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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?
I used the classic equations at my disposal to find all the necessary quantities. First I found vAve
‘ds = vAve * ‘dt
20 cm = vAve * 2sec
vAve = 10 cm /sec
Now I find vf.
vAve = (v0 + vf) / 2
10 cm/sec = vf/2
Vf = 20 cm /sec
Now I find the acceleration of the ball
Vf^2 = v0^2 + 2a * ‘ds
(20cm/sec)^2 = 2a * 20 cm
400 cm /sec = 2a * 20cm
20 cm/sec^2 = 2a
A = 10cm/sex^2
answer/question/discussion:
• 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?
Then I would take 3% of every value and add it to the one that I calculated.
Final velocity = 20cm/sec. 3% of that is 0.6. So the actual value is 20.6 cm/sec
Acceleration = 10cm/sec^2. 3% of that is 0.3. So the actual value is 10.3cm/sec^2
Acceleration is found by dividing change in velocity by change in clock time. The result is not 10.3 cm/s^2, and it differs from the formerly calculated acceleration by something other than 3%.
answer/question/discussion:
• What is the percent error in each?
Percent error = ((calculated – accepted value)/ accepted value) * 100
Percent error = ((20cm/sec – 20.3cm/sec)/(20.3 cm/sec) * 100
20.3 cm/s was not the result of any of these calculations.
Percent error = -1.47 % for final velocity
Percent error = ((10cm/sec^2 – 10.3cm/sec^2) / (10.3cm/sec^2) * 100
Percent error = -2.91 %
answer/question/discussion:
• If the percent error is the same for both velocity and acceleration, explain why this must be so.
They are not the same. The value of final velocity was double the acceleration. Therefore the percent error is about double.
If a quantity is doubled, and then a quantity which differs from it by 3% is doubled, then the two doubled quantities will differ by 3%.
If you double 1.03 x you get 2 * 1.03 x = 1.03 * 2x, which differs from 2x by 3%.
answer/question/discussion:
• If the percent errors are different explain why it must be so.
answer/question/discussion:
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20 minutes
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