Atwood's machine with two connected discs

In summary, the problem involves two discs connected to each other with weights attached on opposite sides. The goal is to calculate the angular acceleration and accelerations of both weights. Using the equations F=ma, α=a/R, M=Iα, and Q=mg, three force equations can be set up for each hanging mass and the disk. By combining these equations and considering the relationships between angular and linear acceleration, the desired values can be calculated.
  • #1
lukast
1
0

Homework Statement


The system looks like this:
image.jpg

I have two discs which are connected.
Disc 1 has ##R_1##(radius) and ##M_1##(mass)
Disc 2 has ##R_2## and ##M_2##
## R_2 > R_1 ##
## M_2 > M_1 ##

on both discs weights are attached on opposite sides.
On smaller ##m_1## is pulling and on bigger ##m_2##

##m_2 > m_1##

i need to calculate angular acceleration and accelerations of both weights

Homework Equations


[/B]
## F = m * a ##
## \alpha = \frac{a}{R} ##
## M = I * \alpha ##
## Q = m * g ##

The Attempt at a Solution



The force that would cause acceleration of system is equal to :

## F = Q_2 - Q_1 ##
## F = m_2*g - m_1*g ##

The force that will cause tangential acceleration of discs would be equal to :

## I * \alpha = M ##
## \frac{1}{2} m * R^2 * \frac{a}{R} = F * R ##
## \frac{1}{2}*m * a = F ##
Now we know that Disc 2 and ##m_2## will have the same accelerations and Disc 1 and ##m_1## will have the same accelerations. We also now that Disc 1 and Disc 2 also have same angular acceleration. So from that i thought i can write this:

## a_1*(\frac{1}{2} * M_1 + m_1) + a_2(\frac{1}{2}*M_2 + m_2) = F ## (force that cause acceleration)

## a = \alpha * R##

##\alpha * R_1 *(\frac{1}{2} * M_1 + m_1) + \alpha * R_2 *(\frac{1}{2}*M_2 + m_2) = F##

and i have everything to get an alpha but its wrong

if somebody solve this on different way, could please explain why is my approach wrong
[/B]
 
Last edited:
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  • #2
lukast said:
## a_1*(\frac{1}{2} * M_1 + m_1) + a_2(\frac{1}{2}*M_2 + m_2) = F ## (force that cause acceleration)
Can you explain how you derived this?

I suggest you set up three force equations: one for each hanging mass and one for the disk. You can combine those equations, adding what you know about the relationships between the angular and linear accelerations.
 

1. How does an Atwood's machine with two connected discs work?

An Atwood's machine with two connected discs consists of two discs of equal mass connected by a string that runs over a pulley. The discs are suspended vertically and the string is wrapped around the pulley. The machine works by the force of gravity pulling on the discs and causing them to move.

2. What are the main components of an Atwood's machine with two connected discs?

The main components of an Atwood's machine with two connected discs are the two equal discs, a string, and a pulley. The discs are suspended vertically and the string runs over the pulley, connecting the two discs.

3. What is the purpose of an Atwood's machine with two connected discs?

An Atwood's machine with two connected discs is used to demonstrate the principles of mechanical advantage and acceleration due to gravity. It can also be used to measure the value of g, the acceleration due to gravity.

4. How does the mass of the discs affect the motion of the Atwood's machine?

The mass of the discs affects the motion of the Atwood's machine by changing the ratio of the masses on either side of the pulley. This affects the amount of force that is applied to the discs and therefore, the acceleration of the system.

5. What are some real-life applications of Atwood's machine with two connected discs?

Atwood's machine with two connected discs has several real-life applications, such as in elevators and cranes. It is also used in physics experiments to demonstrate the principles of mechanical advantage and acceleration due to gravity. Additionally, it can be used to measure the value of g and to study the effects of friction on motion.

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