phy121
Your 'cq_1_9.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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A ball accelerates uniformly as it rolls 20 cm down a ramp, starting from rest, in 2 seconds.
What are its average velocity, final velocity and acceleration?
vAve = `ds / `dt = 20cm / 2sec = 10cm/s
vF = 2vAve - v0 = 2(10cm/s) - 0m/s = 20cm/s
a = vF / `dt = 20cm/s / 2sec = 10cm/s/s
If the time interval is in error so that it is 3% longer than the actual time interval,
then what are the actual values of the final velocity and acceleration?
`dt = `dte - (`dte * .03) = 2 - (2 * .03) = 1.94sec
vAve = 20cm / 1.94sec = 10.31cm/s
vF = 2vAve - v0 = 2(10.31cm/s) - 0 = 20.62cm/s
a = vF / `dt = 20.62cm/s / 1.94 = 10.63cm/s/s
What is the percent error in each?
%error vF = (20.62cm/s / 20cm/s) * 100 - 100 = 3%
%error a = (10.63cm/s/s / 10cm/s/s) * 100 - 100 = 6.3%
If the percent error is the same for both velocity and acceleration, explain why this must be so.
No, they are not. This is due to the fact that acceleration gets a double dose of error due to math involving the quantity in error twice. Compounding error.
If the percent errors are different explain why it must be so.
This is due to the fact that acceleration gets a double dose of error due to math involving the quantity in error twice. Compounding error.
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20min
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