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