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centripetal force lab (DCP, CE)

Extracts from this document...

Introduction

Centripetal Force

Aim: To investigate the relationship between the rotation period T and the hanging mass M when an object is moving at a constant speed in circular motion.

Variables:

Independent variable

Hanging mass

Dependent variable

Rotation period

Control variables

- Number of rotation period

- Length of string

- Mass of the rubber stopper

- Friction/ air resistance

Apparatus:

Meter stick, electric balance, timer, strings, rubber stopper, mass, plastic tube

Method:

image00.png

Data Collection


length of the string L = 35.0 cm ± 0.1cm = 0.350 m ± 0.001 m
mass of the rubber stopper = 38 g ± 1g = 0.038 kg ± 0.001 kg

The uncertainty of the string’s length, mass of the rubber stopper and time is taken to the smallest division of the measuring device (meter stick to measure length of string, electric balance to measure mass of stopper, stopwatch to measure time taken to complete 10 rotation period).


Raw Data

hanging mass/ g ± 1g

time taken for 10 rotation/ s ± 0.01s

Average time for 10 rotation/ s ± 0.01s

Random uncertainty In t (±s)

1st trial

2nd

3rd

4th

5th

50

7.01

7.79

7.37

7.68

7.26

7.42

0.16

100

5.84

5.21

5.41

5.96

6.04

5.69

0.17

150

5.16

4.79

5.35

4.70

4.97

4.99

0.13

200

4.78

4.66

4.50

4.12

4.83

4.58

0.14

250

3.82

4.01

4.41

4.68

4.22

4.23

0.17

300

3.62

3.77

4.06

3.93

4.28

3.93

0.13

Mean

0.15

The random uncertainty of the average time taken for 10 rotations is calculated by image01.pngimage01.png

Eg. Random uncertainty for time taken for 10 rotation period when the hanging mass is 50.0 kg = (7.79-7.01)/5=0.16

Data processing

Mass

...read more.

Middle

0.100

0.58

0.52

0.54

0.60

0.60

0.57

0.02

0.150

0.52

0.48

0.54

0.47

0.50

0.50

0.01

0.200

0.48

0.47

0.45

0.41

0.48

0.46

0.01

0.250

0.38

0.40

0.44

0.47

0.42

0.42

0.02

0.300

0.36

0.38

0.41

0.39

0.43

0.39

0.01

Mean

0.02

image11.png

From the graph, the best fit is does not pass through the origin and it is more like a negative curve. This may suggest a positive linear relationship between image04.pngimage04.png and the hanging mass M.

Time

In order to have a linear graph, I have to plot image04.pngimage04.png against the hanging mass. The average time taken for 1 period of each mass have to be processed to image04.pngimage04.png.

For example, the rotation period when mass is 0.050 kg, is 0.74s. Thenimage02.png

Final Data

Hanging Mass/kg ± 0.001 kg

image03.png ± 0.

...read more.

Conclusion

        The timing process of the rotation period causes a major random uncertainty in this experiment. Since there isn’t a certain point indicating the start and end of a rotation, timing the rotation period involve estimation of the starting/ending point of the rotation and may cause uncertainty.

        Reaction time when using the stopwatch also causes uncertainty. A person cannot start or stop the stopwatch exactly at the point where rotation starts. The reaction time can be kept constant by having the same person as the timer throughout the experiment. However, in most cases, the reaction time starting and stopping the stopwatch may not always be equal and cannot fully cancel each other out. The percentage uncertainty can be reduced by timing more rotation period to reduce the significance of the reaction time on the data.

...read more.

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