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Phy 231
Your 'cq_1_09.1' 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?
answer/question/discussion: ->->->->->->->->->->->-> :
`ds = 20 cm; v0 = 0 cm/s; `dt = 2 s
vAve = `ds / `dt
= 20 cm / 2 s
= 10 cm/s
vAve = (vf + v0) / 2
(2*vAve) = vf + v0
vf = (2*vAve) v0
= (2*10 cm/s) 0 cm/s
= 20 cm/s
a = `dv / `dt; a = (vf v0) / `dt
= (20 cm/s 0 cm/s) / (2 s)
= (20 cm/s) / (2 s)
= 10 cm/s^2
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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?
answer/question/discussion: ->->->->->->->->->->->-> :
`dt = 2 s
x = actual time interval
2 s - .03x = x
x + .03x = 2 s
1.03x = 2 s
x = 2 s / 1.03
x = 1.94 s
vAve = `ds / `dt
= 20 cm / 1.94 s
= 10.3093 cm/s
vAve = (vf + v0) / 2
(2*vAve) = vf + v0
vf = (2*vAve) v0
= (2*10.3093 cm/s) 0 cm/s
= 20.6186 cm/s
a = `dv / `dt; a = (vf v0) / `dt
= (20.6186 cm/s 0 cm/s) / (1.94 s)
= (20.6186 cm/s) / (1/94 s)
= 10.628 cm/s^2
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What is the percent error in each?
answer/question/discussion: ->->->->->->->->->->->-> :
percent error = [(actual estimated) / actual]*(100)
vAve (actual) = 10.3093 cm/s
vAve (estimated) = 10 cm/s
percent error
= [(10.3093 cm/s 10 cm/s) / 10.3093 cm/s]*(100)
= (0.3093 cm/s / 10.3093 cm/s)*(100)
= 3.00 percent error
a (actual) = 10.628 cm/s^2
a (estimated) = 10 cm/s^2
percent error
= [(10.628 cm/s^2 10 cm.s^2) / 10.628 cm/s^2]*(100)
= (0.628 cm/s^2 / 10.628 cm/s^2)*(100)
= 5.91 percent error
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If the percent error is the same for both velocity and acceleration, explain why this must be so.
answer/question/discussion: ->->->->->->->->->->->-> :
The percent error is not the same for both velocity and acceleration.
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If the percent errors are different explain why it must be so.
answer/question/discussion: ->->->->->->->->->->->-> :
The percent errors are different because the error was due to the time interval, and for velocity you divide by time (s) but for acceleration you divide by time squared (s^2).
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About 30 min
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