Uncertainty in Measurement

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Apr 3, 2024

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Physics 4B Name: Uncertainty Activity Purpose: Student Learning OQutcomes: e Recall the difference between error and uncertainty. e Recall how to approximate uncertainty for different measuring devices. e Recall how = to propagate uncertainty for calculated values. Procedure: Using a pen, complete each question. For the calculations, show work and include symbolic equations. You may attach extra pages. Part 1: Methods for Finding Uncertainty Note: There is not a single method to find the uncertainty in any of the examples below. There are many techniques that would work, but there are also many techniques that would not work. Make sure to think about the set up and describe a valid technique. 1. Ifyou are using an alcohol thermometer to measure room temperature, how would you find the uncertainty in the temperature? Explain why this is a valid method to find uncertainty for this device. S 2. Ifyou are using a temperature probe and Logger Pro to measure room temperature, how would you find the uncertainty in the temperature? Explain why this is a valid method to find uncertainty for this device.

3. If you are using a stopwatch to find the time for an event, how would you find the uncertainty in the time? Explain why this is a valid method to find the uncertainty for this device. 4. Ifyou are using a multimeter to measure the current and the values fluctuate from 28.6 mA to 28.8 mA, how would you find the uncertainty in current? Explain why this is a valid method to find the uncertainty for this device. Part 2: Numeric Uncertainty Values Clearly box your answer to each question. 1. For this scale reading, record the mass with uncertainty, in appropriate units. (The value displayed 1s in grams.) 2. For this digital caliper reading, record the distance with uncertainty, in appropriate units. (The value displayed i1s in milimeters.) V il = = A T AL LS ESE

3. For this multimeter, record the resistance with uncertainty, in appropriate units. (The resistance is displayed in Ohms, €2, which is an SI derived unit.) . , — = I e #TF S W \ e , ."l" - * ‘ i3 fi - 4 g - F = ol > St A 4. While measuring voltage you set up the equipment so the voltage should be exactly the same each time. You repeat this identical experiment for twenty trials. The values measured are shown in the table below. (Voltage is measured in Volts, V, which 1s an SI derived unit.) Trial # Voltage (V) Trial # Voltage (V) 1 1.25 11 1.25 2 1.27 12 1.24 3 1.26 13 1.29 4 1.25 14 1.24 5 1,28 15 1.25 6 1.27 16 1.28 7 1.28 17 1.26 8 1.26 18 1.27 9 1.26 19 1.26 10 1.26 20 1.27 Based on these values, show work to find the measured voltage, with uncertainty. Explain the process to find uncertainty and why this 1s a valid technique 1n this case.

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Part 3: Propagation of Uncertainty 1. A sample of an unknown material has a mass of m =245.5£0.1g. When Q =3421+1J of heat are added to the sample, its temperature changes by AT =7.35+0.05K . UsingQ =mc AT , show all work to find the specific heat capacity (with uncertainty). 2. Two resistance boxers are connected in parallel. Measured separately: R =326+2Q and R, =194x£2Q. Using L = L + i , show all work to find the equivalent resistance (with R, R, equivalent uncertainty).

3. A loop has aradius of » =45.6+0.1mm and there is a current of 7 =38.6 1+ 0.2 mA through the loop. (4 x107 T/ 1 2rtan@ This causes a compass inside the loop to deflect by € =42.0° £0.5°. Using B = 2 show all work to find the magnetic field (with uncertainty). Conclusions:

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