Finding acceleration of an Atwood's machine

In summary, the conversation discusses the setup of a problem involving two masses suspended from a pulley, with given values for the mass and radius of the pulley, as well as the constant torque due to friction. The question asks for the acceleration of the suspended masses. The conversation also mentions an initial attempt at solving the problem using an equation, but ultimately recommends using free body diagrams and Newton's laws for a more accurate solution.
  • #1
santoki
34
0

Homework Statement


Two masses are suspended from a pulley:

[PLAIN]http://i.imgur.com/B4x8pzx.png[/PLAIN]

mass of pulley = 0.20kg
radius = 0.15m
constant torque = 0.35Nm due to friction between the rotating pulley and its axle
m1 = 0.40kg
m2 = 0.80kg

What is the acceleration of the suspended masses?

Homework Equations


Fnet = I[itex]\alpha[/itex]

The Attempt at a Solution


I tried to make sense out of this problem using the equation from above initially, but my acceleration was way too big. I know the acceleration is supposed to be somewhat big anyway but it was too big. So instead I searched for helm on google first and found an equation which told me to do this:

I = (1/2)mr2 = (1/2)(0.20)(0.5)2 - 0.025kgm2


a = [g(m1 - m2) - [itex]\tau[/itex]/r]/(m1 + m2 + I/r2)
a = 9.8(0.80+0.40)-(0.35/0.15)/(0.80+0.40+(0.0025/(0.15)2)
a = 1.23 m/s2

If this is right, how can I clean it up to make it relevant to how Fnet = I[itex]\alpha[/itex] is supposed to be set up?
 
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  • #2
santoki said:
If this is right, how can I clean it up to make it relevant to how Fnet = I[itex]\alpha[/itex] is supposed to be set up?
Check your formula:
Fnet I[itex]\alpha[/itex]
 
  • #3
santoki said:
So instead I searched for helm on google first and found an equation which told me to do this:


a = [g(m1 - m2) - [itex]\tau[/itex]/r]/(m1 + m2 + I/r2)
a = 9.8(0.80+0.40)-(0.35/0.15)/(0.80+0.40+(0.0025/(0.15)2)
a = 1.23 m/s2

If this is right, how can I clean it up to make it relevant to how Fnet = I[itex]\alpha[/itex] is supposed to be set up?
You can't arbitrarily pick an equation out of a book and use it without understanding it, even in the unlikely event that it happened to be the right equation. Instead, use free body diagrams of each block and the pulley, and use Newton's laws for translational or rotational motion on each piece.
 

1. What is an Atwood's machine?

An Atwood's machine is a simple mechanical device that consists of two masses connected by a string or cable that runs over a pulley. It is used to study the effects of gravity and acceleration on a system.

2. How do you calculate the acceleration of an Atwood's machine?

The acceleration of an Atwood's machine can be calculated by using the formula a = (m2-m1)g/(m1+m2), where m1 and m2 are the masses on each side of the pulley and g is the acceleration due to gravity (9.8 m/s^2).

3. What factors can affect the acceleration of an Atwood's machine?

The acceleration of an Atwood's machine can be affected by the masses of the objects, the length and tension of the string or cable, and any external forces acting on the system, such as friction.

4. How does the acceleration change if the masses are equal?

If the masses on both sides of the pulley are equal, the acceleration of the Atwood's machine will be zero. This is because the forces on both sides of the pulley are balanced, resulting in no movement.

5. What is the significance of finding the acceleration of an Atwood's machine?

Finding the acceleration of an Atwood's machine allows us to better understand the principles of gravity and motion. It also has practical applications in fields such as physics and engineering, where it can be used to study and design more complex systems.

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