Preparation Class for Physics Laboratory This tutorial is intended to assist students in understanding Significant Figures and Rounding Plotting Graphs for Free Fall Experiment Writing Conclusion http://physics.dogus.edu.tr

Significant Figure Rules The number of significant figures in a quantity is the number of trustworthy figures in it, the last significant digit in a measurement is somewhat uncertain (but still useful), because it is based upon an estimation. All non-zero digits are considered significant. Number S.F. The Numbers 123.45 5 1, 2, 3, 4 and 5 523.7  ? ?  Zeros appearing anywhere between two non-zero digits are significant. 101.12 5 1, 0, 1, 1 and 2. 23.07 ? ? 

Significant Figure Rules Leading zeros are not significant. 0.00052 2 5 and 2. 5020 ?  ? 0.0500 0.003 800.00 Trailing zeros in a number containing a decimal point are significant. 122.300 6 1, 2, 2, 3, 0 and 0. 0.000122300 the zeros before the 1 are not significant 120.00 5 ?  These conventions are not universally used, and it is often necessary to determine from context whether such trailing zeros are intended to be significant.

Significant Figure Rules Examples Number Sig. Fig. 23.21 4 0.062 2 275.4 50.09 5020 3 0.003 1 0.0500 800.00 5 0.00682 1.072 300 300. 300.0 Examples Operations Result 12 + 5.3 17 17.3 9.47 – 2.2 7.3 7.27 8.950 x 10.3 92.2 92.185 12.3216 / 6.8 1.8 1.812 Examples 3 ±1 g 1 2.53 ±0.01 g 2.531 ± 0.001 g Examples 150.0 g H20 + 1.057 g salt = 151.1 g solution Examples Quantity Sig. Fig. 5.2 g 2 5.0 kg 5.000 L 4 0.005 m 1 5.00 x 103 g 3

Significant Figure Rules When numbers are added or subtracted, the number of decimal places in the result should equal to the smallest number of decimal places of any factor in the operation. 12 + 5.3 makes 17 and NOT 17.3 9.47 - 2.2 makes 7.3 and NOT 7.27 When multiplying several quantities, the number of significant figures in the final answer is the same as the number of significant figures in the least accurate of the quantities being multiplied. The same rule is applied to division. 8.950 x 10.3 makes 92.2 and NOT 92.185 12.3216 / 6.8 makes 1.8 and NOT 1.812

Rounding off A number is rounded off to the desired number of significant figures by dropping one or more digits to the right. Rules for rounding off are as follows 1) When the first digit dropped is equal to or more than 5, we add 1 to the last digit retained. e.g. rounding 6.576 to 3 S.F. makes 6.58 e.g. rounding 86.25 to 3 S.F. makes 86.3 2) When it is less than 5, the last digit retained does not change. e.g. rounding 6.573 to 3 S.F. makes 6.57 Round off the following numbers to 3 S.F. i. 13.6 + 22.4 = ? ii. 12.34 + 43.21 = ? iii. 5.6 x 12.65 = ? iv. 67.786 v. 98.913

Free Fall Experiment

Data of Free Fall Experiment y(m) t(s) 5.0 0.88 0.78 10 1.28 1.64 15 1.63 2.68 20 2.18 4.77 25 2.31 5.34

Graph Paper

Plotting the Axes and Writing their Names & Units

Scaling the Axes

Plotting Data

Best Fit

Finding the slope slope

Analyzing A freely moving object moves with a constant acceleration towards the earth and it obeys the following kinematics equation: Slope

Calculating The Error

Random Errors: A random error, as the name suggests, is random in nature and very difficult to predict. It occurs because there are a very large number of parameters beyond the control of the experimenter that may interfere with the results of the experiment.

Example: You measure the mass of a ring three times using the same balance and get slightly different values: 17.46 g, 17.42 g, 17.44 g

How to minimize random errors? Take more data. Random errors can be evaluated through statistical analysis and can be reduced by averaging over a large number of observations.

Systematic Errors: Systematic error is a type of error that deviates by a fixed amount from the true value of measurement. All measurements are prone to systematic errors, often of several different types. Sources of systematic error may be imperfect calibration of measurement instruments, changes in the environment which interfere with the measurement process and sometimes imperfect methods of observation.

Example: The cloth tape measure that you use to measure the length of an object had been stretched out from years of use. (As a result, all of your length measurements were too small.) The electronic scale you use reads 0.05 g too high for all your mass measurements (because it is improperly tared throughout your experiment).

How to minimize Systematic Errors? Systematic errors are difficult to detect and cannot be analyzed statistically, because all of the data is off in the same direction (either to high or too low). Spotting and correcting for systematic error takes a lot of care. How would you compensate for the incorrect results of using the stretched out tape measure? How would you correct the measurements from improperly tared scale?

Conclusion Part: Conclusion is an important part of a laboratory report. The main purpose of the conclusion section is to comment on the results mentioned in the lab report so it requires most critical thinking.

Discuss the significance of the experiment, think about what you learned!!!

When writing your conclusion; Firstly, restate the purpose of experiment. Briefly state whether your data supported the purpose of the experiment - this would be your conclusion. Discuss whether or not the results supported your hypothesis. If they did not, discuss why not.

You can link the results to what you read in the literature, review or other sources mentioned in the introduction. But do not write procedure as your conclusion.

Suggest factors that may have affected the experimental design;for instance, random and systematic errors. Discuss how they can be eliminated in the future. Suggest any changes that can be made to the experimental procedure and how these changes might affect the data received in the lab.