Analyzing Pulley System: Acceleration and Masses

In summary, the conversation is about a pulley system with no mass and a rope with no mass. The person is asking for feedback on their equations and for help with solving the first part of the problem, which involves figuring out which mass has an acceleration greater than g. They are also discussing the principle of the conservation of the length of the string and how it relates to acceleration. One person suggests using the height of each mass from the ceiling as a parameter, while the other suggests using the length of the string between the masses. There is confusion about how to measure these parameters and find the connection between the accelerations of the masses.
  • #1
asi123
258
0

Homework Statement



Hey guys.
look at this pulley system.
I drew all the forces, and also, the pulleys have no mass and so as the rope.
What do you say about the equations I wrote, are they right?
And BTW the first part of the question is to figure which mass has acceleration bigger then g and they say you can figure it out without solving the equations, any idea?

Homework Equations


The Attempt at a Solution

 

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  • #2
asi123 said:
What do you say about the equations I wrote, are they right?

Hi asi123! :smile:

If the last equation is a3 = 2a2 = 2a1, then it's wrong.
And BTW the first part of the question is to figure which mass has acceleration bigger then g and they say you can figure it out without solving the equations, any idea?

erm … T > 0, so isn't it obvious? :wink:
 
  • #3
tiny-tim said:
Hi asi123! :smile:

If the last equation is a3 = 2a2 = 2a1, then it's wrong.


erm … T > 0, so isn't it obvious? :wink:

I meant the size of the accelerations, not direction, isn't that right?
Maybe it's a3 = a2 = 2a1 ?
 
  • #4
asi123 said:
I meant the size of the accelerations, not direction, isn't that right?
Maybe it's a3 = a2 = 2a1 ?

No, you should be getting one equation, not two …

you only have one principle to help you … the conservation of the length of the string! :wink:
 
  • #5
tiny-tim said:
erm … T > 0, so isn't it obvious? :wink:

Yeah, you right, it's pretty obvious, by the equations we can see than m2 accelerate faster then g.

I don't quite understand the principle of the length of the rope, can you please help me with it?
I mean, what is the connection between the length of the rope and the acceleration?

Thanks.
 
  • #6
asi123 said:
I don't quite understand the principle of the length of the rope, can you please help me with it?
I mean, what is the connection between the length of the rope and the acceleration?

The rope starts at m2, and finishes at m3.

Call the positions x1 x2 and x3. What is the length of the rope in terms of x1 x2 and x3?

Then differentiate twice. :biggrin:
 
  • #7
tiny-tim said:
The rope starts at m2, and finishes at m3.

Call the positions x1 x2 and x3. What is the length of the rope in terms of x1 x2 and x3?

Then differentiate twice. :biggrin:

I'm sorry, I don't understand what you mean by x1, x2 and x3.
Do you mean for example that x1 is the length between m1 and m2 or something like that?
 
  • #8
asi123 said:
I'm sorry, I don't understand what you mean by x1, x2 and x3.
Do you mean for example that x1 is the length between m1 and m2 or something like that?

Any three parameters will do.

Personally, I'd choose the height from the ceiling, but your suggestion will work also. :smile:
 
  • #9
Ok, one second, am I right to say a3 = 2a1 ?
 
  • #10
asi123 said:
… a3 = 2a1 ?

only if a2 = 0 … which it isn't! :smile:

(you're trying to oversimplify! :wink:)
 
  • #11
tiny-tim said:
Any three parameters will do.

Personally, I'd choose the height from the ceiling, but your suggestion will work also. :smile:

What do you mean you choose the height from the ceiling? something like I drew in the pic?
 

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  • #12
asi123 said:
What do you mean you choose the height from the ceiling?

(i can't see the pic yet)

I mean the height of each mass below the ceiling.
 
  • #13
tiny-tim said:
(i can't see the pic yet)

I mean the height of each mass below the ceiling.

Well, how can you obviously know that? it's not like they are telling you "this mass is 30 cm beneath and the other on is 60 cm...":smile:, I mean, how can you measure that?

Thanks by the way :smile:
 
  • #14
asi123 said:
Well, how can you obviously know that? it's not like they are telling you "this mass is 30 cm beneath and the other on is 60 cm...":smile:, I mean, how can you measure that?

Thanks by the way :smile:

You're welcome! :smile:

"how can you obviously know that?"… you don't know … that's why they're called unknowns!
 
  • #15
tiny-tim said:
You're welcome! :smile:

"how can you obviously know that?"… you don't know … that's why they're called unknowns!

Well, if you don't know, than how can you find the connection between the accelerations of the masses?
Do you see the pic I posted by the way?
 
  • #16
asi123 said:
Well, if you don't know, than how can you find the connection between the accelerations of the masses?

(still no pic)

Because there is an equation for the lengths of the string, between the masses, in terms of x1 x2 and x3.
 
  • #17
tiny-tim said:
(still no pic)

Because there is an equation for the lengths of the string, between the masses, in terms of x1 x2 and x3.

Ok, I didn't quite get it, but thanks anyway.
 

FAQ: Analyzing Pulley System: Acceleration and Masses

1. How do you calculate the acceleration of a pulley system?

The acceleration of a pulley system can be calculated using the equation a = (m1-m2)/(m1+m2) where m1 and m2 are the masses on either side of the pulley.

2. What is the relationship between mass and acceleration in a pulley system?

The relationship between mass and acceleration in a pulley system is inverse. This means that as the mass on one side of the pulley increases, the acceleration decreases and vice versa.

3. How does the number of pulleys affect the acceleration in a pulley system?

The number of pulleys in a system does not affect the acceleration. The acceleration only depends on the masses on either side of the pulley and the force applied.

4. Can the acceleration of a pulley system ever be greater than the acceleration due to gravity?

No, the acceleration of a pulley system can never be greater than the acceleration due to gravity. The acceleration of a pulley system is limited by the forces and masses involved, while the acceleration due to gravity is a constant value.

5. Are there any other factors that can affect the acceleration of a pulley system?

Friction and air resistance can also affect the acceleration of a pulley system. These forces can slow down the movement and decrease the acceleration of the system.

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