A simple movable pulley not at equilibrium

In summary, when an object is hanging off a single movable pulley, the equilibrium system entails pulling on the free end of the rope with half the weight of the object. If the pulling force is increased to match the weight of the object, the rope will have a uniform tension of the weight and the object will accelerate upwards at a rate of g.
  • #1
DocZaius
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Note: This is not a homework question. I have constructed this question to help me understand a concept.

If I have an object hanging off a single (frictionless, negligible mass) movable pulley, the equilibrium system entails me pulling on the free end of the (frictionless, negligible mass) rope with half as much force as the object weighs.

What happens if I pull harder than that?

See the attached GIF. What would be the behavior of the weight? Would it accelerate up? If so, at what acceleration? What would be the tension in the left side of the rope?

Every resource I have access to that mentions pulleys keeps talking about pulleys in this type of setup in equilibrium. I am interested in furthering my understanding in regards to pulleys not in equilibrium.

Thank you for any help.
 

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  • #2
The tension is uniform throughout the rope. The upward force on the pulley/mass will equal twice the tension. To find the acceleration, just add the vertical forces and apply Newton's 2nd law.
 
  • #3
So me increasing my pulling force from an equilibrium inducing (1/2)mg to mg will cause the rope to have a uniform tension of mg, thus making the total upward force 2mg (the tension of the rope being a uniform "mg"). This accelerate the weight, which weighs mg, upwards at acceleration = g.

Is that correct?
 
  • #4
Yes, that's correct.
 

1. How does a simple movable pulley not at equilibrium work?

A simple movable pulley not at equilibrium is a type of pulley system where the load is not balanced by the effort. In this system, the load is heavier than the effort, and the pulley is attached to the load, which is then lifted by pulling down on the effort. This creates a mechanical advantage, making it easier to lift the load.

2. What are the advantages of using a simple movable pulley not at equilibrium?

The main advantage of using a simple movable pulley not at equilibrium is that it reduces the amount of effort needed to lift a heavy load. This is because the load is distributed between the effort and the pulley, making it easier to lift. Additionally, this type of pulley system can also change the direction of the force, making it useful for lifting objects in tight spaces.

3. How is the mechanical advantage of a simple movable pulley not at equilibrium calculated?

The mechanical advantage of a simple movable pulley not at equilibrium is equal to the number of supporting ropes attached to the load. For example, if you have a single movable pulley attached to the load, the mechanical advantage would be 2. This means that the load is lifted with half the effort that would be required without the pulley.

4. What are some common uses of a simple movable pulley not at equilibrium?

A simple movable pulley not at equilibrium is commonly used in various industries, such as construction, shipping, and transportation. It is also used in gym equipment, such as weight machines, to make lifting heavy weights easier. Additionally, this type of pulley system is often used in rescue operations to lift heavy objects or individuals.

5. Can a simple movable pulley not at equilibrium be used for both horizontal and vertical lifting?

Yes, a simple movable pulley not at equilibrium can be used for both horizontal and vertical lifting. This type of pulley system is versatile and can change the direction of the force, making it suitable for lifting objects in different directions. However, it is important to note that the mechanical advantage may differ depending on the direction of the lift.

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