Question

figure 2.3

EXPERIMENT Experimental Uncertainty (Error) and Data Analysis 2 Laboratory Report TI QUESTIONS 1. Read the measurements on the rulers in Fig. 2.9, and comment on the results Ruler 1 om 5 Ruler 2 cm 6 Ruler 3 TTm 6 Figure 2.9 2. Were the measurements of the block in part tb) of Procedure 2 all done with the same instrument? Explain. 3. Referring to the dart analogy in Fig. 2.3, draw a dart grouping that would represent poor precision but good accuracy with an average value. 4. Do percent error and percent difference give indications of accuracy or precision? Discuss cach 5. Suppose you were the first to measure the value of some physical constant experimentally. How would you provide an estimate of the experimental uncertainty? mens siound tien UC maue wTeauce uc uncena y TOun instructor may wish to set a maximum percent error for experimental results. AVERAGE (MEAN) VALUE Most experimental measurements are repeated several times, and it is very unlikely that identical results will be obtained for all trials. For a set of measurements with pre- dominantly random errors (that is, the measurements are all equally trustworthy or probable), it can be shown math- ematically that the true value is most probably given by the average or mean value. The average or mean value x of a set of N measure PERCENT DIFFERENCE It is sometimes instructive to compare the results of two measurements when there is no known or accepted value The comparison is expressed as a percent difference which is the ratio of the absolute difference between the experimental values E2 and E, and the average or mean value of the two results, expressed as a percent. ments is absolute difference Percent difference x 100% (2.3) - average N N where the summation sign X is a shorthand notation indi- cating the sum of N measurements from x to xy. (x is com monly referred to simply as the mean.) Eg-E (E, E/2 Percent difference x 100% ( 2.2)

Answer 1

answer 1. ans in ruler 3 is ..= 3.7 cm

length is same in all 3 rulers,

ruler 1 : this ruler is centimeter scale but only have integer scale so scale cant measure anything in between . so due to this scale is not enough to measure length properly

ruler 2 : this scale have 0.5 cm markingbut this marking is not enough to measure the other extra length. so due to this scale is not enough to measure length properly

ruler 3 : this scale have more precision than 0.5 cm it can measure upto 0.1 cm precision so this is one valid instrument to measure given length

answer 2. all the measurement is done with the same cm scale ruler but the only difference is the level of accuracy of the instruments only the ruler 3 is more accurate to measure.

answer 3. to solve we need more grouping data to plot a graph . data is not enough.

answer 4.

To calculate percentage error, use the formula: [(exact value - approximate value)/exact value] x 100. First, subtract the approximate value from the exact value. Then, divide that number by the exact value. Finally, convert fractions to decimal form and multiply your answer by 100 to find the percentage error.   

The experimental value is your calculated value, and the theoretical value is your known value. A percentage very close to zero means you are very close to your targeted value, which is good. It is always necessary to understand the cause of the error, such as whether it is due to the imprecision of your equipment, your own estimations, or a mistake in your experiment.

  

Now let's find out when, why and how to use it ...

When Should it be Used?

Percentage Difference is used when both values mean the same kind of thing (for example the heights of two people).

• But if there is an old value and a new value, we should use Percentage Change
• Or if there is an approximate value and an exact value, we should use Percentage Error

Why do we Average the Two Values?

Because there is no obvious way of choosing which value is the "reference" value.

Example : lets have of two people is 15 and 25

• If we use "15" we get 10/15 = 66.6...%
• If we use "25" we get 10/25 = 40%

But which one should we use? And if someone else did the calculations which one would they use?

So it is best to choose a value halfway between so there is no confusion.

answer 5: Experimental uncertanity is always measured in terms of the least count of the measuring instrument

  

X Y R = Z OR OY oZ R X 2 2 SZ Z) SY OR RI X Y

depending on the formula used to provide answer we can find the error contributed by each component . its doesnt matter whether any variable is in multiplication or in division each error will be added to the main formula   are the least count  in X and Y readings  

Dπ, δy

after my experiment i can use this formula to predict my experimental error.