This is a paper I did for my IB HL physics class at UWC Adriatic. It is my first full lab report

1. IB Physics Higher Level
Full lab report on research question:
Galileo’s experiment: measuring from the motion of a
cart on a track
Student:
KlimentSerafimov
with lab partner
Ismail Ombo
under supervision of
Mark Sylvester
30.09.2013

2. Abstract
An experiment was performed to determine the acceleration due to gravity. A cart was placed at the
declined part of a ramp and pushed towards the inclined part. As the cart was moving up and then down
the ramp, its position and velocity were measured with an ultrasound position sensor. The sensor sent
the data to a software called “Data Studio” which was used to draw a velocity – time graph and also
determine the gradient of the velocity over a time interval (also known as the acceleration). This
acceleration was recorded several times for different inclinations of the ramp, and then with the data
gathered, and some formulae, the acceleration due to gravity could be determined.
Hypothesis:
The acceleration of the cart, if friction and air resistance are considered to be negligible,can be
calculated using
Here, α is the angle between the track and the horizontal table. Since α and remain constant
and , the graph should resemble a straight line (a linear function). However, in real
practice this doesn’t happen because of the effects of friction on the cart.
The graph that is obtained from the sensor can be described as follows: while the cart is going upwards,
gravity is helped by friction to slow down the cart faster, thus (the acceleration of the cart when
it’s going up) is greater than what should be. The opposite stands for the part of the graph when
the cart is going down. Now the friction works against gravity, thus (the acceleration of the cart
when is going down) should be less than what should be. In order to eliminate the effects of friction
and correctly determine the following formula should be used:
Here and are measured with the sensor and processed with “best line fit” option from “Data
Studio”.
Apparatus:
A cart with 2 weights;
A ramp, with 100 cm long;
Ultrasound position sensor and a computer to connect the sensor to;

3. Data collection and processing:
In order for the experiment to be consistent, several measurements took place for different inclination
angles. Because the value of the angle was not needed, it was only necessary to change the difference
between the heights of the two ends of the ramp. For each angle of the ramp 4 measurements were
done. For the sake of simplicity, only the heightof the higher end ( ) was changed, and the height of
the lower end ( ), was kept constant, .
Best line fit for the points of the graph that determine :
The velocity - time graph above shows the velocity points when the cart is traveling up (the points
marked with yellow). Here , the length of the ramp is 100cm, so
. The acceleration of the cart is given by the slope of the best line fit for the graph, which in the
example above is
Picture #1

4. Best line fit for the points of the graph that determine :
The graph above is the same one given in picture #1, however here with yellow are marked the points
that show the velocity of the cart when is traveling down. The acceleration of the cart is given by the
slope of the best line fit for the points marked with yellow, which in the example above is
.
These results were gathered 4 times for all of the following : 14cm , 15cm, 16cm, 17cm, 18cm.
Variables relevant to the tables below:
– the height at the inclined end of the ramp;
– the height at the declined end of the ramp;
– the length of the ramp;
– the acceleration when the cart is going up the ramp
– the acceleration when the cart is going down the ramp
; where is the acceleration due to gravity and
Picture #2

5. Table #1:
Table #2:
Table #3:
0,931
Trial #
1 0,71 0,666 0,688
2 0,712 0,675 0,6935
3 0,713 0,673 0,693
4 0,711 0,679 0,695
Average: 0,7115 0,67325 0,692375
Uncertainty: 0,0015 0,0065 0,0035
Trial #
1 0,798 0,757 0,7775
2 0,806 0,758 0,782
3 0,801 0,758 0,7795
4 0,801 0,759 0,78
Average: 0,8015 0,758 0,77975
Uncertainty: 0,004 0,001 0,00225
Trial #
1 0,899 0,816 0,8575
2 0,898 0,836 0,867
3 0,89 0,831 0,8605
4 0,891 0,826 0,8585
Average: 0,8945 0,827667 0,860875
Uncertainty: 0,0045 0,01 0,00475

6. Table #4:
1,029
Table #5:
1,127
Summary of the results:
Uncertainty
14 0,692375 0,0035 0,735
15 0,77975 0,00225 0,833
16 0,860875 0,00475 0,931
17 0,9575 0,01025 1,029
18 1,07 0,005 1,127
Trial #
1 1 0,909 0,9545
2 1,01 0,906 0,958
3 1 0,897 0,9485
4 1,02 0,918 0,969
Average: 1,0075 0,9075 0,9575
Uncertainty: 0,01 0,0105 0,01025
Trial #
1 1,11 1,02 1,065
2 1,13 1,02 1,075
3 1,13 1,02 1,075
4 1,11 1,02 1,065
Average: 1,12 1,02 1,07
Uncertainty: 0,01 0 0,005

7. The following graph corresponds to the summary table above:
At the graph above, 4 best line fits are given:
Best line fit calculated on the points of
Best line fit calculated on the points of
Best line fit calculated on the points of the upper value of the error bar of
Best line fit calculated on the points of the lower value of the error bar of
It is obvious, both from the graph and from the table that . This is because there is a
constant error in the acceleration determined in this experiment, thus , where
is the constant error. The origin of can’t was not able to be determined in the time allowed to perform
the experiment, so it remains a mystery. However, using the graph and data, the value of was
calculated, and
Conclusion:
Unlike the assumption in the hypothesis, the experiment showed that:
As mentioned above, the origin of was not able to be determined. Despite this, the experiment was
straight forward, not encountering any anomalous results or barriers in the data gathering.

8. Some improvements of the experiment include increasing the number of trials for each and also
increasing the number of different . However no difference in the results would have been expected.