Time Uncertainty Propagation - Stoke's Law & Average Time

[adityax26]

Homework Statement

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So basically I am calculating the terminal velocity for a small sphere falling in a measuring cylinder filled with glycerine. The distance traveled is 20 cm (0.20 m), and I have conducted 3 trials for each temperature.

I have measured the displacement of the ball using a smartphone camera with 960 FPS, which gives me a absolute uncertainty of 1/960 = (approximately) ± 0.01 s for time.

Now I am wondering, how do I find the uncertainty in the AVERAGE time of 3 trials at any temperature? Does the absolute uncertainty stay at ± 0.01 s for the average? Do I look at the range? Again; I measured time using a smartphone capturing at 960 FPS.

Homework Equations

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Uncertainty propagation: relative/percentage uncertainty..?

The Attempt at a Solution

Using the same absolute uncertainty for each trial, I could use ± 0.01 s as uncertainty for time.

However, looking at the range, all of my temperatures have a range of around ± 0.06 s (minimum and maximum times differ by around this much for every temperature). Should I use this as my uncertainty?

Thanks!

 

[tnich]

Homework Statement

[/B]
So basically I am calculating the terminal velocity for a small sphere falling in a measuring cylinder filled with glycerine. The distance traveled is 20 cm (0.20 m), and I have conducted 3 trials for each temperature.

I have measured the displacement of the ball using a smartphone camera with 960 FPS, which gives me a absolute uncertainty of 1/960 = (approximately) ± 0.01 s for time.

Now I am wondering, how do I find the uncertainty in the AVERAGE time of 3 trials at any temperature? Does the absolute uncertainty stay at ± 0.01 s for the average? Do I look at the range? Again; I measured time using a smartphone capturing at 960 FPS.

Homework Equations

[/B]
Uncertainty propagation: relative/percentage uncertainty..?

The Attempt at a Solution

Using the same absolute uncertainty for each trial, I could use ± 0.01 s as uncertainty for time.

However, looking at the range, all of my temperatures have a range of around ± 0.06 s (minimum and maximum times differ by around this much for every temperature). Should I use this as my uncertainty?

Thanks!

Part of your problem may be that you are not distinguishing between precision and error. You say the uncertainty in the time measurement is ±0.01s. I assume you mean that the time stamp on each frame is expressed as a time in seconds with two decimal places. That would be the precision of your measurement.
The error of your measurements is affected by various things, like variation of temperature within the fluid, velocity of the sphere when it enters the fluid, etc. The standard deviation of your measurements gives you an estimate of the size of the random component of error. (There may also be bias (non-random) errors which are constant over all of your trials.) The standard error of the mean gives you an estimate of the accuracy of your calculated mean value.

 

[adityax26]

Part of your problem may be that you are not distinguishing between precision and error. You say the uncertainty in the time measurement is ±0.01s. I assume you mean that the time stamp on each frame is expressed as a time in seconds with two decimal places. That would be the precision of your measurement.
The error of your measurements is affected by various things, like variation of temperature within the fluid, velocity of the sphere when it enters the fluid, etc. The standard deviation of your measurements gives you an estimate of the size of the random component of error. (There may also be bias (non-random) errors which are constant over all of your trials.) The standard error of the mean gives you an estimate of the accuracy of your calculated mean value.

oh, we didn't learn any of that, only ever used S.D. in biology as uncertainty. My physics teacher said I could use ± 0.01 s for each trial, and keep this uncertainty for the average in time trials too; would that be fine you think?