Lab 1 - Intro to Measurement PDF

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Chief Executive Officer: Jon K. Earl Vice President, Sales and Business Development: Greg Bartell Regional Acquisitions Manager: Jon K. Earl Project Manager: Hayley Ryan Cover Design: Dan Woods ISBN-13: 978-1-64386-645-1 © 2020 by Qilin Wu and Michael Christenson. © Cover images by Qilin Wu. Published by bluedoor, LLC 10949 Bren Road East Minneapolis, MN 55343-9613 800-979-1624 www.bluedoorpublishing.com All rights reserved. Making copies of any part of this book for any purpose other than your own personal use is a violation of the United States Copyright laws. No part of this book may be used or reproduced in any form or by any means, or stored in a database retrieval system, without prior written permission of bluedoor, LLC. Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1

TA B L E O F CO N T E N T S

L A B O R AT O R Y 1

L A B O R AT O R Y 1 1

Introduction to Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Ref raction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

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L A B O R AT O R Y 1 2

Reaction T ime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Practical Uses of Converging Lenses . . . . . . . . . . . . . . . . . . 45

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L A B O R AT O R Y 1 3

Vector Addition of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

L A B O R AT O R Y 4

L A B O R AT O R Y 1 4

Centripetal Acceleration in Circular Motion . . . . . . . 11

Simple Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

L A B O R AT O R Y 5

L A B O R AT O R Y 1 5

Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Generators and Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

L A B O R AT O R Y 6

L A B O R AT O R Y 1 6

Center of Gravity and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Wave Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

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T he Ballistic Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

L A B O R AT O R Y 8 Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

L A B O R AT O R Y 9 Archimedes’ Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

L A B O R AT O R Y 1 0 Ref lection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

I n t r o d u c t io n t o P h y s ic s | Ta b l e o f C o n t e n t s

Name:

Section:

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L A B O R ATO R Y 1

I N T R O D U C T I O N TO M E A S U R E M E N T Objectives • To develop knowledge of scientific methodologies • To experience some of the limitations of the human senses as measuring devices • To learn about units and unit conversion

Tools and Resources • PhET Interactive Simulations • A ruler with centimeters and inches • If you do not have a physical ruler that can measure in centimeters and inches, you may use an online ruler: https://iruler.net/ where the monitor’s dimension has to be selected for proper measurements.

Discussion How does one “do” physics? It goes something like this: (1) Careful observation of a phenomenon induces an investigator to question its cause; (2) A hypothesis is formed to explain the observation; (3) The scientist devises an experiment to test this hypothesis; (4) The outcome of the experiment often raises more questions that lead to a modification of the hypothesis and subsequent further experimentation; (5) Eventually an accepted hypothesis that has been verified by different experiments can be elevated to a theory, or a law . Clearly physics is an experimental science. Can we, then, trust our senses of sight, hearing, touch, smell and taste to make accurate observations? Methods of measurement that rely entirely upon human senses are called subjective methods. Hot and cold, loud and soft are subjective terms (What seems to be cold to you may be quite comfortable to a polar bear). Sometimes our senses fool us. Because early science relied heavily on the use of subjective methods, scientific progress was slow. During the 17th century, subjective methods were replaced by objective methods, using instruments to obtain measurements of greater precision (measurements that can be more readily reproduced). Objective methods minimize the effects of the observer on the results of an experiment. Of course, if we are not careful, we can be fooled by our instruments too! L a b or a t or y 1 | In t r od u c t ion t o Mea su r em ent

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The basic act of measurement is one of comparison. To measure the height of a person, for instance, we would compare the distance from the floor to the top of the person’s head with some chosen standard length, such as a foot or a meter. A complete measurement of a quantity consists of a number and a unit. For example, a person’s height might be expressed as height (h) = 5.75 ft or height (h) = 1.75 m. It is essential that all measurements be accompanied by appropriate units. In the world today, there are two common systems of measurement. The United States uses the English system, and the rest of the world, for the most part, uses the metric system. An attempt has been made in the United State to switch completely to the metric system, but so far it has not succeeded. One of the strongest features of the metric system is the use of a single set of prefixes to relate larger and smaller units of whatever it precedes. A microgram is a millionth of a gram, a micrometer is a millionth of a meter, and a microvolt is a millionth of a volt. A micro- stands for a millionth of whatever. The same prefix works for all. Prefix

Abbreviation

Factor

Power of ten

peta

P

1015

1,000,000,000,000,000

tera

T

1012

1,000,000,000,000

giga

G

109

1,000,000,000

mega

M

106

1,000,000

kilo

k

103

1,000

deci

d

10-1

0.1

centi

c

10-2

0.01

milli

m

10-3

0.001

micro

μ

10-6

0.000001

nano

n

10-9

0.000000001

pico

p

10-12

0.000000000001

femto

f

10-15

0.000000000000001

Since any quantity, such as length, can be measured in several units, it is important to know how to convert from one unit to another. Units are multiplied and divided just like ordinary algebraic symbols. This gives us an easy way to convert a quantity from one set of units to another. The key idea is that we can express the same quantity in two different units and form an equality. For example, when we say 1 minute (min) = 60

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seconds (s), we mean that 1 min represents the same physical time interval as 60 s. For this reason, the ratio (1 min)/(60 s) equals 1, as does its reciprocal (60 s)/(1 min). We can multiply a quantity by either of these factors without changing that quantity’s physical meaning. To find the number of seconds in 3 min, we write 60 s 3 min = (3 min) = 180 s 1 min If you do your unit conversions correctly, unwanted units will cancel, as in the example above. If instead you had multiplied 3 min by (1 min)/(60 s), your result would have been 1/20 min2/s, which is a rather odd way of measuring time.

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Procedure 1.

The Scientific Method: Simple Harmonic Motion – Object on a Spring

An object of mass m placed on the end of a spring hangs vertically. The original equilibrium position of the lower end of the spring is shown in Figure 1.1(a). When the object is suspended from the spring, the new equilibrium position of the spring-object system becomes the position shown in Figure 1.1(b). When the object is pulled down to a distance A from this new equilibrium position (as shown in Figure 1.1(c), we say that its displacement from equilibrium is A. When released, the object will oscillate with amplitude A and period T. We will investigate the dependence of the period T on the amplitude of the motion.

Figure 1.1: Equilibrium positions of the spring and the spring-object system.

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a. Run the Masses and Springs simulation from University of Colorado’s PhET website or go directly to this link: https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-andsprings_en.html b. Click “Lab” when the simulation opens. Once you are inside the “Lab” page, move the blue timer outside its storage; move the yellow measurement stick outside the storage and under the vertical spring that hangs freely. Place the bottom end of the measurement stick at “Height = 0” so the top end of the stick is aligned with the lowest ring of the spring, as shown in the figure below.

Change the mass of the orange colored known hooked object from 100 g to 50 g (the control box is left of the spring’s top); then place the object at the end of the spring. The spring is stretched, and the object starts to move up and down in an oscillatory motion. When the motion stops, the spring-object is in its equilibrium position. Read and record how much the spring is stretched as y0 = ________________ . Set the damping to “none” by sliding the damping bar all the way left. Click and change the experimental control button from to . Click the timer so it’s on standby. Pull down the object by an arbitrary amount from its equilibrium position. Click the experimental control button to start and stop the oscillatory motion. The timer records the time elapsed during the motion. You need to reset the timer to zero and set it to standby before each time measurement. c. Displace the object downward to y = y0 + 4.0 cm. When you do this, the amplitude of the motion of the object will be A = 4.0 cm. Release the object, and let it oscillate. Measure the time for 10 complete periods and record it in Data and Calculation Table 1.1 as Δt1. Repeat the procedure two more times for this amplitude and record your measurements as Δt2 and Δt3. d. Calculate the average time Δt = (Δt1 +Δt2 + Δt3)/3, round the calculated time to the nearest tenth second and record the result in Data and Calculation Table 1.1. e.

Calculate the period T from T =Δt /10 and record the result in Data and Calculation Table 1.1.

f.

Repeat steps c, d and e for amplitude A = 6.0 cm and 8.0 cm. Make three trials for each amplitude and measure the time for 10 periods for each trial. Record all the measured and calculated results in Data and Calculation Table 1.1.

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Table 1.1: Data and Calculation A (cm)

Δt 1 (s)

Δt 2 (s)

Δt 3 (s)

Δt (s)

T(s)

4.0 6.0 8.0 g. Does your data support the hypothesis that "the period T of this simple harmonic motion is independent of the amplitude A?" Justify your answer.

h. Repeat Steps (b) – (f) for an object of mass 100 g and record your findings in Data and Calculation Table 1.2. y0 = ___________ cm Table 1.2: Data and Calculation A (cm)

Δt 1 (s)

Δt 2 (s)

Δt 3 (s)

Δt (s)

T(s)

4.0 6.0 8.0 i.

Does your new experimental data support the hypothesis stated in Step (g)? Justify your answer.

j.

What experiment(s) would you suggest to further test the hypothesis stated in Step (g)?

2. Methods of Measurement: Subjective Methods and Objective Methods Use the thumbs of both hands to measure the width of this page in ynchs. (In Old English, inch was spelled ynch and was based on the width of the thumb.) Think about the techniques you will apply to make good measurement. Measure the width twice (once by you and once by a family member or friend) and record the two results below. Your measurements may include decimal fractions. L a b or a t or y 1 | In t r od u c t ion t o Mea su r em ent

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We’ll use yn as the abbreviation of ynch. width (w1) = ___________________ yn width (w2) = ___________________ yn Comment on why or why not your results are the same.

Measure the width twice with a ruler and record the results below: width (w1) = ___________________ in width (w2) = ___________________ in Comment on why or why not your results are the same.

3. Units and Conversion of Units: a. i. Measure the width of your lab manual in centimeters using the tape ruler: Width of the table = ___________________ cm. ii. Convert the above measurement into inches (1 in = 2.54 cm): Width of the table (calculation) = __________________ in. iii. Measure the width of the table in inches using the tape ruler: Width of the table (measurement) = ________________ in. iv. Are your results in step (2) and (3) in good agreement? _________ b. The speed of sound at room temperature is 343 m/s. Convert that speed into mi/h using conversion factors 1 mi = 1609 m and 1 h = 3600 s. Follow the strategy shown in the example near the top of Page 3 and further illustrated immediately below. 343

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m m (conversion factor 1)(conversion factor 2) = 343 s s

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