Moment of inertia and Atwood Machine

[doub]

Homework Statement

The question is from a lab. The lab used an Atwood Machine with two masses suspended string looped over a pulley. The time for one mass to reach the ground was measured and acceleration of the mass was calculated. The results were plotted on a graph of weight difference (Y) vs acceleration (x).

The question is from the linear fit, slope value, calculate the moment of inertia of the pulley.

Linear Fit equation y=mx+b

m(slope): 6.762 g/m/s^2

Homework Equations

I= 1/2mr^2

The Attempt at a Solution

Many attempts at trying to determine the moment of interia from the slope, however I get lost because the radius of the pulley was not measured in the lab. The assumption is made that pulley it self in frictionless.

Thanks in advance

 

[SammyS]

Homework Statement

The question is from a lab. The lab used an Atwood Machine with two masses suspended string looped over a pulley. The time for one mass to reach the ground was measured and acceleration of the mass was calculated. The results were plotted on a graph of weight difference (Y) vs acceleration (x).

The question is from the linear fit, slope value, calculate the moment of inertia of the pulley.

Linear Fit equation y=mx+b

m(slope): 6.762 g/m/s^2

Homework Equations

I= 1/2mr^2

The Attempt at a Solution

Many attempts at trying to determine the moment of inertia from the slope, however I get lost because the radius of the pulley was not measured in the lab. The assumption is made that pulley it self in frictionless.

Thanks in advance

Hello doub. Welcome to PF !

Do you know the equation of motion for Atwood Machine ?

You need the two mass values as well as the radius of the pulley. The radius of the pulley gives the connection between the acceleration of the two masses and the angular acceleration of the pulley.

See the Wikipedia article for an Atwood Machine: http://en.wikipedia.org/wiki/Atwood%27s_machine

 

[doub]

I know the two mass values, however we do not know the radius of the pulley.

In the first trial the m1 mass is 122.59 g and the m2 mass is 113.46 g with the accelerations calculated as 0.07 m/s^2

Trial 2 m1 mass 124.34 g m2 mass 111.71 g with the acceleration calculated as 0.21 m/s^2

And a correction on the slope. The slope value s 5.801 g/m/s^2

I'm not sure if that clarifies things

 

[SammyS]

I know the two mass values, however we do not know the radius of the pulley.

In the first trial the m1 mass is 122.59 g and the m2 mass is 113.46 g with the accelerations calculated as 0.07 m/s^2

Trial 2 m1 mass 124.34 g m2 mass 111.71 g with the acceleration calculated as 0.21 m/s^2

And a correction on the slope. The slope value s 5.801 g/m/s^2

I'm not sure if that clarifies things

The best that you can do is to fine I/r² .

You'll have two values for that. One from each trial.

 

[Nickie]

As a scientist, it is important to always consider the limitations and uncertainties in any experiment or measurement. In this case, the lack of measurement for the pulley's radius and the assumption of a frictionless pulley are important factors to consider when trying to determine the moment of inertia from the slope of the linear fit.

To accurately calculate the moment of inertia using the slope, we would need to know the radius of the pulley as well as the mass of the pulley itself. This information could potentially be obtained through further experimentation or by consulting previous research on the specific pulley used in the Atwood Machine.

Alternatively, if the goal is to simply demonstrate the relationship between the weight difference and acceleration, the slope value can still be used to determine the ratio of the masses and their acceleration due to gravity. However, it is not possible to accurately determine the moment of inertia without more information about the pulley.

In conclusion, while the results of the experiment may provide valuable insights into the relationship between weight difference and acceleration, it is important to acknowledge the limitations and uncertainties in the data and to consider further experimentation or research to accurately determine the moment of inertia.