# Lab Report on Centripetal Motion

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Introduction

Fatin

Lab on Centripetal Motion

Lab Report

Duration: 2 hours

Instructor: Mr. Samir Chehab

Fatin Al Alawi

Lab on Centripetal Motion:Lab Report

Aim:

- To study the relationship between frequency, f, and centripetal force, Fc, when radius and mass are constant.
- To study the relationship between frequency, f and radius, when force, Fc, and mass, m, are kept constant.

Calibration of spring:

Data Collection:

Mass Added (g) | Reading on Scale (cm) |

0 | 18 |

20 | 16.8 |

40 | 15.6 |

60 | 14.6 |

80 | 13.5 |

100 | 12.4 |

120 | 11.2 |

140 | 10.2 |

160 | 9.1 |

180 | 8 |

Constants:

- Mass of spring
- Acceleration due to gravity

Data Processing:

First, the results need to be converted to SI units

Mass Added (kg) | Reading on Scale (m) |

0 | 0.18 |

0.02 | 0.168 |

0.04 | 0.156 |

0.06 | 0.146 |

0.08 | 0.135 |

0.1 | 0.124 |

0.12 | 0.112 |

0.14 | 0.102 |

0.16 | 0.091 |

0.18 | 0.08 |

When there was no mass added to the scale, the reading on the scale was 0.18 meters. This means that the extension after adding each mass can be calculated.

Mass Added (kg) | Extension (m) |

0 | 0 |

0.02 | 0.012 |

0.04 | 0.024 |

0.06 | 0.034 |

0.08 | 0.045 |

0.1 | 0.056 |

0.12 | 0.068 |

0.14 | 0.078 |

0.16 | 0.089 |

0.18 | 0.01 |

When the scale is calibrated, the aim is to find the relationship between the force and the extension. This means that the force resulting from the addition of each mass must be calculated in this step.

Mass Added (kg) | Force (N) |

0 | 0 |

0.02 | 0.196 |

0.04 | 0.392 |

0.06 | 0.588 |

0.08 | 0.784 |

0.1 | 0.98 |

0.12 | 1.176 |

0.14 | 1.372 |

0.16 | 1.568 |

0.18 | 1.764 |

Therefore,

Force (N) | Extension (m) |

0 | 0 |

0.196 | 0.012 |

0.392 | 0.024 |

0.588 | 0.034 |

0.784 | 0.045 |

0.98 | 0.056 |

1.176 | 0.068 |

1.372 | 0.078 |

1.568 | 0.089 |

1.764 | 0.1 |

Now, the string constant, k, must be calculated. Since , where F is the force and x

Middle

17.09

26.5

15

14.59

28

14

10.63

25.5

12

8.87

30.5

Constants:

- Radius is meant to be constant; although that is impossible (the radius in the readings has a range of 5 cm, which is quite large)
- Mass of spring and ball

Data Processing

Now, the extension must be calculated.

Reading on Scale (cm) | Extension (cm) |

13 | 5 |

16 | 2 |

15 | 3 |

14 | 4 |

12 | 6 |

The results must now be changed into SI units

Extension (m) | Time for 20 Revolutions (s) | Radius (m) |

0.05 | 9.63 | 0.295 |

0.02 | 17.09 | 0.265 |

0.03 | 14.59 | 0.28 |

0.04 | 10.63 | 0.255 |

0.06 | 8.87 | 0.305 |

In order to find the relationship between the force and the frequency, the results for the readings on the scale must be converted into force (N).

Extension (m) | Force (N) |

0.05 | 0.88725 |

0.02 | 0.3549 |

0.03 | 0.53235 |

0.04 | 0.7098 |

0.06 | 1.0647 |

The readings were taken for the time for 20 revolutions, from this, the time for one revolution must be calculated.

Time for 20 Revolutions (s) | Time for one Revolution (s) |

9.63 | 0.4815 |

17.09 | 0.8545 |

14.59 | 0.7295 |

10.63 | 0.5315 |

8.87 | 0.4435 |

Since then the inverse of the readings for time for one revolution must be calculated

Time for one Revolution (s) | Frequency s-1 |

0.4815 | 2.0768 |

0.8545 | 1.1703 |

0.7295 | 1.3708 |

0.5315 | 1.8815 |

0.4435 | 2.2548 |

Now, a graph of the force against the frequency can be plotted.

The second point seems to be an outlier, it will be excluded from all graphs. Another graph will be plotted of Frequency against Force

The slope of the linear trend line was calculated to be

However, another polynomial trend line was added, since it correlation is higher than that of the linear trend line, it should be explored further.

The formula for Centripetal force is:

This means that frequency squared is proportional to the centripetal force, so, a graph of force against frequency squared will be plotted.

Frequency s-1 | Frequency2 s-2 |

2.0768 | 4.3133 |

1.1703 | 1.3695 |

1.3708 | 1.8791 |

1.8815 | 3.5399 |

2.2548 | 5.0841 |

Conclusion

We had several errors in our lab. Firstly, we are not sure that our measurements are 100% correct. Secondly, we are not exactly sure whether the spring was calibrated all the time and calibrated properly all the time. Thirdly, it was difficult to have a steady force while twirling the ball, so the force was not the same all the time. Fourth, we are not sure whether the reading on the scale was read correctly while twirling the ball. Finally, there was a human error while handling the stopwatch. Humans have a reaction time of around 0.25 seconds and also there might have been counting errors.

Many changes can be done to this lab in order to make it better, but this lab will always have a large error no matter what is done. What can be done to improve is include more than one trial for all the readings. In addition, if this lab was computerized and mechanized then the error would be small. But for now, what can be done is to precision of the data as there are a lot of random errors in the lab.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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