Fall Instructor: Dr. Roman Kezerashvili 1. Welcome to SC H. Honor Class. This is the second of a sequence of 3 Physics 2 courses Physics 2.

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Kezerashvili All rights reserved. No parts of this work may be reproduced or distributed or stored in a retrieval system in any form or any means-electronic, photocopying or otherwise-without the prior written permission of the copyright owner. Request for permission to make copy should be addressed to Gurami Publishing. The work may require you handle high and low voltage power supplies, hot materials, chemicals, and expensive equipments.

To prevent accidents, you need to act with care and observe all safety rules at all time. Physics is the bedrock of all the sciences and technology. The beauty of physics lies in the simplicity of its fundamental theories and laws.

Together with the lecture courses the physics laboratory courses provide the best understanding of the main concepts of physics. A pretty experiment is in itself often more valuable than 20 formulae extracted from our mind Furthermore, it teaches to perform data analysis including statistics, curve fitting and modeling. The experiments have been designed so that each exercise deals with a single important principle of electricity, magnetism or optics.

Although most of the experiments are designed for a single laboratory period, there are some experiments, which contain more material than can be covered during one laboratory period.

Those parts of the experiments, which are marked with an asterisk, are considered to be optional Acknowledgments I would like to express my gratitude to my colleagues at New York City College of Technology, the City University of New York, whose generous criticism, helpful discussions were important in the development of this manual Tam grateful to Dr. Alan Wolfe for his thoughtful and valuable comments on the manuscript of this text.

Particular thanks to Dr. Daria Boudana, whose helpful suggestions and assistance were so important in the development and preparation of this manual. I wish to express my sincere appreciation to Dr. Vladimir Boyko, Dr. My special thanks goes to Dr. Lufeng Leng for her proofreading and comments Acknowledgements are also extended to my student Mr.

Nedzad Joldic for his assistance in the test runs of the most of the experiments included in this book. My thanks are due to people at Gurami Publishing who aided me through the long process of making this book a reality. T owe special thanks to my students of the classes of and for their patience, for they were the first groups to test the feasibility of the most experiments.

My experience with them in the physics laboratory class provided motivation and inspiration for this work. Roman Kezerashvili To the Student The physics laboratory class is a part of the total exposure to the concepts and principles of physics. It is linked to your lecture classes. In physies laboratory you perform experiments designed to verify or exemplify concepts and principles of physics. This book is written for you to use as a guide to mastering college physics. We have some suggestions to help you achieve your objectives.

First of all, you should read the appropriate text before the experiment is attempted. Pay special attention to the objectives of the experiment and physical phenomena that you have to verify. Try to understand the method of measurements and which physical parameters you will measure.

Always check the units of physical quantities you have measured, Laboratory Report Format The laboratory report must be legible. If your handwriting is illegible then you must have your report typed. You can work together on the lab report, but cannot simply copy. Body of the report, containing the following items: Objectives.

A clear short statement of the objectives of the experiment Theory. Each graph must have clear heading. One simple method for specifying the accuracy of a measurement is to state how many significant figures it has.

That is only a certain number of figures are significant. The significant figures of the experimentally measured value include all numbers that can be read directly from the instrument scale plus one doubtful, or estimated, number. So the last digit is estimated. Zeros and the decimal point must be properly dealt with in determining the number of significant figures in a result. This is accomplished as follows: 1, The lefimost nonzero digit is the most significant.

The zeros before the 5 merely locate the position of the first number. If there is no decimal point, the rightmost nonzero digit is the least significant. If there is a decimal point, the rightmost digit is the least significant, even if it is zer0. Example: The 3 in One of the advantages of exponential notation is that it allows the number of significant figures to be clearly expressed. With exponential notation ambiguity can be avoided: if the quantity is known to an accuracy of three significant figures we write 5.

Rounding Off The nonsignificant figures are dropped from the result if they are to the right of, the decimal point and are replaced by zeros if they are to the left of the decimal point. The final result should not be more accurate than the measurements taken in the experiment. In general, the final result should be expressed with the same accuracy as the least accurate measurement taken in the experiment, The following rules make this principle more precise. Note also that to make the final result as accurate as possible when doing a multiple-step calculation on a calculator or a computer, you should wait until the last step to round off your answer.

Rounding off intermediate steps can introduce error. Average or Mean Value Most experimental measurements are repeated several times, and it is very unlikely that identical results will be obtained for all trials. It can be shown mathematically that the best approximation to the true value is the mean value and it corresponds to what most people call the average value. The mean or average value can be denoted by x. Let V. The percent error represents the accuracy of the experimental measurements.

Example: If the computed value of the resistivity of the copper is 1. The comparison is expressed as a percent difference. The percent difference tells nothing about the accuracy of the experiment, but it is a measure of the precision of measurement.

Having obtained a set of measurements and determined the mean value, it is important to find how widely the individual measurements are scattered from the mean. A quantitative description of this scatter of measurements will give an idea of the precision of the experiment and can be described by a deviation. The average of the deviations of the set of measurements is always zero, so the mean of deviations is not a useful way of characterizing the dispersion.

To avoid the problem of a negative value, it is statistically convenient to use square of the deviation. The standard deviation is a measure of the precision of measurement in the following statistical sense.

It gives the probability that the measurements fall within a certain range of the measured mean. Commonly, physical quantities are plotted using rectangular Cartesian coordinates, x and y. The horizontal axis is called the abscissa and the vertical axis is the ordinate. When plotting data, the first thing to do is to choose a scale for each of the axes that would be easy to plot and read. Plotting the data we make a scatter plot.

When the data points are plotted, draw a Fig smooth line described by the points. The line does not have to pass exactly through each point but should connect the general areas of significance of the data points. Most of the graphs for this laboratory are straight lines. Lets consider the main characteristics of a straight line.

This is called the slope-intercept form of the equation of a line. The constant b is called the y-intercept. The m is called the slope of the line and we define the slope as the ratio of change in the y-coordinate to the change in the x-coordinate. The slope m of line that passes through the points A xi,y and B x,y2 is 4 The slope is independent of which two points are chosen on the line. I represents how to find the slope of the line. How do we find a line that best fits the experimental data?

It is reasonable to choose the line that is as close as possible to all the data points in the scatter plot. So, we want the line for which the sum of the distances between the data points and the line is the smallest.

It is better to find the line where the sum of the squares of those distances is the smallest. The resulting line is called the regression line or the least squares line. The formula for the regression line is programmed into most graphing calculators and is presented in Microsoft Excel. Using this software we can model our experimental results. Mathematical models are usefull because they allow us to isolate critical aspects of the thing we are studying and then to predict how it will behave.

How are mathematical models developed? How are they used to predict the behavior of the process? Consider the data, which are the result of your measurements. To see the data trend better make a scatter plot of one physical quantity versus another.

How can we model that data mathematically? If it appears that the points are lying more or less along a line, we can try to fit a line visually to approximate the points in the scatter plot. We learned how to construct linear models of data. What do we do if the data we are studying are not linear?

In that case, our model would be some other type of function that best fits the data.

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