Sample Lab PH201-203
Feedback
“Graph is not in the correct format. Acknowledgements and suggestions for improvement
are missing.”
Purpose
We wish to calculate the free fall accelerations of several balls and test if they are equal to
each other and the accepted value for Salem, Oregon of 9.806 ± 0.001 m/s2.
Raw Data, Initial Uncertainty Estimation, and Observations
We measured the height of the building with a Stanley tape measure. The tape measure
appeared to be worn, but this does not seem significant. The tape was slightly curved in the
middle when fully extended. We weren’t sure if we released each ball from the same height.
The ground was not level, so the measured height depended on where we placed the end of
the tape. Taking into account these problems and the scale limit of the device (1 mm), we
estimated the uncertainty for the height of the building as 6.8 cm.
Height of the building: 33.345 ± 0.068 m.
We measured the mass of the basketball on a Fisher G50 scale. The scale was recently
calibrated and appeared to be fairly new. The ball may have picked up some dirt particles for
subsequent drops.
Mass of the basketball: 0.6251 ± 0.0020 kg.
We measured the mass of the bowling ball and metal ball on a Fisher G120 scale. This scale
was less precise, but it could measure the larger masses. The scale was recently calibrated and
appeared to be new. The balls may have picked up some dirt particles for subsequent drops.
Mass of the metal ball: 2.109 ± 0.003 kg.
Mass of the bowling ball: 6.488 ± 0.003 kg.
We measured the times with a Casio model R2D2 stopwatch. We estimated the uncertainty
for each measurement as 0.10 seconds due to the limitations of human response time and
the scale limit of the stopwatch.
Trial
1
2
3
4
5
Basketball
2.80
2.80
2.78
2.65
2.70
Metal Ball
2.61
2.53
2.59
2.65
2.70
Bowling Ball
2.71
2.66
2.68
2.54
2.69
We noticed that the metal ball and bowling ball dented the ground, possibly causing the
distance traveled to increase for subsequent drops.
Calculations, Uncertainty Propagation, and Graphs
We used a coordinate system with down as the positive direction. We deemed any lateral
motion irrelevant. We also assumed that the y-component of the initial velocity vector was
zero.
Δy = vit + ½at2
Δy = ½at2
a = 2Δy /t2
Sample calculations for basketball
t = (2.80 + 2.80 + 2.78 + 2.65 + 2.70)/5 = 2.75 s.
tmax = (2.90 + 2.90 + 2.88 + 2.75 + 2.80)/5 = 2.85 s.
tmin = (2.70 + 2.70 + 2.68 + 2.55 + 2.60)/5 = 2.65 s.
a = 2(33.345)/2.752 = 8.82 m/s2
amax = 2(33.345 + 0.068)/2.652 = 9.52 m/s2
amin = 2(33.345 – 0.068)/2.852 = 8.19 m/s2
Ball
Basketball
Metal ball
Bowling ball
m (kg)
0.6251
2.109
6.488
± (kg)
0.0020
0.003
0.003
t (s)
2.75
2.62
2.66
tmax (s)
2.85
2.72
2.76
tmin (s)
2.65
2.52
2.56
a (m/s2)
8.82
9.72
9.42
amax (m/s2)
9.52
10.52
10.20
amin (m/s2)
8.19
9.00
8.74
You are not required to make a graph unless the lab instructions specifically say so. Note that the error bars
for theoretical values and mass are too small to be seen.
Conclusion and Acknowledgements
The experimental ranges for the free fall accelerations of the balls overlapped with one
another. Two of the three objects had accelerations that overlap with the accepted value. We
conclude that all objects have the same acceleration regardless of mass and that the accepted
value is correct.
Our time calculations were imprecise since we used a stopwatch. Photo gates or videotape
could be more precise. Air resistance probably played a role since the experimental
accelerations were slightly lower than expected. An experiment in a vacuum would eliminate
this problem. Distance measurements could be improved with a laser range finder. It would
be interesting to try different locations on Earth to see if we could detect differences in
gravity.
I would like to acknowledge Galileo for his experiments on acceleration and Vanilla Ice who
helped me with time measurements.