1. Physics and Measurement (1) Problem Solving Mr. Klapholz Shaker Heights High School

2. How many Figures are Significant? 12.3 800 801 8.00 x 10 2 800.0 0.007 0.0070

3. How many Figures are Significant? 12.3 {3 significant figures} 800 801 8.00 x 10 2 800.0 0.007 0.0070

4. How many Figures are Significant? 12.3 {3 significant figures} 800 {1 significant figure} 801 8.00 x 10 2 800.0 0.007 0.0070

5. How many Figures are Significant? 12.3 {3 significant figures} 800 {1 significant figure} 801 {3 significant figures} 8.00 x 10 2 800.0 0.007 0.0070

6. How many Figures are Significant? 12.3 {3 significant figures} 800 {1 significant figure} 801 {3 significant figures} 8.00 x 10 2 {3 significant figures} 800.0 0.007 0.0070

7. How many Figures are Significant? 12.3 {3 significant figures} 800 {1 significant figure} 801 {3 significant figures} 8.00 x 10 2 {3 significant figures} 800.0 {4 significant figures} 0.007 0.0070

8. How many Figures are Significant? 12.3 {3 significant figures} 800 {1 significant figure} 801 {3 significant figures} 8.00 x 10 2 {3 significant figures} 800.0 {4 significant figures} 0.007 {1 significant figure} 0.0070

9. How many Figures are Significant? 12.3 {3 significant figures} 800 {1 significant figure} 801 {3 significant figures} 8.00 x 10 2 {3 significant figures} 800.0 {4 significant figures} 0.007 {1 significant figure} 0.0070 {2 significant figures}

10. Significant Figures after a Calculation 12.3 + 4.567 + 0.8912 = ? Without thinking about significant figures, the sum is 17.7582 But we are confident only know about the 0.# decimal place, so the result is 17.8 For addition or subtraction, keep your eye on which digits are significant.

11. Significant Figures after a Calculation 12.3 x 4.567 = ? Without thinking about significant figures, the product is 56.1741 But we are confident only of 3 significant digits, so the result is 56.2 For multiplication and division, keep your eye on how many digits are significant.

12. Propagation of Error Addition, Subtraction If a string is so long that it takes two rulers to measure it, then its length could be 30.0 ± 0.1 cm PLUS 20.0 ± 0.1 cm. So the length is 50 ± ? cm. For addition (or subtraction) just add the absolute errors. 0.1 cm + 0.1 cm = 0.2 cm. So the string is 50 ± 0.2 cm long.

13. Propagation of Errors (Multiplication and Division) Speed = Distance ÷ Time. If you travel 90.0 ± 0.2 meters in 10.0 ± 0.3 seconds, then your speed = 9.00 ± ? m s -1. For multiplication (or division) add the fractional errors and then use the result to find the error of the answer. 0.2 / 90.0 = 0.00220.3 / 10.0 = 0.03 0.0022 + 0.03 = 0.032 0.032 x 9.00 = 0.29 The speed is 9.00 ± 0.3 m s -1.

14. Propagation of Errors (The ‘quick and dirty’ method that works for everything) If A = 9.0 ± 0.2, and B = 1.4 ± 0.1, then A B = ? A B ≈ 9.0 1.4 ≈ 21.7 ± ? The greatest it could be is: 9.2 1.5 = 27.9 (that’s a difference of 6.2). The least it could be is: 8.8 1.3 = 16.9 (that’s a difference of 3.8). Average: (6.2 + 3.8) ÷ 2 = 5 A B = 22 ± 5

15. Additional PPTs on Vectors are available under separate titles.

16. Tonight’s HW: Go through the Physics and Measurement section in your textbook and scrutinize the “Example Questions” and solutions. Bring in your questions to tomorrow’s class.