Lab #17 Free Fall

Sample LabPH111

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 Error Estimation, and Observations

We measured the height of the building with aStanley 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. 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 error 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 in good condition, so we estimated the error as the scale limit of the device.

Mass of the basketball: 0.6250 ± 0.0001 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 in good condition, so we estimated the error as the scale limit of the device.

Mass of the metal ball: 2.109 ± 0.001 kg

Mass of the bowling ball: 6.488 ± 0.001 kg

We measured the times with a Casio model R2D2 stopwatch. We estimated the error for each measurement as 0.10 seconds due to the limitations of human response time and the scale limit of the stopwatch.

The metal ball and bowling ball dented the ground, possibly caused the distance traveled to increase for subsequent drops.

Calculationsand Graphs

Note that you do not need to provide this high level of detail in your calculations in your lab reports.

h = height of building

h = 33.345 m.

t1 = average time for basketball

t1 = (2.80 + 2.80 + 2.78 + 2.65 + 2.70)/5 = 2.75 s.

t2 = average time for metal ball

t2 = (2.61 + 2.53 + 2.59 + 2.65 + 2.70)/5 = 2.62 s.

t3 = average time for bowling ball

t3 = (2.71 + 2.66 + 2.68 + 2.54 + 2.69)/5 = 2.66 s.

We used a coordinate system with down as the positive direction. We deemed any lateral motion irrelevant. We also assumed that the initial velocity was zero.

h = height

a = acceleration

h = ½at2

a= 2h/t2

a1 = acceleration of basketball

a1 = 2(33.345)/2.752 = 8.82 m/s2

a2 = acceleration ofmetal ball

a2 = 2(33.345)/2.622 = 9.72 m/s2

a3 = acceleration of bowling ball

a3 = 2(33.345)/2.662 = 9.42 m/s2

The above graph is not particularly informative, but it is here to show the approved format for graphs. You are not required to make a graph unless the lab instructions specifically say so.

Conclusion

The experimental values for the free fall accelerations of the ballsdo not match the theoretical values. Two of the three objects had accelerations significantly under the accepted value. We conclude that not all objects have the same acceleration and that the accepted value is incorrect.

Our time calculations were imprecise since we used a stopwatch. Photogates or videotape could be more precise. Air resistance probably played a role since the experimental accelerations were lower than expected. An experiment in a vacuum would eliminate this problem. Distance measurements could be improved with a laser range finder.