Solving for Acceleration in a Complex Pulley System

In summary, the conversation discusses the acceleration of m1 in a scenario with no friction and pulleys connected to the ceiling. The person is unsure of their formula for the acceleration of M2 and requests help in understanding the correct formula. They also mention a recent photo of their attempted solution and the need to account for friction and moment of inertia if necessary. The expert advises to start at a more basic level and to define the direction of acceleration, and expresses doubts about the equations provided.
  • #1
TheLil'Turkey
66
0
Mecaacutenica%20Teoacuterica_zpsk4q6fegh.png
Mecaacutenica%20Teoacuterica_zpspvblj0ca.png
1. Homework Statement
What is the acceleration of m1? There is no friction so the pulleys don't rotate. The top rope is connected to the ceiling.

Homework Equations


See photo. I think my formula for the acceleration of M2 is only right if m1 = m2 and wrong in all other situations, but I'm not sure what the correct formula is.

The Attempt at a Solution


See photo.
 
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  • #2
In the equation for the acceleration of M2, I forgot to multiply it by g.
I uploaded a more recent photo of my attempted solution. It's in the OP above the original photo.
 
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  • #3
You don't explain the basis for any of your equations, so you need to start at a more basic level. Assign an unknown to each tension and write out the ∑Fi=ma equation for each mass.
By the way, when a pulley is described as frictionless it nearly always means merely that there is no frictional torque at its axis. It does not usually mean there is no friction between the pulley and the rope. (If no friction there then it might as well just be a round mass, no need for it to be a pulley.) Thus, if the pulley has mass and a known radius then you should take into account its moment of inertia. However, if no radius is provided then clearly you have no way to take it into account.
 
  • #4
There are no radii given. So it's best to assume it's truly frictionless. The problem is difficult enough without friction. If you or anyone else sees any mistakes in my equations I'd appreciate any help you could provide.
 
  • #5
TheLil'Turkey said:
There are no radii given. So it's best to assume it's truly frictionless. The problem is difficult enough without friction. If you or anyone else sees any mistakes in my equations I'd appreciate any help you could provide.
As I posted, your working is not immediately intelligible because you do not explain how you get any of your equations. Either explain them, or start at a more fundamental level with unknowns for tensions and a ∑F=ma equation for each mass.

You also need to define which way the various acceleration variables are defined. Are they all positive upwards? It doesn't look like it.

For what it's worth, your equations do not smell right to me. I would expect a m1+m2 term in your first equation.
 

Related to Solving for Acceleration in a Complex Pulley System

1. How does a system of pulleys work?

A system of pulleys works by using multiple pulleys, each with a rope or cable running through it. The pulleys are connected together and the rope or cable is looped around them in a specific way to create mechanical advantage. When one end of the rope is pulled, the load on the other end of the rope is lifted or moved. This allows for heavy objects to be lifted with less force than would be required without the pulleys.

2. What are the different types of pulleys in a complicated system?

There are three main types of pulleys used in a complicated system: fixed pulleys, movable pulleys, and compound pulleys. A fixed pulley is attached to a fixed point and changes the direction of the force applied. A movable pulley is attached to the load and changes the direction of the force applied. A compound pulley combines both fixed and movable pulleys to create a greater mechanical advantage.

3. What are the advantages of using a complicated system of pulleys?

The main advantage of using a complicated system of pulleys is that it allows for heavy objects to be moved or lifted with less force. This can significantly reduce the physical effort required and increase efficiency. Additionally, using multiple pulleys can distribute the weight of the load evenly, reducing strain on the pulleys and ropes or cables.

4. What are some real-life examples of complicated systems of pulleys?

There are many real-life examples of complicated systems of pulleys. Some common examples include elevators, cranes, and sailboat rigging systems. In these examples, the pulleys are used to lift or move heavy objects, such as people, building materials, or sails. Pulleys are also used in exercise equipment, such as weightlifting machines, to provide resistance and make lifting weights easier.

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

The mechanical advantage of a complicated system of pulleys is calculated by dividing the load by the effort. The load is the weight of the object being lifted or moved, and the effort is the force applied to the rope or cable. For example, if a system of pulleys is used to lift a 100-pound object with an effort of 25 pounds, the mechanical advantage would be 100/25 = 4. This means that the object can be lifted with one-fourth of the force that would be required without the pulleys.

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