Physics Problem Solving  Objectives  Systematic Approach  Prefix Conversion  Dimensional Analysis  Significant Figures  Precision & Accuracy  Error

A Systematic Approach to Solving Physics Problems Read & Analyze Problem Plan Clarify the known and unknown. Steps/EQN from known to unknown. Prepare a visual summary of steps. Solution Check Factor Label Method & Dimensional Analysis UNITS MUST CANCEL! Answer needs to reflect the dimensions of the problem

1.Find the difference between the exponents of the two prefixes. |10 x -(10 x )|= Decimal Displacement 2. Move the decimal that many places to the Right or Left. SI Prefix Conversions

move left move right SI Prefix Conversions

1) cm = ______________ m 2) A = ______________ mA 3) 454  m = ______________ nm 4) 805 dm = ______________ km Sample Prefix Conversions Use Scientific notation when necessary

Dimensional Analysis Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

Sample Dimensional Analysis How many grams does a 10-lb. bag of potatoes weigh? 10 lb 1 kg 2.2 lb = 4500 g lbg 1000 g 1 kg

Significant Figures The level of confidence or reliability in a measurement or result Approximate: mass, length—anything MEASURED. No measurement is perfect. When a measurement is recorded only those digits that are dependable are written down. Rule: All digits are significant starting with the first non-zero digit on the left.

The number of significant figures in a measurement depends upon the measuring device.

Rules for Determining Significant Figures Leading zeros are not significant. If the measured quantity has a decimal point start at the left of the number and move right until you reach the first nonzero digit. Count that digit and every digit to it’s right as significant. Numbers such as 5300 L are assumed to only have 2 significant figures. A terminal decimal point (or a bar) is often used to clarify the situation, but scientific notation is the best! Zeros that end a number and lie either after or before the decimal point are significant; thus ml has four significant figures, and L has four significant figures also. If the measured quantity does not have a decimal point start at the right of the number and move left until you reach the first nonzero digit. Count that digit and every digit to it’s left as significant.

Zeros & Sig. Figs: Exceptions to the Rule Rule: All digits are significant starting with the first non-zero digit on the left. Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant. 2 nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant. 3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant. These zeros are showing how accurate the measurement or calculation are.

Sample Sig Figs x ,000,

More Sig Figs ,083,000,

More Sig Figs ,000,050,

Precision and Accuracy Errors in Scientific Measurements Random Error - In the absence of systematic error, some values that are higher and some that are lower than the actual value. Precision - Refers to reproducibility or how close the measurements are to each other. Accuracy - Refers to how close a measurement is to the real value. Systematic error - Values that are either all higher or all lower than the actual value.

precise and accurate precise not accurate Precision and accuracy in the laboratory

systematic error random error Precision and accuracy in the laboratory