Pulley system, calculate acceleration

In summary, we are discussing a complex pulley system with different masses and accelerations. The main question is how to calculate the ratio of the accelerations and the tension in the system. The key to solving this problem is to consider the relative accelerations of the masses and use the equation relating the acceleration of the 5kg mass to the acceleration of the 1kg mass relative to P2. The presence of the 5kg mass adds complexity to the problem.
  • #1
dodo lee
IMG_2742.JPG
1. Homework Statement
this is a pulley system,
each masses are moving with acceleration with a1,a2,a3..
question)
1) How can i calculate the ratio a1:a2:a3 ?
2) How can i calculate the T(tenstion)?


2. Homework Equations

a1,a2,a3: acceleration of each masses.
g=10m/s2
weight of all pulleys : 0
The mass 5kg does not spin.

The Attempt at a Solution



i think this is atwood system , but not simple, very complex.
help me...
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
As drawn, the right side is going to jamb the pulley and then act as a single mass. Are you sure its drawn correctly?
 
  • #3
chopnhack said:
As drawn, the right side is going to jamb the pulley and then act as a single mass. Are you sure its drawn correctly?
I missed the condition " the mass 5kg does not spin'
Others, all correctly drawn.im sure...
 
  • #4
Then wouldn't you treat this as 2kg vs 6kg?
 
  • #5
chopnhack said:
Then wouldn't you treat this as 2kg vs 6kg?
Then a1, a2, a3 would be same...?
If i treat this as 2kg vs 6kg, all the a=5m/s2,
I would be happy if The answer is so simple./o\
 
Last edited by a moderator:
  • #6
chopnhack said:
Then wouldn't you treat this as 2kg vs 6kg?
Anyway thank you very much for your replies.
 
  • #7
chopnhack said:
As drawn, the right side is going to jamb the pulley and then act as a single mass.
I don't think so. Imagine P2 position as fixed. P3 can move up x while a2 moves down x and a3 moves up 2x.
 
  • #8
haruspex said:
I don't think so. Imagine P2 position as fixed. P3 can move up x while a2 moves down x and a3 moves up 2x.

you are right. if P3 is fixed, M3 moves up 2x, m2 moving down 1x, but P3 is also moving up, by 1x.the M2 is drawing with 2T tension. so net of M3 is 3x.the not fixed P3 makes this problem complicated.
 
  • #9
dodo lee said:
the not fixed P3 makes this problem complicated
So work in terms of relative accelerations. What equation can you write relating the acceleration of the 5kg relative to P2 to the acceleration of the 1kg relative to P2?
 
  • #10
IMG_2745.JPG
 
  • #12
haruspex said:
You seem to have written 2x in one place and 3x in another. Which is it?

while 1kg, moves up 2x to p3, p3 moves up 1x, so 1kg will move 3x to p2.

whe
 
  • #13
dodo lee said:
while 1kg, moves up 2x to p3, p3 moves up 1x, so 1kg will move 3x to p2.

whe
Very good.
So, what equation does that give you for the accelerations?
 
  • #14
IMG_2746.JPG
haruspex said:
Very good.
So, what equation does that give you for the accelerations?
 
  • #15
dodo lee said:
Don't worry about masses and forces yet, just think about the relationships that must apply to the accelerations because of the string lengths remaining constant.
In terms of a1, a2 and a3:
- what is the acceleration of P2?
- what is the acceleration of the 5kg mass relative to P2?
- what is the acceleration of the 1kg mass relative to P2?
- according to what you found in post #12, what equation connects those?
 
  • #16
haruspex said:
Don't worry about masses and forces yet, just think about the relationships that must apply to the accelerations because of the string lengths remaining constant.
In terms of a1, a2 and a3:
- what is the acceleration of P2?
- what is the acceleration of the 5kg mass relative to P2?
- what is the acceleration of the 1kg mass relative to P2?
- according to what you found in post #12, what equation connects those?
good morning sir,
i can calculate a1 a2 a3 to pulleys
but about equation of motion, I am very confused because of existence of 5kg.

5kg is connected to p3 and also tp p2.
T= 1*a3 + 1*g'---p3 equation
3T-5*a2=5g'
then, what?
i m not sure the motion equation to each pulley, p1,p2,p3.
 
  • #17
dodo lee said:
i can calculate a1 a2 a3 to pulleys
I don't know what you mean by that. Please answer my questions in post #15.
 

What is a pulley system?

A pulley system is a simple machine consisting of a wheel with a groove in which a rope or chain can run. It is used to change the direction of a force and can also provide mechanical advantage by reducing the amount of force needed to lift an object.

How do you calculate acceleration in a pulley system?

To calculate acceleration in a pulley system, you need to know the mass of the object being lifted and the force being applied. The formula for acceleration is a = F/m, where a is acceleration, F is force, and m is mass. In a pulley system, the force applied is equal to the weight of the object being lifted. So, to calculate acceleration, divide the force by the mass of the object.

What are the types of pulley systems?

There are three types of pulley systems: fixed, movable, and compound. In a fixed pulley system, the pulley is attached to a fixed point and only changes the direction of the force. In a movable pulley system, the pulley is attached to the object being lifted and reduces the amount of force needed. A compound pulley system combines both fixed and movable pulleys to provide even greater mechanical advantage.

What is the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system is the ratio of the output force to the input force. In a simple pulley system, the mechanical advantage is equal to the number of ropes supporting the object being lifted. So, if there are three ropes supporting the object, the mechanical advantage is 3. In a compound pulley system, the mechanical advantage is equal to the number of ropes attached to the object being lifted.

How do pulley systems make work easier?

Pulley systems make work easier by reducing the amount of force needed to lift an object. They also allow for the direction of the force to be changed, making it easier to lift objects in difficult or awkward positions. Additionally, compound pulley systems can provide even greater mechanical advantage, making it possible to lift heavy objects that would be impossible to lift with just human strength.

Similar threads

Replies
25
Views
2K
  • Introductory Physics Homework Help
Replies
22
Views
3K
  • Introductory Physics Homework Help
Replies
15
Views
2K
  • Introductory Physics Homework Help
2
Replies
40
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
30
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
Back
Top