Pulley & Angle: Tension Calculation

In summary, the tension force in the wire is greater when there's an angle between the wire and the pulley.
  • #1
RorschachDK
5
0
Hello everybody

Im trying to calculate the tension in wire (se attached image). the wire is wrapped around a pulley and combined in the end at which you pull with 50 kN. As far as I understand, if youdon´t have this angle so that that the wire ends follow the red dotted line then one can just divide the pulling strength by a factor of 2. But how does this angle influence?

Best regards
 

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  • #2
decompose the tension force on the string into two components. One of the components ought to be parallel to the red line while the other component will be perpendicular
 
  • #3
dauto said:
decompose the tension force on the string into two components. One of the components ought to be parallel to the red line while the other component will be perpendicular

If the wire is bend a certain angle A, then the tension in the wire would be F*cos(A)?, then this would make the tension in the wire smaller - I have done this experiment in real life and experienced a smaller force was nessecary in order to brake the wire compared to a normal pull in the wire.
Am I not understanding you rigth?
 
  • #4
RorschachDK said:
If the wire is bend a certain angle A, then the tension in the wire would be F*cos(A)?, then this would make the tension in the wire smaller - I have done this experiment in real life and experienced a smaller force was nessecary in order to brake the wire compared to a normal pull in the wire.
Am I not understanding you rigth?

It's the other way around - the tension in the wire is greater not smaller when there's an angle. You may have multiplied somewhere when you should have divided? Show your work and someone here will spot the problem.
 
  • #5
,

I can provide a solution to your question about tension calculation in a pulley system. The angle at which the wire wraps around the pulley plays a crucial role in determining the tension in the wire. This is because as the angle increases, the amount of force required to lift the load also increases.

To calculate the tension in the wire, you can use the formula T = F / (2sinθ), where T is the tension, F is the pulling strength, and θ is the angle between the wire and the horizontal plane. As you mentioned, when the angle is 90 degrees, the tension is simply half of the pulling strength. However, as the angle decreases, the tension increases significantly.

This is because as the angle decreases, the vertical component of the force acting on the pulley also decreases, while the horizontal component remains the same. Therefore, to maintain equilibrium, the tension in the wire must increase.

In your specific case, with a pulling strength of 50 kN and assuming the angle is 45 degrees, the tension in the wire would be approximately 70.7 kN. This is significantly higher than the tension at 90 degrees, which would only be 25 kN.

I hope this explanation helps you understand how the angle affects tension in a pulley system. If you have any further questions or need clarification, please don't hesitate to ask. Best regards.
 

1. What is a pulley and how does it work?

A pulley is a simple machine that consists of a grooved wheel with a rope or cable wrapped around it. It is used to change the direction of a force, typically to lift or lower an object. The pulley works by distributing the weight of the object evenly among the multiple ropes, reducing the amount of force needed to lift it.

2. How do you calculate tension in a pulley system?

To calculate the tension in a pulley system, you need to know the weight of the object being lifted and the number of ropes supporting it. The tension in each rope will be equal to the weight of the object divided by the number of ropes. For example, if a 100-pound object is being lifted by 4 ropes, the tension in each rope will be 25 pounds.

3. What is the angle of a pulley and how does it affect tension?

The angle of a pulley refers to the angle at which the rope is wrapped around the pulley. The greater the angle, the more tension there will be in the rope. This is because the weight of the object is distributed over a smaller area, increasing the force needed to lift it. In a single pulley system, the angle will always be 180 degrees, resulting in the maximum tension in the rope.

4. Can a pulley system increase mechanical advantage?

Yes, a pulley system can increase mechanical advantage by reducing the amount of force needed to lift an object. This is because the weight of the object is distributed among multiple ropes, making it easier to lift. The mechanical advantage of a pulley system is equal to the number of ropes supporting the object.

5. How do you calculate the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system is equal to the number of ropes supporting the object. For example, if a 100-pound object is being lifted by 4 ropes, the mechanical advantage of the pulley system is 4. This means that the force needed to lift the object is only 25 pounds, making the task much easier.

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