1. Physics and Measurement (1) Here we learn the language and the tools of physics. Mr. Klapholz Shaker Heights High School

2. Magnitude The mass of the universe is about 1 x 10 50 kg. Even though this is a very large mass, we have no trouble writing it in scientific notation. The mass of an electron: 10 -30 kg. How much more massive is the universe than the electron? (Please use your calculator). 1x10 50 kg / 1x10 -30 kg = 10 80 What are the units? Notice again how easily scientific notation let’s us deal with this.

3. Fundamental Units IdeaUnitSymbol Lengthmeterm Masskilogramkg Timeseconds Electrical currentampereA TemperatureKelvinK Amount of mattermolemol Intensity of lightcandelacd

4. Some Derived SI Units IdeaUnitSymbol Speedmeter / secondm s -1 ForceNewtonN = kg m s -2 EnergyJouleJ = kg m 2 s -2

5. Significant Figures This is a system of honestly reporting a value, but not claiming to know more than we do know. For example, if the edge of a cube is 1.2 cm, then what is its volume? V = L 3 = (1.2) 3 = 1.728 cm 3. But wait, it is not honest to start with 2 digits, and end up with 4 digits. So, V = 1.7 cm 3. The I.B.O. allows us to disagree by one significant figure without being penalized. We will explore this more in the Problem Solving section

6. Uncertainty and Error No measurement is perfect. “Random” errors make a measurement too great as often as they make it too small. One way to cope is to repeat the measurement many times. “Systematic” errors tend to make the measurement either always too great or too small. One way to cope is to make the same measurement using a different method.

7. Uncertainty and Error If you use a ruler to measure the width of a piece of printer paper, you would notice that it is about 21.00 cm. Often we take the uncertainty to be half of the smallest division. Since the markings on the ruler show every millimeter, (10 mm = 1 cm), it would be reasonable to say that the uncertainty (the error) in our measurement was about 0.5 mm.0.5 mm = 0.05 cm. So the width of the paper is 21.00 ± 0.05 cm. This means that most likely, the width of the paper is between 20.95 and 21.05 cm.

8. Examples of Errors Examples of Random Errors: – Unpredictable changes in room temperature. – Variation among items that were supposed to be identical. Examples of Systematic Errors: – Doing an experiment outdoors as the sun heats up the apparatus. – Not ‘zeroing’ a balance.

9. Accuracy vs. Precision (1 of 2) http://www.wellesley.edu/Chemistry/Chem105manual/Lab04/AccuracyPrecision.jpg

10. Accuracy vs. Precision “Accuracy” describes how close a measurement comes to the ‘true’ value. “Precision” describes how closely a group of measurements agree with each other.

11. Uncertainties in Data Tables are often shown as column headings Time / s ± 0.2 Position / m ± 0.3 0.01.4 0.92.5

12. Uncertainties are shown on a graph using “error bars” (or boxes). https://www.graphpad.com/faq/viewfaq.cfm?faq=106

13. Slope (“gradient”) and y-intercept have uncertainties. Draw the best line and the “extreme lines”. http://w3eos.whoi.edu/12.747/notes/lect03/egspan.gif

14. “Scalars” are quantities that do not have direction. Examples: Time Mass Energy Temperature

15. “Vectors” are quantities that do have direction. Examples: Velocity Acceleration Force Momentum

16. When we handwrite the symbol of a vector, we put an arrow over it. When we type the symbol of a vector, we use bold.

17. Adding Vectors: A + B = C http://img.sparknotes.com/content/testprep/bookimgs/sat2/physics/0011/parallelogram_2.gif

18. Components of vectors http://www.phys.unsw.edu.au/PHYS1169/beilby/vectors.html

19. Calculating the components of vectors http://www.niiler.com/phy130/vector3.png Use ‘sin’ for opposite Use ‘cos’ for adjacent

20. Get magnitude from components using Pythagorean theorem: A 2 = A x 2 + A y 2