Phy231
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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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:
`ds=2m
`dt=0.64s
vAve=`ds/`dt=2m/.64s=3.125m/s
v0=0
Assuming constant acceleration from rest:
vf=2*vAve=2*3.125m/s=6.25m/s
`dv=vf-v0=6.25m/s-0=6.25m/s
a=`dv/`dt=6.25m/s/.64s=9.77m/s^2
• 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:
`ds=5m
`dt=1.05s
vAve=`ds/`dt=5m/1.05s=4.76m/s
v0=0
Assuming constant acceleration from rest:
vf=2*vAve=2*4.76m/s=9.52m/s
`dv=vf-v0=9.52m/s-0=9.52m/s
a=`dv/`dt=9.52m/s/1.05s=9.07m/s^2
• 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 is but the second is off a bit.
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30 minutes
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Very good. Whether the two results are consistent depends on the accuracy of the instruments used. Assuming distance of fall is measured accurately, the difference observed here could have resulted from a 4% uncertainty in time measurement. If timing was hand-triggered we would expect at least a 4% uncertainty. If timing was electronic (and set up correctly) the uncertainty would be much less than 4%.