Investigation
7: Measuring g with a simple pendulum
Name:
Emil Heinäaho
Group:
Tanja Ohra-aho, Anna-Karin Teir, Filip Norrgård, Antti Kataja
Date:
17.9.99
Emphasized criteria: Pl (a), Pl (b), DC, DA, Ev
AIMS
The
research question in this investigation was to use a simple pendulum to find
out the value of gravity acceleration. The formula that was used in the
investigation can be found in Giancoli: Physics, 5th edition on page
319. Based on that, the following hypothesis was made: the gravity acceleration
is always the same. This means that the value would be 9,81 m/s^2, because the
gravity acts always in the same way on the objects. The key variables were the
time values that were gotten from the pendulum, because they were not going to
be as exact as hoped.
METHODS
The
following apparatus was selected: a “foot”, a string, a small weight and some
timing watches. There was used two watches to get an average value which would
give then a better result. The variables were controlled by choosing an enough long
string so that the escalations would be enough big. When the escalations are
big it is easier to measure the time. The raw data was collected by taking the
time of five escalations and then calculating the time for one escalation. One
escalation started at the “foot”, went to right, came back and went up to left
and when it passed the “foot” it had escalated ones. In other words, every
second “foot passing” was an escalation. The investigation was done twice with
two different string lengths.
RESULTS
The raw
data was collected with the method above with some small problems with the time
taking but they could be handled. The data is presented in a table.
|
The length of the string: |
0,43 m |
0,24 m |
|
The length of one oscillation: |
1,30 s |
1,08 s |
The uncertainties of the data are estimated to be negligible in the lengths but the time values have some small uncertainties.
DATA
ANALYSIS
The raw
data was processed in the following way: the values were used in the formula, T
= 2*Pi*( l/g )^½. The formula was used to solve the g, so it had to be
transferred in to a form: g = l / ( T^2 / 4*Pi^2 ). By using the formula there
was gotten the values that can be seen in Figure 1. The result of this
analysis is that the value of gravity acceleration based on the experiment is
9,08 m/s^2. Based on the book and the knowledge there can be said that the
value should be 9,81 m/s^2 which is known as the gravitational acceleration
constant. The effect of the uncertainties on this is easily seen. The reason
for this is the timing which was not as exact as there was wanted.
EVALUATION
The
conclusion of this investigation is that the value of the gravity acceleration
is always 9,81 m/s^2 so in every formula and theory where the symbol g is
stated to be the gravity acceleration the value 9,81 m/s^2 is valid to use.
There has to remembered that this value works only on Earth! The weakness of
the procedure is the time taking which effects have been already stated. The
following improvements are suggested: there could be used a real pendulum where
the motion would be more stable and maybe the time taking could be at least a
bit easier.
APPENDIX
The
instructions can be seen on page 7.
|
STRING |
|
GRAV. ACC. |
|
|
LENGHT |
|
VALUE |
|
|
0,43 |
m |
10,04 |
m/s^2 |
|
0,24 |
m |
8,12 |
m/s^2 |
|
|
|
|
|
|
|
Average : |
9,08 |
m/s^2 |
Figure 1