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course Phy 241
12/10 5
Domino DataLength | Width | Height
7.9cm 1.3cm 3.9cm
What is the volume of the domino you measured?
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7.9cm long, 1.3cm thick, 3.9cm wide
volume is 40.053cm^3
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What do you find to be the uncertainties in length, width and thickness?
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edges are beveled, on the corners they are beveled in 3 directions. so the percent uncertainty should be much greater than origionally thought.
from the flats, it was 7.85cm, to the longest side it was 7.9cm. so the bevel took away roughly 5mm. give or take more. lets say 3 times that for 8 corners and 8 sides,
so very roughly I could say 5mm(3)(4corners) + 8sides(5mm) = 100mm. this is rounding down. so volume is give or take 10cm^3 this reflects a 25% uncertainty. Which is quite a lot but given our measurement techniques,
It seems reasonable.
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What therefore are the percent uncertainties in length, width and thickness?
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length: .25*7.9cm = +- 1.96cm
Width: .25*1.3cm = +- 0.325cm
Height: .25*3.9cm = +- 0.96cm
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Which measurement has the greatest percent uncertainty and why?
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well the longest side because the more length, then more that percentage of uncertainty is accounted for because of the largly beveled corners.
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What is the uncertainty in your calculated volume, based on percent uncertainties in your measurements of length, width and thickness?
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total volume is 40.053cm^3. based on uncertainty is +- 10cm^3 because 25% of 40 is 10. so anywhere from 30cm^3 to about 50cm^3
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Good thinking about the bevel, but there's no way it reduces the volume by 25%.
The effect of the bevel on the length, width and thickness measurements would be must less than +- 25%. You know very well that the length is very significantly greater than 6 cm and very significantly less than 10 cm.
In fact, if you measured carefully, even 7.7 cm or 8.1 cm would be clearly greater than the length. So your uncertainty is almost certainly less than +- .2 cm.
Are you accurate within +-.1 cm? What about +- .05 cm?
What do you think is the limit of your accuracy in finding the length?
The same questions apply to the width and thickness.
What are the corresponding percent errors?
If you ignore the bevel, what are the percent uncertainties in length, width and thickness, and what is the percent uncertainty in volume?
Now, about the bevel. The bevel doesn't extend 5 mm, which would be .5 cm, from the original edge. Think of the thinnest edges of the domino. They are mostly flat (otherwise they wouldn't be very stable when balanced on that edge), and they are only about 13 mm wide. If the flat part is only half the width, that still leaves only about 6 mm for the two bevels, meaning that the bevels are at most 3 mm. I suspect they are closer to 2 mm.
Assuming the bevel is more or less in the shape of a quarter-circle, how many mm^3 of material would have to be removed from one of the long edges? How much from all 6 edges?
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