Roel
6/7/2011
6/8/2011
lab Christopher #1
The Pendulum and Error Analysis
Purpose
In this lab a metal ball was attached to a length of string from a fixed position. Time intervals
and the length of string the pendulum was attached to, were used to calculate gravity. Absolute and
relative error analysis equations were also used to account for human error.
Materials
The materials used in this experiment consisted of; a metal holder attached to a table, a length
of string, a steel ball, a protractor, a ruler and a timer. To being the procedure, a length of string was
measured to 50cm and then remeasured 5 times to calculate the possible error analysis that the string
was off by. Then the ball was released from 3 different angles (15, 30 and 80) and let swing for a
time of 10 periods (1 period is a back and forth swing) which was called 10T. 10T was then divided by
10 to come up with the time it took for the pendulum to swing and return to its starting. The error for T
was then calculated using .2 seconds as a response time.
Then the angle of 15 was held constant with the length of the pendulum being increased after
every 10T interval. The length of the pendulum was measured 5x which gave us a relative error for the
measurement. Relative errors for the timing of 10T was also calculated. Using this as well as (relative
error), graphs were constructed to represent the relationship between values.
Observations
Measurement # L of pendulum
1 50cm
2 50cm
3 49cm
4 49cm
5 50.5cm
angle
10T
15 13.8s
30 13.9s
80 15.7s
L
20cm
40cm
60cm
80cm
100cm
10T
9.0s
12.3s
15.2s
17.5s
19.4s
Summary and Calculations
Based on the slightly varying lengths for the pendulum in the first table of observations. The
relative error of the length was able to be calculated:
L calculated by:
For the angles 15, 30 and 80 it was possible to calculate a single T period from the original
10T segment that was recorded. From there, relative error was able to be calculated taking into account
human reaction time.
angle
1 0T
15 13.8s
30 13.9s
80 15.7s
T
T
1.38 .028
1.39 .028
1.57 .028
T calculated by:
T calculated part by:
For III absolute error of the length, period T, T, T^2, T^2, L^2 and L^2 were all
calculated.
L
20cm
40cm
60cm
80cm
100cm
L
.19cm
.24cm
.1cm
.3cm
.15
10T
9.0s
12.3s
15.2s
17.5s
19.4s
T
.9s
1.23s
1.52s
1.75s
1.94s
T
.028s
.028s
.028s
.028s
.028s
T^2
.81s^2
1.51s^2
2.31s^2
3.06s^2
3.76s^2
T^2
.05s
.069s
.085s
.098s
.109s
L^2
400cm^2
1600cm^2
3600cm^2
6400cm^2
10000cm^2
L^2
7.6cm
19.2cm
12cm
28cm
30cm
L calculated by:
T calculated by:
T calculated by:
T^2 calculated by:
L^2 calculated by:
L^2 calculated by:
Based on these numbers, graphs were then plotted using these numbers to represent the relationship
between these values.
Graph 1, M calculated by:
Error in slope calculated by:
Graph 2, M calculated by:
Graph 3, M calculated by:
G calculated by:
Error in G calculated by:
Questions:
1. The period T does vary with the angle , although the periods for 15 and 30 do overlap,
making them equal.
2. An angle of 15 was used as opposed to 30 or 80 because it had the smallest period and it was
thought that it would demonstrate a more linear relationship with the increasing length. This
will allow us to find a more accurate value of G.
3. The errors for L and T in parts I and III were absolute errors.
4. Equation 8 represents a relative error.
5. Relative errors are plotted on the graphs.
6. The graph best represented by a straight line is the graph: L=k(T^2)
7. The graph of L=k(T^2) will give us the most accurate slope as well as the most accurate reading
for gravity.
8. K(2^2)=g
9. g= 10.29 m/s^2 .095 m/s^2
Conclusion:
Looking over the lab I was very confused about the equation in question 8. I derived a different
formula to calculate G and got a somewhat close answer of g=10.29m/s^2 .095m/s^2. While I know
this is not a perfect value, it is much closer than what I got when given the equation in question 8.
While at times I was confused during this experiment I think it turned out surprisingly well despite the
sloppiness as well as human error factors that played in when using the stop watch to calculate time and
when releasing the pendulum at a certain angle.