Experimental Physics Lab Handbook: Measuring and Reporting Uncertainties, Lab Reports of Physics

Download Experimental Physics Lab Handbook: Measuring and Reporting Uncertainties and more Lab Reports Physics in PDF only on Docsity! l\rrrrrrrrrrrrrrr laFrrrrrrrrrrrrrrrrrrrrrrr tr l'a I Read Me First! Read Me First! 1 Hints for doing labs This section is to introduce you to the methods of experimental physics, as well as to familiarize you with techniques that are common to many of the labs. The overall outline of a physics lab is: 1. Theoretical description of the phenomenon to be studied. 2. Experimental description of the how the phenomenon can be measured. 3. specific information about the equipment used for measurement. 4. Procedures for making and recording measurements. 5. Analysis of the data to give experimental results. 6. Conclusions and discussion of results. In the labs that follow, there are 'Pre-lab' exercises and questions to ger you familiar with the theoretical and experimental basis for the labs; the pre-lab should be done prior to coming to lab, but not so far ahead of time that you forget what the lab is about by the time you actually do the lab. While setting up and doing the lab, you should be asking yourself 'am I getting consistent results'? 'Where are the errors'? Dashing off some quick calculations and rough graphs while you are doing the lab can be very useful to let you know when things aren't going quite right. If you discover problems while you are doing the lab, you have a chance of correcting the problems, remeasuring, etc. A problem found later will be much harder to correct. This is also why you should record as much information as you can about the condi- tions under which you are doing the lab, the setup, all measurements, etc. Sometimes /> 10 the extra data (even if the procedure doesn,t ask for it) provides let you untangle what really happened. Don't rely on your memory down! Doing your analysis and conclusions will be much easier if you've analysis during the lab, have written down everything, and given sources of error while setting up and performing the lab. Read Me First! the vital clue to for this: write it done some rough sorne thought to 2 Measurements and Errors Whenever you make a measurement of a quantity, there is inevitably some uncertainty or 'error' in the measurement. As an example, suppose that you weigh yourself on a bathroom scale. What you measure is limited by your ability to accurately estimate fractions between the marks on the dial of the scale (if an analog scale) or in the number of digits displayed (if a digital scale). Perhaps the dial is moving slightly (or digits flickering) as you breath and move slightly, so taking a single measurement will have some uncertainty about how well it represents an 'average' weight. In addition, one should ask how well the scale is calibrated: is a precisely 1kg mass recorded as exactly 1.00kg? or does the scale show (for example) 1.03kg? All of these (and more) contribute experimental error to your measurement. One of your goals in these labs is to reduce the amount of experimental error to a minimum, and another is to quantify the amount of error that inevitably remains. While all measurements are subject to error, with a good understanding of the sources and amounts of the error, one can still get results that are a very good estimate of the underlying 'true' values. 3 Rounding and Significant Fisures If a friend tells you that they got on the scale and have a mass of 76 kg, one would be justified in thinking that the friend's 'true' mass is somewhere between Zb.5 kg and 76.5 kg; because one would typically not weigh oneself with tremendous accuracy, and just round off to the nearest kilogram. But if the friend tells you that they have a mass of 76.7254kg, one would conclude that they di'd take extreme steps to measure their mass accurately. Similarly, if they say that they mass 'about 70 kg' one might conclude that it is only a rough estimate of their mass, based both on the 'about', and. the fact that the mass is giuul to the Read Me First! the square root of the 13 (3) number of measurements: o(*) tm' :"ilHf:H_:1"^": 1": weight measurements shourd be*' fl1l*ul*':,: :irY* i#;ilffi;:il-HlX.:: reported as 75'2 * 0 1 kg, and can be reduced uv t"r.,,,s th.ffi;:?';#H:il'*xxl,T.l,j,",r'*t 4.L precision, Systematic Error, and Bias The precision of your measuremeats is how closely they represent the ,true, value i,.t'i.?',TJ':i:.fi.ffi :Jff ,nlJ,T.il:' u, "..u,u.r' one can .r1* u",,the true value), and precis" *uurur"ments that har ry precise (they all differ fromprecise, but there is a-tot or,r.ufiur, in the ;";r;;#JJ$ accuracv (the average isTo use our weighi"g u"u*p1u"ug"irr, ,"oo"* ,rrli the scare reads row by b kg. w.could have hightv ieptJautili;-;;"rurements, but there wilr arways be a b kg error.The b kg offset in trre r;;;-j; * exampre of a systematic L""o", a, of yourmeasurements are 'systematically'low by t6.'w; louta remove this systematic e*orby calibrating.the scare,-;;;;il* some ,known, masses on the scale and recordingffg!:ffi':#:f H-;ft ' :ffiy;;F # J;1.# 3"0* c" u et*.en -..J u, t h e scar e (There would i-1t]',lt **t rv".matic error from how we, known the ,known,masses are' but it would pru.u*Jbry be a *r;-r;;;er error.)similarlv one could ttu* u;.!i ,yrtu-uti. u.r#'rro* tidar effects: the gravita_tional attraction of the *oo" nuoutl a..r.*;l;.;*ight measured. A theoreticar;:til:l]l1"[:'i-!'.'f'at' tt'i'"'i'iu*u*i" "rro, quitu accuratery, but it,s unrikery to one particular form of systematic error rs called bias. Bids comes from a system_ ,T#"TT"H:.has the.effeci "io*r,tr* on.', *u*Jul*.r,t, consistentry too hish or Again with our weighing exampre, suppose that you_weigh yourserf at differenttimes of day' but you ro.g;t to eripty your pockets" before stepping on the scale.sometimes your po"k.t, ur?-*o"rri, **ptv, other times you have some coins in yourpockets that increases your *t*orld weight. n. "r.i"tion in how much you have inyour pockets will decrease ttt" .uproaucibitity or trre mJasurements (statisiicar error),but taking the mean of many *;;;.*ents can overcome that. However, there will H i:*il:f f;TJil;l#;;llii!ft'"L'l *own as a, s t at is t i car error,, l 74 Read Me First! still be an overall bias towards larger weights (non-empty pockets always make youheavier' never lighter) that even *uny repeated measurements will not overcome. Itj:Jr: case where careful experimental procedure can reduce or eliminate a source systematic errors are g€nerally more difficult to eliminate than statistical errors;the first step is tg trv.and identify ,our.., of systematic errors, estimate (throughmeasurement or theory) the size of their :f9.t, then try to remove the errors throughimproved procedures, calibrations, or additionar rneasurements. You will always have many possible sources of ,yrtu*"tic errors, but the overallerror is nearly always dominated by a single systemaiic error that is largest in magni-tude' so one's effort in reducing systematic error should always be directed towardsthe largest error first: you'll neue, see the systematic error from tides when weighingsomeone unless you first get them to empty their pockets before stepping on the scale. I I ; a I I I a I a I a I a I a I t t - ! , rt ) rt !̂ a - -I\-