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course PHY 231
10/30 9:42 am
`q001. If the acceleration of an Atwood system with total mass 80 grams is 50 cm/s^2, then:• How much mass is on each side? Note that this can be reasoned out easily without a complicated analysis, using the same type of reasoning that led us to conclude that a system with 31 g on one side and 30 g on the other accelerates at 1/61 the acceleration of gravity.
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• 36, 44
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We can reason that since 50 cm/s^2 is about 1/20 the acceleration of gravity, the difference in the masses should be 1/20 the total mass. That would be a 4 gram difference, implying masses of 38 grams and 42 grams.
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I used that 1/20 reasoning but my mistake was that I didn't see it was a TOTAL difference of 4 and not 4 on both, making the difference btw 38,42 and 36,44.
I could tell what you were thinking the first time; very easy mistake to make.
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• Assuming uniform acceleration in each case, is a graph of acceleration vs. number of clips linear?
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• No, if it were linear then each clip would add the same amount of travel time and it doesn't because the times are not linear, +3clips = +3.5s.
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travel time is not proportional to acceleration, nor is it inversely proportional
How would travel time be expected to vary with net force if acceleration vs. number of clips was linear?
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Right, because here it's t= sqrt(2x/a), since x0 and v0 = 0 and x is constant, so t is proportional to the sqrt of the inverse of a. If it was linear the proportion would be t=ka, and so an increase in a would translate to a (k*'da) increase in t. Linear also meaning 'a constant multiple of'.
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Good. Can you use this reasoning to figure out if uniform acceleration is possible for the given data? Don't get bogged down, because this is still a tricky question.
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