Measuring Gravitational Acceleration using Timing Gates( continued)
YEARS 7 – 12 IDEAS ARTICLES FOR THE CLASSROOM
Measuring Gravitational Acceleration using Timing Gates( continued)
2. Each steel ball bearing is rolled slowly off the top light gate so it drops through both light beams. To improve the aim in the experiment the ball is aligned with a thin groove on the top of the light gate over the centre of the light beam. This groove is shown in the image below.
3. The time intervals t 2 between the ball breaking each beam were recorded for successful runs. This data was recorded to microsecond precision( 6 decimal places).
{ In our experiment a problem was found for large values of h 2
. If the aim was poor so the ball missed the lower light beam the clock did not stop. The clock is stopped by passing a finger through the light gate, giving a large unrealistic value that must be neglected. The following runs might then be successful.}
Results: Raw Data for the times t 2( in seconds) and looking for outliers.
Standardised Residuals t 2
( second) for various h 2( value-mean)/ SD
|
h 2
( mm)
|
93 |
281 |
1027 |
93 |
281 |
1027 |
run1 |
0.099564 |
0.197552 |
0.413608 |
-0.03971 |
0.454012 |
-0.7572 |
run2 |
0.099456 |
0.196776 |
0.414252 |
-0.52703 |
-0.77442 |
0.004733 |
run3 |
0.099384 |
0.197644 |
0.414220 |
-0.85191 |
0.59965 |
-0.03313 |
run4 |
0.099724 |
0.197300 |
0.414520 |
0.682247 |
0.055089 |
0.321811 |
run5 |
0.099396 |
0.195996 |
0.414532 |
-0.79776 |
-2.00918 |
0.336008 |
run6 |
0.099180 |
0.196584 |
0.414004 |
-1.7724 |
-1.07836 |
-0.28868 |
run7 |
0.099620 |
0.197468 |
0.415720 |
0.212976 |
0.321038 |
1.741563 |
run8 |
0.099788 |
0.198156 |
0.412412 |
0.971028 |
1.410159 |
-2.17222 |
run9 |
0.099920 |
0.197648 |
0.414680 |
1.566641 |
0.605982 |
0.511111 |
run10 |
0.099696 |
0.197528 |
0.414532 |
0.555905 |
0.416019 |
0.336008 |
count |
10 |
10 |
10 |
|
|
|
mean |
0.0995728 |
0.197265 |
0.414248 |
|
|
|
st. dev. |
0.000222 |
0.000632 |
0.000845 |
|
|
|
st. error |
0.000070 |
0.000200 |
0.000267 |
|
|
|
As expected, the results of any measurement process show some variation. Collecting and processing the data in a spreadsheet allows formulas to be used and copied. These data all lie within
3 standard deviations of the mean, so there are no outliers. If they do occur, these outliers are often neglected.
60 SCIENCE EDUCATIONAL NEWS VOL 67 NO 3