Acceleration of a triple Atwood Machine

In summary, the conversation discusses a pulley system with three blocks of different masses connected by a mass-less string. The question of why the acceleration of block 3 is not equal to the other two blocks is raised, and it is explained that the freedom of movement of the blocks and the forces acting on them determine their individual accelerations. The different number of sections in the string also plays a role in determining the relationship between the accelerations.
  • #1
Calpalned
297
6

Homework Statement


http://photo1.ask.fm/723/921/945/-419996993-1shh761-9gamg0f647hgbk/original/IMG_4081.jpg [Broken]
There is no friction at all and this is a pulley system. The pulleys and string are mass-less. The numbers correspond to the block weight (ex: 3 = 3kg).

Homework Equations


F = ma

The Attempt at a Solution



From my solutions guide, it seems that the acceleration of block 3 is not equal to the other two blocks. I do not understand this. They are all connected by the same string and therefore are influenced by the same force of tension.
 
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  • #2
Calpalned said:

Homework Statement


There is no friction at all and this is a pulley system. The pulleys and string are mass-less. The numbers correspond to the block weight (ex: 3 = 3kg).

Homework Equations


F = ma

The Attempt at a Solution



From my solutions guide, it seems that the acceleration of block 3 is not equal to the other two blocks. I do not understand this. They are all connected by the same string and therefore are influenced by the same force of tension.

What forces act on the hanging block?

The length of the rope is unchanged, but it is shared among the two horizontal pieces and the two (equal) vertical pieces. They do not need to change with the same rate. Imagine that block 2 is very-very-very heavy, so it is practically stationary...
 
  • #3
I see... so the blocks don't have the same acceleration?
 
  • #4
If that's the case why do the two blocks below have the same acceleration? Here the blocks have different masses and are connected by the same string. The pulley system in my first post also only uses one string, but yet acceleration varies?
GIANCOLI.ch04.p52.jpg
 
  • #5
Calpalned said:
If that's the case why do the two blocks below have the same acceleration? Here the blocks have different masses and are connected by the same string. The pulley system in my first post also only uses one string, but yet acceleration varies?
It's a different situation.
In post #1, if you hold one of the blocks still, the other two blocks still have freedom to move. But in that picture in post #4, if you hold one of the blocks still, the other block cannot move (without the rope becoming slack).

Can you see how if block 3 in post #1 was fixed, block 1 and 2 can still move left or right? This is why they don't have to have the same acceleration; there is more freedom in the system.
You can see block 1 and 2 have the same force of tension acting on them (right?) so they will in fact have different accelerations.
 
  • #6
Calpalned said:
If that's the case why do the two blocks below have the same acceleration? Here the blocks have different masses and are connected by the same string. The pulley system in my first post also only uses one string, but yet acceleration varies?
GIANCOLI.ch04.p52.jpg
In that picture, the string consists of just two straight sections, and the sum of the lengths must be constant. You can write that down as an equation and differentiate it twice to show the relationship between the two accelerations. In the diagram at the start of this thread, there are four sections. Again, the sum of the lengths is constant, and that gives you an equation relating the accelerations, but in this case there are four variables, so there are many possible solutions to this equation. You need to look at forces to figure out all the acelerations.
 

1. What is a triple Atwood machine?

A triple Atwood machine is a type of mechanical system that consists of three masses connected by strings or ropes, and is used to study acceleration and tension in a simulated gravity field.

2. How does the acceleration of a triple Atwood machine differ from a regular Atwood machine?

The acceleration of a triple Atwood machine is greater than that of a regular Atwood machine due to the added mass and tension from the additional string. The acceleration can be calculated by dividing the net force by the total mass of the system.

3. What factors affect the acceleration of a triple Atwood machine?

The acceleration of a triple Atwood machine is affected by the masses of the three objects, the tension in the strings, and the force of gravity acting on the system. Additionally, the angle of the strings and the friction between the pulleys and strings can also affect the acceleration.

4. How can the acceleration of a triple Atwood machine be measured?

The acceleration of a triple Atwood machine can be measured using a variety of methods, such as using a photogate to measure the time it takes for the masses to move a set distance, or using a motion sensor to track the position of the masses over time. The acceleration can then be calculated using the equations of motion.

5. What are the practical applications of studying the acceleration of a triple Atwood machine?

Studying the acceleration of a triple Atwood machine can help us better understand the principles of mechanics and gravity, and how forces act on a system. This knowledge can be applied in various fields such as engineering, physics, and even sports, where understanding acceleration and tension is important for designing and optimizing equipment and techniques.

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