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

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.