Sample Science Lab Report: Centripetal Force on a Whirling Object

The following is a sample physics lab report along with notes on some of the principles of writing lab reports. This text was adapted from a report submitted by a student (Leung Chun-wai)at SKH Lam Woo Memorial Secondary School in Hong Kong (Note: In this report, the student had adopted the practice of rounding up gravity to 10.0 m/s2).


Centripetal Force on a Whirling Object

Abstract

In this experiment, the weight of a given mass was compared to the centripetal force calculated by measuring the mass of the whirling object, the radius of the orbit and the angular velocity and then using the equation f = mω2r. Theoretically, the values for weight and centripetal force should be the same. However, in the experiment, the weight of the mass was 0.71 N while the calculated centripetal force was 0.85 N. The values do not closely match.

In the discussion section, several possible reasons are given for the discrepancy between the two figures.

Language notes
(1) The abstract section includes a brief summary of the objectives, findings and conclusions. This section is optional for short lab reports, but you should include it in long reports. If you have a table of contents, the abstract comes before that.
(2) When writing about theory (e.g., ‘Theoretically, the values for weight and centripetal force should be the same‘), use simple present tense and/or modal verbs like ‘should’.
(3) When writing about objectives (e.g., ‘the weight of a given mass was compared to…‘), use simple past tense.
(4) When writing about statistical findings (e.g., ‘The weight was 7.1 N‘), use simple past tense.
(5) When interpreting the findings (e.g., ‘The values do not closely match‘), use simple present tense.
(6) If you refer to a part of the report (e.g., ‘In the discussion section, several possible reasons are given for…‘), use simple present tense.

1. Introduction

Centripetal force is a that acts on a body moving in a circular path and that is directed towards the center around which the body is moving. The kind of centripetal force examined in this experiment involves uniform circular motion in which a mass is tethered to a rotational axis and is rotated at a constant angular rate ω (see Figure 1).

Figure 1. Centripetal Force

Language notes
(7) You normally don’t normally cite sources for definitions, equations and common scientific theories.
(8) Diagrams, graphs, charts and other kinds of images are called ‘figures’.
(9) When using a diagram, graph, chart or other kind of image, you should give it a figure number and title. The figure number and title go BELOW the figure.
(10) When using a diagram, graph, chart or other kind of image, you should refer to the figure in the main text using an expression like ‘See Figure 5’ or ‘As Figure 6 shows,’ and ‘are shown in Figure 6’. This introductory text is known as a callout. It is written in simple present tense and it should come BEFORE the figure.

1.1 Theory

In this experiment, a mass M of screw nuts attached to one end of the nylon string provides a downward tension force on the length between the screw nuts and the top of the plastic tube. When the rubber bung is whirled, a centripetal tension force is created on the nylon string between the bung and the top of the plastic tube. When the centripetal force on the whirling bung balances the weight of the mass of the screw nuts, the mass will remain stationery. The weight F of the mass of screw nuts can be determined by the equation:

F = Mg

(1)

Theoretically, this value should be equal to the value of the centripetal force on the rubber bung. When a mass m attached to a string is whirled round a horizontal circle of radius r, the centripetal force f necessary for maintaining the circular motion of angular velocity ω is represented by the equation:

f = mω2r

(2)

The angular velocity of the whirling bung can be determined using the equation:

ω= 2 π/t (rads-1)

(3)

Language notes
(11) The theory part does not need it’s own heading (and if a heading is used, you may prefer another term like ‘Background‘) .
(12) In this report, the equations are numbered to make it easier to reference them later on.
(13) The theory part tends to feature simple present tense.

1.2 Objectives

The objectives of the experiment were:

  • to determine the weight of a mass
  • to determine the centripetal force of that mass whirling horizontally on a string using the equation:
                                                       f = mω2r
  • to compare the two values

Language notes
(14)The objectives part does not need its own heading.
(15) The objectives are normally written in simple past tense.

2. Apparatus

The following apparatus was used:

  • 1 rubber bung
  • 1 plastic tube 15 cm in length
  • 3 screw nuts
  • A 1.5 m length of nylon string 
  • 4 labels
  • 1 paper marker
  • 1 metric rule
  • 1 stop watch
  • 1 electronic balance

Language notes
(16) When using point form lists, you should introduce them with a phrase (e.g., “The following apparatus was used).
(17) In the apparatus section, you normally use simple past tense and passive voice.

3. Procedures

The following procedures were carried out:

  1. The mass m of the rubber bung was measured using the electronic balance and recorded.
  2. The three screw nuts were weighed together and their mass was recorded.
  3. The apparatus was assembled as shown in Figure 2.
  4. The length L of the nylon string from the rubber bung to the glass tube was chosen to be 1.0 m.
  5. A label was affixed to the nylon string between the screw nuts and the glass tube. It was affixed 1 cm below the end of the glass tube.
  6. The glass tube was held vertically and the bung was whirled slowly above the head in a horizontal. circle. The speed of the bung was increased until the paper marker remained stationary just below the end of the tube. The angular speed was kept constant and the circular path was kept horizontal. 
  7. The timer was started. It was stopped after 50 revolutions of the bung. The time was recorded. This value could then be used to determine angular velocity using Equation 2.
  8. Steps 6 and 7 were repeated once.
  9. Steps 4 to 8 steps were repeated with the following lengths of nylon string: 0.90 m, 0.80 m and 0.70 m
  10. The weight of the mass was determined using Equation 1.
  11. The average period for each revolution was calculated.
  12. The angular velocity was calculated for each set of trials using Equation 3
  13. The tension force was calculated for each set of trials using Equation 2 and the mean tension force was obtained.
  14. The percentage error for each set of trials was calculated.
  15. The weight of the mass was compared to the mean tension force. The difference between the two values was used to determine the percentage error. This percentage error was then compared to the percentage errors in each trial.

Figure 2: Apparatus Assembly

Language notes
(18) In the procedures section, you normally use simple past tense and passive voice.
(19) In would be better to have put the diagram immediately after Step 3 (as it appeared in the original report)

4. Results

The mass of screw nuts was found to be 71.14 g (± 0.01 g). Therefore, using Equation 1, the weight of the screw nuts was calculated to be 0.71 N (0.07114 x 10).

The mass m of the rubber bung was found to be 16.37 g (± 0.01 g, with a percentage error of 0.06%).

The times recorded for the experiment (± 2 sec.) using different lengths of string (± 0.01m) are shown in Table 1 below.

Table 1. Time Taken for 50 Revolutions

The average period for each revolution (± 0.04 sec.) is shown in Table 2. Table 2 also shows the values obtained for angular velocity (calculated using Equation 3) and centripetal tension (calculated using Equation 2).

Table 2. Average Period (± 2 s), Angular Velocity, Tension

The mean tension on the string for all the trials was 0.85 N, which is not equal to the actual weight of the screw nuts (0.71 N). 

The calculations used to determine percentage error for each set of trials is shown below

  • Percentage error in mω2 L:Set 1 = 0.01/71.14 + 2(0.04/0.83) + .01/1.00 = 10.1%
  • Percentage error in mω2 L:Set 1 = 0.01/71.14 + 2(0.04/0.83) + .01/1.00 = 10.1%
  • Percentage error in mω2 L:Set 1 = 0.01/71.14 + 2(0.04/0.83) + .01/1.00 = 10.1%
  • Percentage error in mω2 L:Set 1 = 0.01/71.14 + 2(0.04/0.83) + .01/1.00 = 10.1%

The percentage error describing the difference between the actual weight of the screw nuts and the mean centripetal tension was calculated as follows:

Percentage error = (0.85 – 0.71) / 0.85 x 100% = 16.5%

The percentage error of the mean centripetal tension compared to the actual weight of the screw nuts (16.5%) is greater than percentage error that was estimated for each set of trials (10.1% to 12.0%). Therefore, the actual weight of the screw nuts did not fall within the range of the tensions calculated.

Language notes
(20) Results are normally written in simple past tense.
(21) As with using figures, any time you use a table you should give it a callout (e.g., ‘As shown in Table 2’), a number and a title. Unlike diagrams, graphs and charts, a table is simply called ‘table’. Also, while figure titles usually BELOW the figure. Table titles usually go ABOVE the table.

5. Conclusion

The. the weight of the screw nuts was 0.71 N. Therefore, the centripetal force expected to be acting on was 0.71 N.

The centripetal tension acting on the rubber bung (as obtained by measuring the mass of the whirling object, the radius of the orbit and the angular velocity and by using the equation f = mω2r) was 0.85 N.

The values for the weight of the screw nuts and centripetal tension—0.71 N and 0.85 N, respectively—are relatively close, but the difference exceeds that which can be accounted for by the percentage error estimates in the measurements of time and distance.

Language notes
(22) The conclusion section is normally very short, and in this section, the conclusions should closely match the objectives. For example, in this sample report, there were three objectives. In the conclusion, each of these objectives is ‘answered’ simple past tense.
(23) In the section, when describing statistical findings, simple past tense is used (e.g., ‘The weight was 0.71 N‘). However, when describing your interpretation of the findings simple present tense is used (e.g., ‘These figures are relatively close‘).

6. Discussion

The expected values were not obtained. This is likely due to the limitations of the experiment. There were several possible sources of error.

As the apparatus was hand-held, different kinds of human error may have been introduced into the experiment.

  • The axis of motion (the hand-held plastic tube) would not have been perfectly fixed in one spot and the circular motion would not have been perfectly uniform. For example, it was observed that the paper label sometimes moved too far away from the plastic tube or entered the tube. This indicates that the motion was not uniform. Thus, there may have been differences in the measured L and the actual L. 
  • In addition, the experimenter could not maintain a perfectly horizontal revolution. 

Other possible sources or errors were related to the physical characteristics of the apparatus.

  • The nylon string was not weightless. It would have slightly shifted the center of mass of the system so that LsinƟ would not have been equal to the radius of rotation. The effective value of L would have been slightly smaller than the actual length of the string. Also, additional force would also have been required to rotate the string. This would lead to the actual value of centripetal tension being slightly higher than the measured tension.
  • Air resistance may have slowed down the motion of the rubber bung. Extra force would have been required to overcome air resistance. This would also have led to a higher value for centripetal tension.
  • Friction between the string and the plastic tubing would also lead to extra force being required to whirl the bung.
  • As the string was elastic, it would stretch when a tension was acting on it. During the rotation of the rubber bung, the string would become longer, leading to the effective L becoming longer than the actual L. This would result in a lower calculated tension.
  • Although knots were tied on the rubber bung and the screw nuts, these knots may have moved during the experiment, varying the length of the string,  

The inability of the experimenter to provide perfectly uniform motion in terms of angular velocity and angle of rotation would likely have had the greatest effect on the accuracy of the experiment.

There are several ways to eliminate or reduce these sources of error. To eliminate human error, a mechanical centripetal force apparatus could be used to ensure that the motion is uniform. Using this kind of apparatus would also eliminate errors caused by the weight and elasticity of the string. To eliminate air resistance, the experiment would have to be conducted in a vacuum. To reduce friction, oil could be used as a lubricant.   

Language notes
(24) This section can deal with different topics: (a) the limitations of the research and how such problems could be avoided in future, (b) how your findings and/or conclusions relate to existing research, (c) the implications your findings and/or conclusions have for society and/or (d) suggested avenues for future research. In this report, the findings didn’t go as planned, so the writer focused on the limitations of the research.
(25) In you are discussing limitations, you may use a lot of modal verbs and present perfect tense (e.g., ‘This could have resulted in…’) and simple present tense (e.g., ‘To prevent this problem, a machine can be used to…‘).

Language notes
(26) Numbering the sections is optional.
(27) Ask your teacher for further information regarding where and how to include your name(s), date and other relevant information.


Image Credits: Figure 1 is from commons.wikimedia.org/wiki/File:Centripetal_force_diagram.svg


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