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course Phy 241
1. If a ball requires 2 seconds to accelerate from rest along 3 dominoLengths of track, what was its average speed during that time? 1.5 Dominos/Sec
2. Answer the same question if the time interval for the 3 dominoLength distance is 1 second, and again if the time is 1.5 second
3 Dominos/Sec and 2 Dominos/Sec
3. Does the average speed change as much between the 1 second and 1.5 second time intervals as between the 1.5 and 2 second intervals?
It changes more from 1 to 1.5 the average speed is 2/3 of the original compared to 1.5 to 2 where the average speed is ¾ of the original
4. For the case where the ball required 1.5 seconds to coast from rest through 3 dominoLengths, the initial speed of the ball was zero. You have calculated its average speed. What final speed, averaged with the initial speed, would result in the same average speed?
4 Dominos/Sec
5. Assuming the final speed is the one you just calculated, how quickly was the speed changing during the 1.5 seconds? Your final answer to this question should be one single quantity.
~2.67 Dominos/sec2
6. For the 1 second and 2 second intervals, how quickly was the speed changing?
For 1 second 6 Dominos/sec2 For 2 seconds 1.5 dominos/sec2
7. If you had four dominoes with thicknesses 10 mm, 11 mm, 12 mm and 13 mm, and repeatedly scrambled and stacked them into stacks of two, it would be possible to get stacks of equal height and stacks of unequal height.
How many different heights are possible?
6
8. What height differences are possible between the two stacks (0 would be regarded as a height difference)?
0mm 2mm 4mm
9. What would be the probability of each of the possible height differences?
0mm 1/12 2mm 5/6 4mm 1/12
10. If you had six dominoes with heights 10, 10.5, 11, 11.5, 12 and 12.5 cm, what height differences are possible when comparing stacks of three, and what is the probability of each on a random stacking?
.5mm 1.5mm 2.5mm 3.5mm 4.5mm
11. If each domino pip is a hemisphere and the diameter of a pip is 1/4 of the domino's width and 1/2 of its thickness, then what percent of the domino's volume would need to be removed to make a single pip?
~1.5% (1/2 * 1/8 * 1/4)
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If the pip was a cube this would be accurate.
However the pip is only a hemisphere, which would fit inside the lower half of the cube.
The ratio of sphere volume to cube volume is 4/3 pi r^3 / (2 r)^3 = 4/3 pi r^3 / (8 r^3) = pi/6, a bit more than 1/2.
So your 1.5% gets whittle down to .75% right away, then to pi/6 times this. I think the result comes out around .41% (compare to half of .75%, which would be .375%).
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12. How much would the presence of pips add to the percent uncertainty in the volume of a domino?
~19% (12 * 1/8 *1/2 *1/4)
13. If the thicknesses of a set of dominoes varies by as much as 5%, then how much uncertainty would you expect in the actual weight of an object which was found to be equal to that of 4 randomly selected dominoes?
21%
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4 dominoes, each off by 5% in the same direction, would be off by 20% of the weight of a single domino. But the object 's weight is that of 4 dominoes.
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Good work, but check my notes.
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