Atwood Machine Lab: Graphing and Finding Moment of Inertia | Homework Help

[rttackle]

Homework Statement

Good Morning, my teacher is making us redo this lab with data he collected. I was wondering if someone could check to see if I did it right so far. I have to graph the left side of equation B (in the spreadsheet) and the same for A. then I have to find the moment of inertia. This is different then what I have seen on here or elsewhere. It is difficult because he doesn't teach or explain well and the class is struggling. Any helpl is appreciated.
[/B]

Homework Equations

Did I do equation B right?
How do I get the moment of Inertia from this data?
Any other useful information one can provide is nice. [/B]

The Attempt at a Solution

 

[andrevdh]

Plot the the difference between the two weights, W₁ - W₂,
minus the resultant force, m_totala , as a function of the acceleration, a,
of the system. The gradient is the effective mass of the pulley and the y-intercept is
the friction in the system. We approximate the pulley with a disc so its moment of
inertia is then its mass time the square of its radius. Your accelerations look a bit
low though.

 

[rttackle]

Thanks, I'll try that when I get home. I'll look into why the acceleration is low. So the left side of the equations are essentially the weight differences between masses and difference between resultant forces?

Plot the the difference between the two weights, W₁ - W₂,
minus the resultant force, m_totala , as a function of the acceleration, a,
of the system. The gradient is the effective mass of the pulley and the y-intercept is
the friction in the system. We approximate the pulley with a disc so its moment of
inertia is then its mass time the square of its radius. Your accelerations look a bit
low though.

 

[andrevdh]

For these two masspieces
m₁ = 0.0432 kg and m₂ = 0.0072 kg
one get that the acceleration should be about 7 m/s²
assuming no friction and that the pulley has minimal influence (which
is what one would expect for the small mass of only five grams), where
as you get about 6 m/s².

Yes the equation basically says that the weight difference minus the
friction in the system gives us the resultant force, which is the total
mass (including the efffective mass of the pulley) times the acceleration
of the system.

 

[rttackle]

Thanks for the help. Just wondering if there is a better way to solve for the acceleration in this problem for future reference. Thanks again.

For these two masspieces
m₁ = 0.0432 kg and m₂ = 0.0072 kg
one get that the acceleration should be about 7 m/s²
assuming no friction and that the pulley has minimal influence (which
is what one would expect for the small mass of only five grams), where
as you get about 6 m/s².

Yes the equation basically says that the weight difference minus the
friction in the system gives us the resultant force, which is the total
mass (including the efffective mass of the pulley) times the acceleration
of the system.

 

[rttackle]

Also how do I get inertia

Thanks for the help. Just wondering if there is a better way to solve for the acceleration in this problem for future reference. Thanks again.

 

[andrevdh]

You seemed to have used a pulley with a photogate for the measurements
since you gave values for the angular acceleration of the pulley.
Just how you got the value for the angular acceleration is not clear.
You have several options that can be explored to get the acceleration
using such a system. It is always best to get the required value from a graph
of data and not just a single value. That way you have more confidence
in the final value that you require. Maybe a graph of the angular velocity
of the pulley as a function of time. You can also use the dimensions of
the pulley to calculate the distance through which the system travelled.

What is (the) inertia (of the system) measured in?

What type of graph will give you the inertia (of the system) as its gradient?