[Music] [Applause] [Music] [Applause] our first instructional video for general physics one and our first unit will be all about uncertainties and deviations in measurement but before you start with our lesson answer first the pre-assessment on the assessment sheets provided on you on your learning packet we have first lesson on our first unit and that is reporting measurement value we have four objectives for this particular lesson first differentiate accuracy from precision second use short annotation in reporting measurement uncertainties third estimate uncertainty of a derived quantity from estimated values and uncertainties of directly measured quantities and calculate the sum and difference of uncertainty of directly measured quantities now let us begin by defining what is uncertainty do you have any idea of what is an uncertainty or have you heard the word uncertain maybe you have heard that and let us define this the uncertainty is also called the error in physics okay because it indicates the maximum difference there is likely to be between the measured value and the true value okay so uncertainty is what we called as the error okay for example there is an accepted value that you want to measure but you didn't get it and there is uncertainty or there is error with that okay for example the measurement you want to get is 47 meters but you only get 44 meters so there is an error or uncertainty that is derived from your measurement and how do we classify those uncertainty we have what we call the precision and accuracy okay so contributions to uncertainty in measurement of physical quantities accrue from limitations in accuracy and limitations in precision inherent in all measurement process okay so but what is the difference with the two precision refers to the degree which successive measurement agree with each other okay for example when you walk from the school to a near shop you always count your steps and you always get a value of 15 steps okay so that is a precise measurement because the steps that you always count or that the steps that you always get is equivalent to 15 and that is a precise measurement now what is an accuracy accuracy is the nearness of a measurement x accepted value okay let's say for example the normal body temperature of a human is 37.0 degrees celsius okay but the when you measure the temperature on a thermometer you get a value of 36.9 degrees celsius and that is smeared to a value that is accepted which is 37.0 degrees celsius and that is only an accurate measurement because it is only near to the accepted value that should be get from the thermometer okay again position the successive measurement agrees with each other and an accuracy is the nearness of a measurement to an accepted value i hope you understand that next we often indicate the accuracy of a measurement value that is how close it is to be likely or how close it is likely to be the true value by writing the number then the symbol plus minus and a second number indicating the uncertainty of the measurement example we have x as a variable for the first number plus minus as the uncertainty symbol and the second number indicating the uncertainty of the measurement okay first an example the length of the table is 2.51 plus minus 0.02 meters what is the range of the true value or accuracy okay so as said earlier the reporting of measurement uncertainty is just like this we have the first value which is the derived quantity 2.51 and then we have uncertainty symbol plus minus okay what does it say it says that there is a higher amount or a lower amount that is uncertain to its derived value and what is that amount or value it is 0.02 okay so what does it says so it says that 2.51 may have a higher of higher value of 0.02 meters or a lower value deducted from it which is an another 0.02 meters so now we will indicate what is the range of true value or accuracy so how do we get that okay let us have the solution we have 2.51 plus 0.02 we will get first the higher value of the range by adding the uncertainty 0.02 meters so two point fifty one plus zero point zero two so it is get here or derive from you you will get two point fifty three meters okay for confirmation you may have a calculator and then type type the values and then we get the lower value by subtracting 0.02 from the base number 2.51 so 2.51 minus 0.02 is equal to 2.49 so likely the value exists between 2.49 and 2.53 and that is the uncertainty that we have okay so now how we will report this uncertainty for the report of the uncertainty we have 2.51 two meters so what where these two came from okay so this is the shorthand of the uncertainty that we have we have uncertainty value of 0.02 to write it on a report of measurement uncertainty we will just use the last value that is present on this uh derived uncertainty so the last value that we have is 2 so that will be written inside a parenthesis and that will be written after the base value 2.51 so our report will be 2.51 2 meters so it indicates that 2 is the uncertainty which is originally 0.02 okay let us have another example the diameter of a steel rod is given as 56 plus minus 0.02 millimeters what is the range of true value we have here 56 as the base number an uncertainty of 0.02 millimeters so we will do the first procedures that we did earlier so the solution we have we will get first the higher value of the 56 so we will add 0.00 0.02 millimeters to 56 and that will be simply 56.02 millimeters now we will get the lower value by subtracting 0.02 from the base number 56 and that is 56 minus 0.002 millimeters is equal to 55.98 millimeters so how we do the report is we will write 56 two millimeters again the base number is written first and uncertainty we will just get the last number from its uncertainty which is two and then enclose it on a parent in a parenthesis and write the unit of millimeters so we have 56 two millimeters okay what if the uncertainty is not written as a normal number or just like the 0.02 millimeters what if it is written in percentage okay for example 52 seconds plus minus 10 percent okay so it means that the maximum time is 52 seconds plus minus 10 percent of 52 which is 5.2 okay but in 5.2 so we should you should uh you will just type 52 times 10 and then percent symbol in your calculator or 52 times 0.0 or 0.1 so that's how you get the 10 of 52 okay so again an even is 52 seconds plus minus 10 it is also written in your learning packet so we have 52 seconds plus minus 10 percent of 52 so the 10 of 52 when we derive it it is equal to 5.2 okay now that we get the exact amount of uncertainty and it is derived from the percentage of 50 to 10 of 52 now what is the range of the true value let us have a solution first so we have already find the 10 percent of 52 which is 5.2 and now we will get d and the range of the uncertainty we have 52 plus 5.2 seconds is equal to 57.2 seconds and then we get the lower range we will subtract it so 52 minus 5.2 seconds is equal to 46.8 seconds and there is a difference between reporting um measurement value that is written on percentage all right so the report will be just like this we have 5.2 seconds over 52 seconds okay so the uncertainty which is 5.2 is written first in a parenthesis and then you will write the base value 52 seconds over it okay so you will put a bar line so we have 52 seconds over sorry 5.2 seconds over 52 seconds so that will be our final report okay next error propagation rules are clear when the derived quantity can be expressed as a sum difference quotient or product of the other okay now we will try if there are problems associated with calculating the sum or difference of uncertainties that can be get from a measurement okay we have a solved problem number one suppose the mass of the object one is x okay let us uh use that as a variable and is estimated to be 80 plus minus one gram well the mass of object is y and estimated to be 65 plus minus 2 grams how should the total mass z is equal to x plus y be reported okay so let us trim down the question okay it says here that we need to get the total mass of two objects that have both each uncertainties okay so object one meron shang uncertainty 80 plus minus one gram there is a one gram that is uncertain for that measurement and for object two meron taiyong 65 plus minus two grams which is z is equal to x plus y okay we have pe six steps okay so let us check if p6 is just easy okay it is not just uh difficult as you think so we have given values object one or x is 80 plus minus 1 gram and then object to y which is 65 plus minus 2 grams so that is our given values so how do we solve for the total mass of two objects with uncertain uncertainties so we have first get the total mass of the given values okay we will get the what the sum of the two values so we will get first their uh base number we have 80 and 65 and then add them up to get the total mass of the given values so we have total mass equal to mass of the object one plus mass of the object two and that is our object one is eighty and our object two is sixty five so eighty plus sixty five is equal to one hundred sixty one hundred 145 grams okay so we plus or we add 80 to 65 and that is equivalent to 145 grams that is so easy okay and that is for step one only let's proceed to second step get the higher mass of x and y by adding the uncertainty then add the derived values this will be your total higher mass okay so let us deal first we did higher mass okay so what we will do when we get the higher mass we add the uncertainty to the base value okay so the base value for the object one we have 80 for object two we have 65 so we will plus the uncertainty to them so we have higher mass of x or object one we have mass of object one plus one grams one gram i should say okay so 80 plus one is equal to 81 grams now for the higher mass of y or object 2 we have mass of object 2 plus 2 grams since we have 65 plus 2 so we have 65 plus 2 is equal to 67 grams so that is those are the higher masses of the two objects for the object one we have 81 grams and for object 2 we have 67 grams and we should get the total higher mass by adding the derived values okay so add the derived value so this is your total higher mass so we have total higher mass equal to higher mass of x which is 81 plus higher mass of y which is 67 when we add those two we have 148 grams 81 plus 67 that is 148 grams and that is our total higher mass okay next we get the lower mass of the two given values now so by subtracting the uncertainty we have lower mass of x equal to mass of object one again it is equivalent to 80 grams minus 1 grams so that will be 79 grams for lower mass of b or object number 2 or y you should say we have 65 minus 2 grams so we have 63 guns and then just like what we did earlier we get the total higher mass we will also get the total lower mass and that is total lower mass is equal to lower mass of x or object 1 minus lower mass of y that is object to we have 79 minus 6 79 plus 63 we have 142 grams okay again total lower mix so 79 plus 63 we have 142 grams and then the fourth step subtract the total mass from the total higher mass and total lower mass the value that you will get is the new uncertainty okay so that is total higher mass minus total mass you know a total higher mass is 148 grams minus nothing young sub 145 grams which is the total mass in kanina so going bava the nut and contaminate values again total must not end at 145 grams total higher mass is 148 grams and then total lower mass we have 142 grams at the next step so we have total higher mass minus total mass which is 148 grams minus 145 grams it is equal to three grams or positive three grams is a total lower mass minus total mass we have 142 minus 145 grams so that is negative 3 grams okay so now we have our final report okay the total mass should therefore be reported as 145 at the internal mass plus minus three grams and adding avoidance step four at the audio positive three and negative three pagasa my lung and reported as one we have 145 plus minus three grams and that is how should we report our total mass okay now what if we are asked to get the mass difference the total mass how about mass difference so same process or same procedure okay so we have mass difference total mass so mass difference is equal to mass of object one minus mass of object two again on object one not then we have 80 grams and an object two we have 65 grams so 18 minus 65 that is 15 grams and that is our mass difference next get the higher mass of x and y by adding the uncertainty then subtract the derived values this is your higher mass difference so we have higher mass is equal to mass of object one plus one gram of dominina so we have 80 grams plus one grams is equal to 81 grams okay and then higher mass of y is equal to mass of object to which is 65 plus two is equal to 67 grams now we will get the higher mass difference plus nothing 81 and 67 now we will subtract them okay so we have higher mass x minus higher mass y is equal to 81 minus 67 and you will get 14 grams [Music] next get the lower mass of x by subtracting the uncertainty then subtract the derived values this is your lower mass difference again lower mass x is equal to mass of object one minus one gram of minus a minute and so 80 minus one is equal to 79 grams and then lower mass y is equal to mass object 2 minus 2 grams so 65 minus 2 is equal to 63 gram and then we will subtract the lower mass of x and y to get the lower mass difference we have 79 minus 63 is equal to 16 grams okay subtract the mass difference from the higher mass difference and lower mass difference the value that you will get is the new uncertainty okay so we have higher mass difference minus mass difference we have 14 you know what not green is higher mass difference and then your mass difference is 15 grams when we subtract 80 minus 65 okay so 14 minus 15 is equal to negative one and then lower mass difference minus mass difference in the one that is a lower mass difference is 16 gram and then again your mass difference can ena is 15 grams that is 80 minus 65 so 16 minus 15 is equal to one gram now we will write our final report report we have mass difference is 15 you know nothing much difference plus minus one grams okay okay so that ends our discussion now to learn more about measurement uncertainties and how should they be reported open the file on your flash drive propagation of uncertainties that is a pdf file or if you have a cell phone with qr code scanner scan this to direct you to the link which is all about propagation of uncertainties okay so let me leave you with these values or with this quotation life is uncertain and that's part of it moving to the unknown can be frightening no matter how fast the world is changing uncertainties never go away now that we are in the middle of a worldwide crisis how should we deal with uncertainties brought by the kobe 19 pandemic okay write your answer on the values integration area on your learning packet okay let's check how you understood our lesson answer unit 1 activity 2 and 3 on the assessment sheets on page 4. ok so i will leave you with this bible verse be anxious for nothing but in everything by praying and simplification with thanksgiving let your requests be made known to god and the peace of god which passes all will guard your hearts and mind through jesus christ philippians 4 6-7 thank you and god bless