Topic 1 - Measurement and Uncertainties

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<p>21/07/2018</p><p>Measurement and Uncertainties</p><p>International Baccalaureate Physics topic 1</p><p>W Richards</p><p>Education Using PowerPoint</p><p>1.1 – Measurements in Physics</p><p>21/07/2018</p><p>21/07/2018</p><p>Standard Form and prefixes</p><p>Prefix	Symbol	Multiplier</p><p>Giga	G	109</p><p>Mega	M	106</p><p>Kilo	K	103</p><p>Milli	m	10-3</p><p>Micro	μ	10-6</p><p>Nano	n	10-9</p><p>Pico	p	10-12</p><p>Even harder questions!</p><p>What is 1mm2 in m2?</p><p>What is 1μm2 in m2?</p><p>What is 10mm3 in m3?</p><p>How many pm3 fit in a cubic kilometre?</p><p>Try these questions…</p><p>What is 1cm in m?</p><p>What is 15mm in m?</p><p>What is 10μm in m?</p><p>What is 600nm in m?</p><p>21/07/2018</p><p>International System of Units</p><p>There are six basic quantities we need to know about. Their units are called S.I. units:</p><p>Base quantity	Base unit	Symbol</p><p>Length	metre	m</p><p>Mass	kilogram	kg</p><p>Time	second	s</p><p>Current	ampere	A</p><p>Temperature	Kelvin	K</p><p>Amount of substance	mole	mol</p><p>Question: Why is it important to have a common system across the world in science?</p><p>10 question quiz</p><p>21/07/2018</p><p>What is the standard form for giga?</p><p>Nano?</p><p>Pico?</p><p>What is the prefix for 106?</p><p>10-6?</p><p>Name all six base quantities</p><p>Name the six base units that go with these quantities</p><p>What is the wavelength of blue light (400nm) in standard form?</p><p>One atom is roughly 1x10-10m wide. Express this in nm and pm.</p><p>Ted’s new iPhone 7 has 32Gb storage. Express this in standard form and in terms of Kb.</p><p>21/07/2018</p><p>Derived Units</p><p>Derived units are units that are made up out of base units. For example, the unit for speed (metre per second) comes from the base units for distance and time.</p><p>Newton (force)</p><p>Joule (energy)</p><p>Pascal (pressure)</p><p>Watt (power)</p><p>Coulomb (electric charge)</p><p>The following units are derived. Use suitable equations to express each unit in terms of base units:</p><p>Estimations</p><p>21/07/2018</p><p>Estimate the following and give your answers in a suitable unit and to a suitable number of significant figures:</p><p>The length of this classroom</p><p>The diameter of a 1p coin</p><p>The width of a 1p coin</p><p>The mass of a 1p coin</p><p>The internal and external diameter of a copper pipe</p><p>The mass of a block of metal</p><p>The volume of a block of metal</p><p>The density of a block of metal</p><p>1.2 Uncertainties and Errors</p><p>21/07/2018</p><p>True Value and Accuracy</p><p>21/07/2018</p><p>The “true value” is the value that would be obtained with ideal measurements. A measurement is judged to be “accurate” if it close to that value. For example, what does this thermometer read?</p><p>I reckon it’s 26OC</p><p>I reckon it’s 24OC</p><p>I reckon it’s 22OC</p><p>My measurement was the most accurate as it was closest to the true value!</p><p>Uncertainty</p><p>21/07/2018</p><p>Consider the same thermometer readings again:</p><p>Is it 22OC, 24OC or 26OC?</p><p>“Uncertainty” means “the interval within which the true value would lie” with a given level of probability, e.g. “the temperature is 24OC ± 2OC”</p><p>In this case:</p><p>Absolute uncertainty = 2OC</p><p>Fractional uncertainty = 2/24 = 0.08</p><p>Percentage uncertainty = 2/24 x 100 = 8%</p><p>21/07/2018</p><p>Micrometers</p><p>Micrometers are more accurate and can be used to measure the width or depth of an object to an accuracy of 0.01mm…</p><p>21/07/2018</p><p>21/07/2018</p><p>21/07/2018</p><p>21/07/2018</p><p>Uncertainties in Measurements</p><p>21/07/2018</p><p>Task:</p><p>Measure the width of a 100g mass using:</p><p>A metre ruler</p><p>A normal ruler</p><p>A micrometer</p><p>Now work out the % uncertainty in each measurement.</p><p>Measurement Error and % difference</p><p>21/07/2018</p><p>A “measurement error” is defined as “the difference between a measured value and the true value”, e.g:</p><p>Here’s my friend. I’ve just measured him with a metre ruler and I think he’s 170cm tall.</p><p>Unlucky. I’m actually 175cm tall.</p><p>What is the difference between these results and what is the percentage difference between them?</p><p>Precision</p><p>21/07/2018</p><p>“Precise measurements” are measurements that show very little spread around the mean average value.</p><p>Which of the following two sets of data are the most precise?</p><p>Conc. of acid	Time taken for magnesium to react/s			Average time/s</p><p>Attempt 1	Attempt 2	Attempt 3</p><p>Low	50	52	54	52</p><p>High	20	24	22	22</p><p>Notice that precision depends only on random errors – it gives no indication of how close results are to the true value!</p><p>Random errors</p><p>21/07/2018</p><p>Random errors can occur with any experiment but some experiments can have more random errors than others. For example, here are two experiments:</p><p>Hooke’s law, where different forces are hung on a spring and the extension is measured.</p><p>Choice chambers, where woodlice are “invited” to choose their living conditions.</p><p>Which one of these experiments would probably have the most random errors and what would do about it?</p><p>21/07/2018</p><p>Zero Errors</p><p>What’s wrong with this balance reading?</p><p>Systematic Error</p><p>21/07/2018</p><p>A systematic error is one where the measurement differs from the true value by a consistent amount each time, e.g:</p><p>Notice that a zero error usually results in a systematic uncertainty.</p><p>21/07/2018</p><p>Systematic Errors on a Graph</p><p>Resistance of wire/Ω</p><p>Length of wire/cm</p><p>x</p><p>x</p><p>x</p><p>x</p><p>x</p><p>x</p><p>x</p><p>x</p><p>0</p><p>According to this graph, a wire that’s zero cm long has some resistance, which can’t be right. What went wrong?</p><p>Errors</p><p>21/07/2018</p><p>Nathan wants to go on the Stealth ride at Thorpe Park. He looks on a map and draws a straight line from school to Thorpe Park and sees that the distance is 39.2 miles. He then drives to Thorpe Park and, on parking in the car park, sees that he’s actually driven 41.2 miles.</p><p>Why was Nathan’s measurement wrong? Think of at least 3 reasons.</p><p>What is the minimum and maximum distance he measured on the map?</p><p>What is the minimum and maximum distance he could have actually travelled?</p><p>Error Bars and Error Boxes</p><p>21/07/2018</p><p>Consider an experiment where a student is measuring the mass of water in different sizes of container:</p><p>Length of container/cm	Mass/g</p><p>1	1.1</p><p>2	2.0</p><p>3	2.9</p><p>4	4.1</p><p>5	5.0</p><p>Error Bars and Error Boxes</p><p>21/07/2018</p><p>Step 1: Work out the uncertainty for each measurement.</p><p>Length of container/cm	Mass/g</p><p>1	1.1</p><p>2	2.0</p><p>3	2.9</p><p>4	4.1</p><p>5	5.0</p><p>E.g. for this middle value, length = 3 ± 0.5cm and mass = 2.9 ± 0.05g. Therefore:</p><p>The length could be between 2.5cm and 3.5cm</p><p>The mass could be between 2.85g and 2.95g.</p><p>Error Bars and Error Boxes</p><p>21/07/2018</p><p>Step 2: Draw the graph</p><p>Length /cm	Mass/g</p><p>1	1.1</p><p>2	2.0</p><p>3	2.9</p><p>4	4.1</p><p>5	5.0</p><p>Length/cm</p><p>0	1	2	3	4	5	0	1.02	2.0099999999999998	2.98	4	5.01	Error Bars and Error Boxes</p><p>21/07/2018</p><p>Length /cm	Mass/g</p><p>1	1.1</p><p>2	2.0</p><p>3	2.9</p><p>4	4.1</p><p>5	5.0</p><p>Length/cm</p><p>Step 3: Label these uncertainties on the x and y plots:</p><p>E.g for the middle measurement:</p><p>The length could be between 2.5cm and 3.5cm</p><p>The mass could be between 2.85g and 2.95g.</p><p>0	1	2	3	4	5	0	1.02	2.0099999999999998	2.98	4	5.01	Uncertainties in Gradients</p><p>21/07/2018</p><p>Consider another graph of results from a different experiment:</p><p>The gradient of this line is 1. What else could it be? Draw the steepest and least steep lines you can and work out the uncertainty:</p><p>0	1	2	3	4	5	0	1.02	2.0099999999999998	2.98	4	5.01	Uncertainty</p><p>21/07/2018</p><p>The diameter of a tube has been measured in 3 different places as 21, 22 and 26mm. Assuming none of these results are anomalous, what is the uncertainty and % uncertainty?</p><p>Method 1</p><p>Average of these values = 23mm</p><p>Half of the range = 2.5mm</p><p>Therefore value is 23mm ± 2.5mm</p><p>% uncertainty = 2.5/23= 23mm ± 11%</p><p>Method 2</p><p>Average of these values = 23mm</p><p>Maximum difference = 3mm</p><p>Therefore value is 23mm ± 3mm</p><p>% uncertainty = 3/23 = 23mm ± 13%</p><p>Uncertainties are an estimate so both methods are fine but EXPLAIN YOUR WORKING!!!</p><p>Compounding Uncertainties</p><p>21/07/2018</p><p>To find the total error in a measurement, follow these guidelines from the data booklet:</p><p>If</p><p>Then</p><p>If</p><p>Then</p><p>If</p><p>Then</p><p>In other words, if quantities are being added or subtracted then the total error is found by adding the absolute uncertainties.</p><p>In other words, if quantities are being multiplied or divided then the total error is found by adding the fractional or percentage uncertainties.</p><p>In other words, if a quantity is being raised to an</p><p>exponential power then the total uncertainty is the absolute (or percentage) uncertainty multiplied by the power.</p><p>1.3 Vectors</p><p>21/07/2018</p><p>21/07/2018</p><p>Vector vs. scalar</p><p>Scalar quantities have size (“magnitude”) only and no direction.</p><p>Vector quantities have both size and direction.</p><p>Scalar or vector???</p><p>Scalar</p><p>Vector</p><p>1. Mass</p><p>2. Distance</p><p>3. Displacement</p><p>4. Speed</p><p>5. Velocity</p><p>6. Energy</p><p>8. Power</p><p>7. Time</p><p>9. Momentum</p><p>10. Current</p><p>11. Force</p><p>12. Acceleration</p><p>21/07/2018</p><p>Vectors</p><p>100ms-1</p><p>5ms-1</p><p>10km</p><p>10km</p><p>14.1km</p><p>100.1ms-1</p><p>21/07/2018</p><p>Resolving Vectors</p><p>Consider a diagonal push:</p><p>F</p><p>θ</p><p>This force is given by:</p><p>F1 = F sin θ</p><p>This force is given by:</p><p>F2 = F cos θ</p><p>F1</p><p>F2</p><p>21/07/2018</p><p>Resolving Vectors – example questions</p><p>Calculate the horizontal and vertical components of the following:</p><p>1)</p><p>3)</p><p>4)</p><p>2)</p><p>50O</p><p>35O</p><p>80O</p><p>10N</p><p>20N</p><p>10N</p><p>8N</p><p>Work out the size and direction of the resultant force:</p><p>50O</p><p>45O</p><p>15N</p><p>20N</p><p>30O</p><p>image1.png</p><p>image2.png</p><p>image3.jpeg</p><p>image4.jpeg</p><p>image5.png</p><p>image6.png</p><p>image7.png</p><p>image8.png</p><p>image9.jpeg</p><p>image10.png</p><p>image11.jpeg</p><p>image12.jpeg</p><p>image13.jpeg</p><p>image14.jpeg</p><p>Microsoft_Excel_Worksheet.xlsx</p><p>Sheet1</p><p>0		0</p><p>1		1.02</p><p>2		2.01</p><p>3		2.98</p><p>4		4</p><p>5		5.01</p><p>0	1	2	3	4	5	0	1.02	2.0099999999999998	2.98	4	5.01</p><p>Sheet2</p><p>Sheet3</p><p>Microsoft_Excel_Worksheet1.xlsx</p><p>Sheet1</p><p>0		0</p><p>1		1.02</p><p>2		2.01</p><p>3		2.98</p><p>4		4</p><p>5		5.01</p><p>0	1	2	3	4	5	0	1.02	2.0099999999999998	2.98	4	5.01</p><p>Sheet2</p><p>Sheet3</p><p>Microsoft_Excel_Worksheet2.xlsx</p><p>Sheet1</p><p>0		0</p><p>1		1.02</p><p>2		2.01</p><p>3		2.98</p><p>4		4</p><p>5		5.01</p><p>0	1	2	3	4	5	0	1.02	2.0099999999999998	2.98	4	5.01</p><p>Sheet2</p><p>Sheet3</p><p>image15.png</p><p>image16.png</p><p>image17.png</p><p>image18.png</p><p>image19.png</p><p>image20.png</p>