1. Why do you think uncertainty in measurement occurs? Give...

1. Why do you think uncertainty in measurement occurs? Give at least two reasons [2 Points]. 2. If x = 2.5 ± 0.1 cm and y = 3.1 ± 0.1 cm, and z = x + y, determine $z_0$ and the upper bound of $delta z$ [1+1 = 2 Points]. $z_0 = x_0 + y_0$ = 2.5 + 3.1 $z_0$ = 5.6 cm upper bound of $delta z = sqrt{delta x^2 + delta y^2}$ $= sqrt{0.1^2 + 0.1^2}$ upper bound of $delta z$ = 0.14 3. The volume of a cylinder is given by $V = pi r^2 l$, where r is the radius and l is the length of the cylinder. If we measured r = 2.10 ± 0.05 cm, and l = 3.40 ± 0.05 cm, determine the uncertainty in volume. Show your calculation [Hint: Use Equation 4] [2 Points].

Transcript

00:01 In this problem we have two questions which are all related to some uncertainties.

00:09 And let's get started with the first one.

00:14 Here we are asked to give two at least two reasons for the sources or the reasons of uncertainties in measurements.

00:27 So actually there are two sources of uncertainty.

00:30 So let me just write them down.

00:35 Sources of uncertainties in measurements.

00:43 The first one is the limitation of the measuring instrument.

00:51 Limitation of the measuring instrument.

01:04 And the second one is the skill of the experimenter who performs this measurement.

01:17 So it's a human issue, basically.

01:21 So skill of the experimenter performing the measurement.

01:39 So these are our two sources of uncertainties in measurements.

01:47 Now, let us do the second one.

01:50 Second question.

01:52 We have two numbers that contains some errors.

01:55 So x equal to some x bar plus minus delta x.

02:01 So i am writing it in this form so that you know my notation.

02:06 So we have y equal to y bar indicating that it is a central value plus minus delta y.

02:14 Then we define this quantity z to be x plus y.

02:20 And we are going to compute the central value of this z number and the upper bound of the delta z, namely the error of this number.

02:34 So it's express this x bar plus minus delta z.

02:41 So z bar is simply given by x bar plus y bar.

02:48 So we have 2 .5 plus 3 .1 centimeters.

02:57 So this is just 5 .6 centimeters.

03:07 And we have this delta z given by delta x squared plus delta y squared.

03:21 Okay, maybe i should put some parentheses here so that these are the squares of errors, not the errors of the squares.

03:30 So this is 0 .1 squared plus 0 .1 squared and we have this huge number 0 .1 .1421 centimeters.

03:50 I am writing this in this form to point out to point out to something.

04:00 We have z equal to 5.

04:04 6 plus minus some error...

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