PHYS 121: Fundamentals of Physics I September 6, 2006 50
Perez, Miguel, Features Writer has reference to this Academic Journal, PHwiki organized this Journal PHYS 121: Fundamentals of Physics I September 6, 2006 Reminders & Announcements I would like to start using clickers this week. Your clicker should look like this: You will need to register your clicker: http://www.clickers.umd.edu/ First homework on WebAssign, due Sunday at midnight Outline Clicker setup Measurement Units Dimensional Analysis
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Clicker Setup The clicker channel as long as this lecture hall will be To set the channel on your clicker: Press GO Light should blink red/green Enter 2-digit channel number (50) (Newer clickers only) Press GO again Light should turn solid green as long as a few seconds 50 In January, the days get: Longer Shorter Stay the same Measured quantities A measured quantity can be treated as if it is the algebraic product of these three items.
What have we learned A physics equation is not just numbers. This equation is OK: 1 inch = 2.54 cm So is this: 1 = (2.54 cm)/(1 inch) It says: 1 = L1 / L2 which means these two lengths are the same no matter how we measure them. We can treat units as if they are algebraic symbols, multiplying them, canceling them, etc. Units A unit is the specific choice of arbitrary scale we make to measure a particular quantity that has a particular dimension. We can choose to measure length in meters centimeters inches yards furlongs light-years Accuracy in addition to Precision No measurement in science is ever perfect. A critical element in measurement is underst in addition to ing how well you know it. Accuracy means how correct the measurement is. Precision means how many significant figures you have.
Some Questions Which is better A measurement of high accuracy in addition to low precision A measurement of low accuracy in addition to high precision Which statement is precise Which is accurate The earth is a sphere. There is a point in the center of the earth such that if you measure the distance to the surface in any direction, you will get the same result to within 1%. Dimensions For every new arbitrary scale we choose, we assign a dimension. A dimension specifies the kind of measurement (or combination of measurements) we are measuring to get the number. This term we introduce measurements of length (L) time (T) mass (M) We write the dimensions of a combined quantity like this: v = 6.5 m/s [v] = L/T Careful! Dimensions are not algebraic symbols they are type labels. 6 ft + 9 ft = 15 ft [6 ft] + [9 ft] = [15 ft] L + L = L (Not 2L !) We sometimes use L (or M or T) as long as algebraic symbols to specify a particular length or mass or time. You have to know whether you are doing a dimensional analysis or a calculation!
Dimensional Analysis Why do we care Since the measurement scale as long as a dimension is arbitrary, we could change it. A dimensional analysis tells us how a quantity changes when the measurement scale is changed. Any equation which is supposed to represent a physical relation must retain its equality when we make a different choice of scale. Letting dimensional analysis work as long as you In physics, if we try to add or equate quantities of different dimensions we get nonsense. If we didnt maintain dimensional correctness, an equality that worked in one measurement system wouldnt work in another. This is a very good way to check your work with equations. (But its hard to do if you put numbers in too early!) Which of these equations can represent a physical equality 3 meters = 3 seconds 1 meter = 1 meter2 3 meters = 1 meter + 2 meter2 4 meters2 = 1 meter2 + 3 meter2 All of them None of them More than one but not all
Example What measurement would I assign to each of the following if I measured them in centimeters – a 1 meter rope – a cardboard square 1 meter on a side – a cubical container as long as water 1 meter on a side. Answer n on your clickers as long as 10n. Making Dimensions Work as long as You Find the error in the following calculation by using dimensional analysis. [x] = L [v] = L/T [a] = L/T2 [t] = T D means change in What have we learned In physics we have different kinds of quantities depending on how they were measured. These quantities change in different ways when you change your measuring units. Only quantities of the same type may be equated (or added) otherwise an equality as long as one person would not hold as long as another.
Problem Solving Strategy Visualize Analyze Assess Problem Solving Strategy Read the problem Identify the nature of the problem What exactly are you being asked Visualize the situation Draw a diagram Some types of problems require very specific types of diagrams Problem Solving cont. Label the physical quantities Can label on the diagram Use letters that remind you of the quantity Many quantities have specific letters Choose a coordinate system in addition to label it Identify principles in addition to list data Identify the principle involved This is often the most challenging step List the data (given in as long as mation) Indicate the unknown (what you are looking as long as )
Problem Solving, cont. Choose equation(s) Based on the principle, choose an equation or set of equations to apply to the problem Substitute into the equation(s) Solve as long as the unknown quantity Substitute the data into the equation Obtain a result Include units Problem Solving, final Check the answer Do the units match Are the units correct as long as the quantity being found Does the answer seem reasonable Check order of magnitude Are signs appropriate in addition to meaningful This is the most important step!
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