behavior of objects in similar situations.
 

1. What is tension in rope wrapped around a pole?

Tension in a rope wrapped around a pole is the force exerted by the rope on the pole in order to keep the rope in place. It is a result of the rope being pulled in opposite directions by the weight of the object it is holding and the resistance of the pole.

2. How is tension calculated in a rope wrapped around a pole?

Tension can be calculated using the formula T = F * d, where T is the tension, F is the force applied to the rope, and d is the distance between the force and the point where the rope is wrapped around the pole. It is important to note that this formula assumes that the rope and pole are both in a state of equilibrium.

3. What factors affect tension in a rope wrapped around a pole?

The tension in a rope wrapped around a pole can be affected by several factors, including the weight of the object being held by the rope, the thickness and material of the rope, the angle at which the rope is wrapped around the pole, and the strength and stability of the pole itself.

4. How does the angle of the rope around the pole affect tension?

The angle of the rope around the pole can have a significant impact on the tension in the rope. As the angle increases, the tension also increases, as more force is required to hold the object in place. This is due to the component of force acting perpendicular to the pole, known as the "horizontal component."

5. What happens when there is too much tension in a rope wrapped around a pole?

When there is too much tension in a rope wrapped around a pole, the rope may become stretched or even break. Additionally, the pole may also become damaged or unstable. It is important to ensure that the tension in the rope is within a safe range to prevent any accidents or damage.

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