PHYSICS 101Preparation 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

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  ? ? 

Significant Figure Rules

Zeros appearing anywhere between two non-zero digits are significant.

101.12 5 1, 0, 1, 1 and 2.

23.07 ? ? 

Trailing zeros in a number containing a decimal point are significant.

122.300 6 1, 2, 2, 3, 0 and 0.

0.000122300 6 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.

Leading zeros are not significant.

0.00052 2 5 and 2.

5020 ?  ?

0.0500 ?  ?

0.003 ?  ?

800.00 ?  ?

Significant Figure Rules

Significant Figure Rules

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 1

2.531 ± 0.001 g 1

Examples

150.0 g H20 + 1.057 g salt = 151.1 g solution

ExamplesNumber Sig. Fig.

23.21 40.062 2275.4 450.09 45020 3

0.003 10.0500 3800.00 5

0.00682 31.072 4300 1300. 3

300.0 4Examples

Quantity Sig. Fig.5.2 g 25.0 kg 25.000 L 40.005 m 1

5.00 x 103 g 3

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

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

Significant Figure Rules

Rounding offA 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. 67.786v. 98.913

Free Fall Experiment 0

0

o

oy

y

v

0oy

gm5y

m10y

m15y

m20y

m25y

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

2 2t (s )

Data of Free Fall Experiment

Graph Paper

Plotting the Axes and Writing their Names & Unitsy(

m)

t2 (s2)

Scaling the Axes

0 1 2 3 4 5 6

5

10

15

20

25

y(m

)

t2 (s2)

Plotting Data

0 1 2 3 4 5 6

5

10

15

20

25

y(m

)

t2 (s2)

Best Fit

0 1 2 3 4 5 6

5

10

15

20

25

y(m

)

t2 (s2)

0 1 2 3 4 5 6

5

10

15

20

25

y(m

)

t2 (s2)

Finding the slope

m .10y

2s 5.2x2m/s 0.4

5.2

.10

x

y

slope

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

Analyzing

2

2

1gttvyy oyo

2

2

1gty 2

2t

yg

22exp m/s 8.0m/s 4.0x 2 g

Slope

Calculating The Error

x100%error exp

true

true

g

gg

19%x10081.9

81.90.8%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.