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CALIFORNIA STATE UNIVERSITY, LOS ANGELES

Department of Phys!s an" AstronomyPhys!s#$$ % Se!ton $&' $(&)*

Measurement Exercise

Prepare" +y Ro"ney P-.a"a

Performan!e Date T-es"ay,/an-ary $0, #1$2S-+msson D-e T-es"ay, /an-ary #$, #1$2

Professor Yese /3 Fe4peTh-rs"ay $&1 pm3 5 011 p3m3

/an-ary #1$2

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Experiment No 1: Measurement Exercise

I. PURPOSE The purpose of this lab to gain experience using uncertainties and use the

Vernier, micrometer and meter stick comparing measurement.6 = m/V

V = (47r3)/3 = (7/)d3,

calculations for the densit! of the sphere "ill be performed. #here $ is the

densit! in (kg/m3 ), m is the mass in (kg) and V is the %olume of the sphere in

(m3 ). The d and r stand for the diameter and the radius of the sphere

respectfull! both in (m). #e "ill also be calculating the uncertaint! in thediameter in order to &nd the uncertaint! in the %olume then &nall! in the

densit!. 'inall!, the experimental %alue of $.

II. INTRODUCTION

#hen "e make a measurement, "e generall! assume that some exact or true

%alue exists based on ho" "e de&ne "hat is being measured. #hile "e ma!

ne%er kno" this true %alue exactl!, "e attempt to &nd this ideal uantit! to the

best of our abilit! "ith the time and resources a%ailable. s "e makemeasurements b! di*erent methods, or e%en "hen making multiple

measurements using the same method, "e ma! obtain slightl! di*erent results.

+o ho" do "e report our &ndings for our best estimate of this elusi%e true

%alue The most common "a! to sho" the range of %alues that "e belie%eincludes the true %alue is-

easurement = best estimate uncertaint!

ccurac! is the closeness of agreement bet"een a measured %alue and a true

or accepted %alue. easurement error is the amount of inaccurac!.0recision is a measure of ho" "ell a result can be determined ("ithout

reference to a theoretical or true %alue). 1t is the degree of consistenc! andagreement among independent measurements of the same uantit!2 also the

reliabilit! or reproducibilit! of the result.

 The statement of uncertaint! associated "ith a measurement should include

factors that a*ect both the accurac! and precision of the measurement.

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III. DATA AND ANALSISTa!"e No 1: Measurements

 Table o -easurement

eter+tick(cm)

Vernier(cm)icrometer(c

m)

5ero 6eading 7 7 78ength (8) 9 9.7 9.7

 :8 (cm) 7.7; 7.77; 7.7779

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$or t'e *ernier:).).#. $rom Ta!"e 1

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Ta!"e No): Resu"ts rom ca"cu"ations

  eter +tick Vernier icrometer

Volume (cm3) 4.79 3.4 3.E

@ensit! (g/cm3) ?.93 ?.3 ?.334

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• Jsing these uncertainties "e can &nd out "hether our measurements

"ere accurate, precise, and realistic.

/II Reerences

• @epartment of 0h!sics and stronom! (Mditionn.,Jni%ersit! Nookstore

Fustom 0ublising, pp. 4K

• Triola, ario '. , Mlementar! +tatistics. Tenth Mdition. assuchussets.977.