SPH4U  Acceleration of Gravity  20030916 Mr. Taylor 

The purpose of this experiment is to observe the acceleration of an object caused by the Earth's gravity.
The acceleration of gravity is 9.8 m/s^{2} near the Earth's surface and when air resistance is negligible.

Thank you, Jian, for letting me use your diagram. 
Start Time 
Midpoint Time  Time Interval 
Change in Distance 
Distance from start d 
Speed 

0.0 s 
0.05 s 
0.1 s 
5.1 cm 
5.1 cm 
51 cm/s 
0.1 s 0.2 s 
0.15 s 
0.1 s 
14.5 cm 
19.6 cm 
145 cm/s 
0.2 s 0.3 s 
0.25 s 
0.1 s 
23.8 cm 
43.4 cm 
238 cm/s 
0.3 s 0.4 s 
0.35 s 
0.1 s 
33.8 cm 
77.2 cm 
338 cm/s 
0.4 s 0.5 s 
0.45 s 
0.1 s 
41.7 cm 
118.9 cm 
417 cm/s 
Acceleration = (change in speed)/(change in time)
From our observations, we can calculate four or five (assuming initial speed of 0 cm/s) values of acceleration. For example:
Acceleration = (145 cm/s  51 cm/s)/(0.15 s  0.05 s) = 940 cm/s^{2}
The first interval is smaller than the others:
Acceleration = (51 cm/s  0 cm/s)/(0.05 s  0.00 s) = 1020 cm/s^{2}
The following table shows the acceleration calculated for each interval:
Interval  Acceleration 

0.0 s 0.05 s 
1020 cm/s^{2} 
0.05 s 0.15 s 
940 cm/s^{2} 
0.15 s 0.25 s 
930 cm/s^{2} 
0.25 s 0.35 s 
1000 cm/s^{2} 
0.35 s 0.45 s 
790 cm/s^{2} 
Average  936 cm/s^{2} 
The following graphs show the position of the weight and the speed of the weight during the 0.5 s that the weight was falling. The acceleration of the weight is represented by the slope of the speedtime graph.
The speedtime graph shows that the line of best fit through most of the points has a slope of approximately
(430 cm/s)/(0.45 s) = 956 cm/s^{2}
This is another way of finding an "average" acceleration from our set of data.
Precision is the amount of variation in our measurements or calculated values.
Precision = (Biggest  Smallest)/Average = (1020 cm/s^{2}  790 cm/s^{2)}/ 936 cm/s^{2} = 0.25 = 25%
Accuracy = (Expected  Average)/Expected = (980 cm/s^{2}  936 cm/s^{2})/ 980 cm/s^{2} = 0.045 = 4.5%
For the slope of our line of best fit:
Accuracy = (Expected  Average)/Expected = (980 cm/s^{2}  956 cm/s^{2})/ 980 cm/s^{2} = 0.024 = 2.4%
Our hypothesis was based on typical reported values of the acceleration of gravity at the Earth's surface (see textbook). The expected value is 9.8 m/s^{2} = 980 cm/s^{2} . In this experiment, we found an average value of 936 cm/s^{2} for an accuracy of 4.5%, or using graphical methods, we found a value of 956 cm/s^{2} for an accuracy of 2.4%. With the type of equipment available in a high school science lab, an accuracy of less than 10% is acceptable, and we can say that this experiment supports our hypothesis.
The precision of our measurements was not very good  25% variation shows that there were many sources of error. The last measurement departed the most from the line of best fit. It is possible that the last measurement included a part of the time when the weight hit the school bag and slowed down. It would have been better to raise the buzzer and the starting point farther above the floor. Other possible sources of error may be air resistance, friction of the ticker tape through the buzzer, inaccurate release time, and variations in buzzer timing. Some of these problems may be overcome by using a timing and recording method that does not interfere with the movement of the weight. For example, we could try taking a video of a falling weight, with pictures being taken at very short intervals of time.
It is usually better to take a lot of measurements than just a few. In this lab, you could have exchanged results with other members of your team (since each member of the team should have had their own ticker tape to measure). In this way you could have had 15 or 20 acceleration values instead of just 5. For example:
Person 1  Person 2  Person 3  

Interval  Acceleration  Acceleration  Acceleration 
0.0 s 0.05 s 
1020 cm/s^{2} 
1020 cm/s^{2} 
760 cm/s^{2} 
0.05 s 0.15 s 
940 cm/s^{2} 
940 cm/s^{2} 
850 cm/s^{2} 
0.15 s 0.25 s 
930 cm/s^{2} 
900 cm/s^{2} 
890 cm/s^{2} 
0.25 s 0.35 s 
1000 cm/s^{2} 
1030 cm/s^{2} 
930 cm/s^{2} 
0.35 s 0.45 s 
790 cm/s^{2} 
790 cm/s^{2} 
830 cm/s^{2} 
Average  936 cm/s^{2} 
936 cm/s^{2} 
852 cm/s^{2} 
From this table we can calculate an overall average acceleration of 908 cm/s^{2}. this is actually LESS accurate than the first set of results, because the third member of the team had the poorest accuracy. However, it does indicate a systematic error: all the results are giving an acceleration less than our hypothesis. To reduce this error, we should look for factors in our experiment that were slowing the weight  for example, friction.