Physics and Measurement (1)

Problem Solving

Mr. KlapholzShaker Heights

High School

How many Figures are Significant?• 12.3• 800• 801• 8.00 x 102 • 800.0• 0.007• 0.0070

How many Figures are Significant?• 12.3 {3 significant figures}• 800• 801 • 8.00 x 102

• 800.0• 0.007• 0.0070

How many Figures are Significant?• 12.3 {3 significant figures}• 800 {1 significant figure}• 801• 8.00 x 102 • 800.0 • 0.007 • 0.0070

How many Figures are Significant?• 12.3 {3 significant figures}• 800 {1 significant figure}• 801 {3 significant figures}• 8.00 x 102

• 800.0• 0.007• 0.0070

How many Figures are Significant?• 12.3 {3 significant figures}• 800 {1 significant figure}• 801 {3 significant figures}• 8.00 x 102 {3 significant figures}• 800.0• 0.007 • 0.0070

How many Figures are Significant?• 12.3 {3 significant figures}• 800 {1 significant figure}• 801 {3 significant figures}• 8.00 x 102 {3 significant figures}• 800.0 {4 significant figures}• 0.007• 0.0070

How many Figures are Significant?• 12.3 {3 significant figures}• 800 {1 significant figure}• 801 {3 significant figures}• 8.00 x 102 {3 significant figures}• 800.0 {4 significant figures}• 0.007 {1 significant figure}• 0.0070

How many Figures are Significant?• 12.3 {3 significant figures}• 800 {1 significant figure}• 801 {3 significant figures}• 8.00 x 102 {3 significant figures}• 800.0 {4 significant figures}• 0.007 {1 significant figure}• 0.0070 {2 significant figures}

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.

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.

Propagation of ErrorAddition, 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.

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 = 0.0022 0.3 / 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.

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 AB = ?• AB ≈ 9.01.4 ≈ 21.7 ± ? • The greatest it could be is: 9.21.5 = 27.9 (that’s

a difference of 6.2).• The least it could be is: 8.81.3 = 16.9 (that’s a

difference of 3.8).• Average: (6.2 + 3.8) ÷ 2 = 5• AB = 22 ± 5

Additional PPTs on Vectors are available under separate titles.

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.