measurement and uncertainty - memorial university€¦ · physics 1020 laboratory #1 measurement...

Physics 1020 Laboratory #1 Measurement and Uncertainty

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Measurement and Uncertainty

Any experimental measurement or result has an uncertainty associated with it. In todays lab you will perform a set of very simple measurements. You will have to estimate the random uncertainty associated with each of them. As a rule of thumb the precision of your measuring device (for example a ruler) is always a very good starting value for your uncertainty. Furthermore you will be asked to perform some calculations using the values you just measured. The results of those calculations will also have an uncertainty associated with them. To obtain those values you will have to follow a set of rules. They are explained on page X of this book in “Making Measurements in Physics” section. Finally you will collect a set of 10 measurements of the same quantity from your classmates and asked to calculate their average. That result also has an uncertainty associated with it. Your instruction will tell you how to calculate it.

Also recall that the perimeter 𝑃 of a rectangular object is the total length of all the sides, i.e

𝑃 = 𝐿 + 𝐿 + 𝑊 + 𝑊 = 2𝐿 + 2𝑊

where 𝐿 is the length of the object and 𝑊 is the width.

Similarly the area 𝐴 of a solid rectangular object is

𝐴 = 𝐿 × 𝑊

Below is a summary of some of the rules you will need for your uncertainty calculations: Addition/Subtraction Rule

When finding a result by adding or subtracting uncertain quantities, the absolute experimental uncertainty in the result is the sum of the absolute experimental uncertainties of the uncertain quantities.

𝐼𝐹 𝒛 = 𝒙 + 𝒚 𝑂𝑅 𝒛 = 𝒙 − 𝒚 𝑇𝐻𝐸𝑁

𝜹𝒛 = 𝜹𝒙 + 𝜹𝒚


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Example:

𝐴 = (122 ± 5) 𝑚, 𝐵 = (207 ± 2) 𝑚

𝐶 = 𝐴 + 𝐵 = 122 𝑚 + 207 𝑚 = 329 𝑚

𝛿𝐶 = 𝛿𝐴 + 𝛿𝐵 = 5 𝑚 + 2 𝑚 = 7 𝑚

𝐶 = (329 ± 7) 𝑚

Multiplication/Division Rule

When finding a result by multiplying or dividing uncertain quantities, the relative experimental uncertainty in the result is the sum of the relative experimental uncertainties of the uncertain quantities.

𝐼𝐹 𝒛 = 𝒙 × 𝒚 𝑂𝑅 𝒛 =𝒙

𝒚 𝑇𝐻𝐸𝑁

𝜹𝒛

𝒛=

𝜹𝒙

𝒙+

𝜹𝒚

𝒚

Example:

𝐴 = (120 ± 5)𝑚, 𝐵 = (200 ± 10)𝑚

𝐶 = 𝐴 × 𝐵 = 120 𝑚 × 200 𝑚 = 24000 𝑚2

𝛿𝐶

𝐶=

𝛿𝐴

𝐴+

𝛿𝐵

𝐵=

5 𝑚

120 𝑚+

10 𝑚

200 𝑚= 0.0917

𝛿𝐶 =𝛿𝐶

𝐶× 𝐶 = 0.0917 × 24000 𝑚2 = 2200 𝑚2

𝐶 = (24000 ± 2000)𝑚2 𝑜𝑟 (2.4 ± 0.2) × 104𝑚2

Note: The uncertainty 𝛿𝐶 = 2200 𝑚2 has been rounded to one significant figure, so it

becomes 2000 𝑚2.

Important: the only difference in the two rules is one uses absolute experimental uncertainty and one uses relative experimental uncertainty. If you use the multiplication rule, you can always get the absolute experimental uncertainty from the relative experimental uncertainty.


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Prelab Questions These questions need to be completed before entering the lab. Please show all workings. Prelab 1

A rectangular object has length L = 25.3 0.2 cm and width W = 18.6 0.5 cm.

• What are the absolute uncertainties in length and width?

• Find the relative uncertainties in length and width.

Prelab 2 Given a set of length measurements: 60.4, 60.0, 61.1, 60.8, 60.6 cm.

• Find the average (mean) length

• Find the standard error (refer to the introductory pages of your Lab

Workbook).

Marker’s Initials


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Laboratory Worksheet Name and Student Number: ___________________________ Partner: ___________________________ Date: ___________________________ Table 1:

Value Units

Length

Width

QUESTION 1: QUESTION 2:

𝛿𝐿 =

𝛿𝑊 =

QUESTION 3:

𝐿 =

𝑊 = QUESTION 4:

𝛿𝐿

𝐿=

𝛿𝑊

𝑊=


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QUESTION 5: CHECKPOINT: Instructor Initial QUESTION 6:

𝑷 = QUESTION 7:

𝜹𝑷 = QUESTION 8:

𝑷 = QUESTION 9:


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Table 2:

Value Uncertainty Units

Length


𝑨 = 𝑳 × 𝑾 = QUESTION 12:

𝜹𝑨

𝑨=

QUESTION 13:


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QUESTION 14:

𝜹𝑨 =

𝑨 =


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graph paper is 1 cm 1cm squares


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Table 3:

Value Uncertainty Units

Area



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Table 4:

Li (cm) Wi (cm)

L

W

L (cm)

W (cm)

N = (no units) N = (no units)

LL

N (cm)

WW

N (cm)

QUESTION 17:

�̅� =

𝜹�̅�

�̅�=


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QUESTION 18:

�̅̅̅� =

𝜹�̅̅̅�

�̅̅̅�=

QUESTION 19:

QUESTION 20:

measurement and uncertainty - memorial university€¦ · physics 1020 laboratory #1 measurement...

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