1. D. Roberts PHYS 121 University of Maryland PHYS 121: Fundamentals of Physics I September 6, 2006

2. D. Roberts PHYS 121 University of Maryland 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

3. D. Roberts PHYS 121 University of Maryland Outline Clicker setup Measurement –Units –Dimensional Analysis

4. D. Roberts PHYS 121 University of Maryland Clicker Setup The clicker channel for 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 for a few seconds 50

5. ? In January, the days get: 1234567891011121314151617181920 2122232425262728293031323334353637383940 1.Longer 2.Shorter 3.Stay the same ?

6. D. Roberts PHYS 121 University of Maryland Measured quantities A measured quantity can be treated as if it is the algebraic product of these three items.

7. D. Roberts PHYS 121 University of Maryland 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 = L 1 / L 2 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. 

8. D. Roberts PHYS 121 University of Maryland 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

9. D. Roberts PHYS 121 University of Maryland Accuracy and Precision No measurement in science is ever perfect. A critical element in measurement is understanding how well you know it. Accuracy means how “correct” the measurement is. Precision means how many significant figures you have.

10. D. Roberts PHYS 121 University of Maryland Some Questions Which is better? –A measurement of high accuracy and low precision? –A measurement of low accuracy and 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%.

11. D. Roberts PHYS 121 University of Maryland 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

12. D. Roberts PHYS 121 University of Maryland 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”) for 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!

13. D. Roberts PHYS 121 University of Maryland Dimensional Analysis Why do we care? Since the measurement scale for 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.

14. D. Roberts PHYS 121 University of Maryland Letting dimensional analysis work for you In physics, if we try to add or equate quantities of different dimensions we get nonsense. If we didn’t maintain dimensional correctness, an equality that worked in one measurement system wouldn’t work in another. This is a very good way to check your work with equations. (But it’s hard to do if you put numbers in too early!)

15. ? Which of these equations can represent a physical equality? 1.3 meters = 3 seconds 2.1 meter = 1 meter 2 3.3 meters = 1 meter + 2 meter 2 4.4 meters 2 = 1 meter 2 + 3 meter 2 5.All of them 6.None of them 7.More than one but not all

16. D. Roberts PHYS 121 University of Maryland 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 for water 1 meter on a side. Answer “n” on your clickers for 10 n. ?

17. D. Roberts PHYS 121 University of Maryland Making Dimensions Work for You Find the error in the following calculation by using dimensional analysis. [x] = L [v] = L/T [a] = L/T 2 [t] = T “  ” means “change in”

18. D. Roberts PHYS 121 University of Maryland 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 for one person would not hold for another.  

19. D. Roberts PHYS 121 University of Maryland Problem Solving Strategy Visualize Analyze Assess

20. D. Roberts PHYS 121 University of Maryland 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

21. D. Roberts PHYS 121 University of Maryland 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 and label it Identify principles and list data –Identify the principle involved This is often the most challenging step –List the data (given information) –Indicate the unknown (what you are looking for)

22. D. Roberts PHYS 121 University of Maryland 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 for the unknown quantity –Substitute the data into the equation –Obtain a result –Include units

23. D. Roberts PHYS 121 University of Maryland Problem Solving, final Check the answer –Do the units match? Are the units correct for the quantity being found? –Does the answer seem reasonable? Check order of magnitude –Are signs appropriate and meaningful? This is the most important step!