PHY 201
Your 'cq_1_7.1' 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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Seed Question 7.1
A ball falls freely from rest at a height of 2 meters. Observations indicate that the ball reaches the ground in .64 seconds.
Based on this information what is its acceleration?
answer/question/discussion:
First we must find VAve
vAve = 'ds/'dt
vAve = 2/.64
vAve = 3.125
Then we need to find vF and we already know v0 = 0
vAve = (vF+v0)/2
3.125 = (vF)/2
vF = 6.25
**I should have known just to double the average velocity since the object started out at rest.
Then we know that 'dv = 6.25 m/s
So acceleration therefore:
a = 'dv/'dt
a = 6.25/.64
a = 9.77 m/s/s
Is this consistent with an observation which concludes that a ball dropped from a height of 5 meters reaches the ground in 1.05 seconds?
answer/question/discussion:
vAve = 5/1.05
vAve = 4.76 m/s
v0 = 0 m/s
vF = 9.52 m/s
'dv = 9.52 m/s
a = 9.52/1.05
a = 9.07 m/s/s
No the acceleration has decreased a small amount.
Are these observations consistent with the accepted value of the acceleration of gravity, which is 9.8 m / s^2?
answer/question/discussion: The first object falling from a short heighth was closer to the acceleration of gravity than the one dropped from 5m. I believe this is due to friction in the air possibly as the object gains speed. If the object were in a frictionless environment then it would have a free fall acceleration of 9.8 m/s/s
This depends on how accurate you think the observations are.
The two results for acceleration differ by about 7%.
Assuming that the uncertainty in distance measurement is insignificant, a 3.5% uncertainty in measuring the time interval will result in a 7% uncertainty in the calculated acceleration.
This is because in the process of finding acceleration we divide twice by the time interval, once when finding average velocity and once when finding average rate of change of velocity. The uncertainty is therefore compounded. The first division results in a 3.5% uncertainty; the second adds another 3.5% to the uncertainty.
If the timing uncertainty is less than about 3.5% then the difference in accelerations is probably significant. If the timing uncertainty is more than about 3.5% then the difference is probably not significant.
There's more to it than this. However to fully answer the question of significance would require more use of statistics than is appropriate to this course, for which a prior statistics course is not a prerequisite.
&#Your work looks good. See my notes. Let me know if you have any questions. &#