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Old Oct 7th 2018, 09:54 AM   #1
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Theoretical vs. Expermental values

I did a Half-Atwood machine experiment using a car where I obtained 3.6% of difference between the theoretical and experimental force, while the percent difference between the theoretical and experimental acceleration was 18%!! The experimental force was the mean of a Force vs. Time graph, while the experimental acceleration was the slope of a Velocity vs. Time graph.

What are the reasons for the differences between theoretical and experimental values? Does the experimental acceleration have a higher percent of difference because of friction?
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Old Oct 7th 2018, 04:59 PM   #2
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Well, according to propagation of errors in quadrature, you would expect a percentage error in the acceleration to be the same as the percentage error in the resultant force. However, all sorts of things might be responsible for the greater error. For example:

1. Your apparatus may be set up imprecisely (e.g. horizontal beam isn't horizontal, mass is different to the model value, etc.)
2. Inaccurate representation of the resultant force because of "intrusive" forces (like air resistance, friction, movement of apparatus, etc.)
3. The precision on your speedometer or clock may be poor

There's more too, but you'd have to consider the situation you have and try and gauge what may be the biggest factors affecting your uncertainty.
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Old Oct 8th 2018, 06:29 AM   #3
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You mention that the force was the mean of a force vs time graph

How was the force determined?
was it not just mass times gravity?
in which case how did it vary with time?

It can be informative to do the experiment many times,
and analyse the statistical variability of the results.
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Old Oct 8th 2018, 08:10 AM   #4
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I did various runs and still obtained the same acceleration. The experimental force was the mean in a force vs. time graph and the theoretical one was determined by multiplying the car + sensors mass x the theoretical acceleration.
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Old Oct 8th 2018, 08:11 AM   #5
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Originally Posted by benit13 View Post
Well, according to propagation of errors in quadrature, you would expect a percentage error in the acceleration to be the same as the percentage error in the resultant force. However, all sorts of things might be responsible for the greater error. For example:

1. Your apparatus may be set up imprecisely (e.g. horizontal beam isn't horizontal, mass is different to the model value, etc.)
2. Inaccurate representation of the resultant force because of "intrusive" forces (like air resistance, friction, movement of apparatus, etc.)
3. The precision on your speedometer or clock may be poor

There's more too, but you'd have to consider the situation you have and try and gauge what may be the biggest factors affecting your uncertainty.
Thank you, I will evaluate my results considering those factors.
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Old Oct 8th 2018, 02:38 PM   #6
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Don't forget that there is friction in the apparatus - in the pulleys and especially in the wheel/axle bearings and between wheels and the table. This may the major source of reduction of acceleration from theoretical.
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