PHYSICS - - Physics is a branch of science that involves the study of the physical world: energy, matter, and how they are related (motions of electrons and rockets, the energy in sound waves and electric circuits, the structure of the proton and of the universe) The potential difference (voltage), across a circuit equals the current multiplied by the resistance in the circuit. V (volts) x I (amperes) = R (ohms) o Ex. What is the resistance of a light bulb that has 0.75 amperes current when plugged into 120-volt outlet? SI UNITS DIMENSIONAL ANALYSIS - Dimensional analysis is used to check that an answer will be in the correct units. SIGNIFICANT DIGITS: - The valid digits in a measurement Ex. 14.3: Two you are sure of (1 and 4); one (3) is estimated. The last digit of any measurement is the uncertain digit 1. All non-zero numbers ARE significant (33.2 has THREE significant figures) 2. Zeroes between two non-zero digits ARE significant (2051 has FOUR significant figures) 3. Leading zeroes are NOT significant (0.54 has only TWO significant figures; 0.0032 also has TWO significant figures) 4. Trailing zeroes to the right of the decimal ARE significant (92.00 has FOUR significant figures) 5. Trailing zeroes in a whole number with the decimal shown ARE significant (540. indicates that the trailing zero IS significant; there are THREE significant figures in this value) 6. Trailing zeroes in a whole number with no decimal shown are NOT significant (540 has TWO significant figures) 7. Exact numbers have an INFINITE number of significant figures. This rule applies to numbers that are definitions. (1 meter = 1.00 meters = 1.0000 meters = 1.0000000000000000000 meters, etc.) 8. For a number in scientific notation: N x 10x, all digits comprising N ARE significant by the first 6 rules; "10" and "x" are NOT significant (5.02 x 104 has THREE significant figures: "5.02." "10 and "4" are not significant) 9. Adding: Least significant digits after decimal point (100. + 100 has ONE significant figure) 10. Multiplication: Least significant digits of each number (82 * 53298 has TWO significant digits) Examples: 5.0 g has two significant digits. 14.90 g has four significant digits. 0.0 has one significant digit. 300.00 mm has five significant digits. 5.06 s has three significant digits. 304 s has three significant digits. 0.0060 mm has two significant digits (6 and the last 0). 140 mm has two significant digits (just 1 and 4). SCIENTIFIC METHODS - - - Scientific method: o Observations, experiments, create models/theories, explain results, predict new answers o Obtain data, make predictions, create compelling explanations that quantitatively describe many different phenomena (experiments and results must be reproducible) Hypothesis: an educated guess about how variables are related (Test: conduct experiments, take measurements, and identify what variables are important and how they are related) Models, laws, and theories: o Scientific models are ideas, equations, structures, or systems that can model a phenomenon (based on experimentation) o Scientific law: a rule of nature that describes a pattern/phenomenon in nature (Ex. Law of conservation of charges) o Scientific theory: an well-supported explanation [for laws] supported by experimental results (best available explanation of why things work as they do) Scientific ideas change in response to new data MEASUREMENTS - - A measurement is a comparison between an unknown quantity and a standard Precision vs. Accuracy: Both precision and accuracy are characteristics of measured values. Precision: The degree of exactness of a measurement is called its precision. Smaller the precision range, the more accurate it will be (within ± 0.1 cm). Precision depends on the instrument and technique used to make the measurement. The device that has the finest division on its scale produces the most precise measurement. The precision of a measurement is one-half the smallest division of the instrument. (5.253782 is more precise than 5.3 and 5.25) Accuracy: describes how well the results of a measurement agree with the “real” value; that is, the accepted value as measured by competent experimenters. A common method for checking the accuracy of an instrument is called the two-point calibration (Real World Situation: accuracy of the radiation output of the machines used to treat cancer) - - One common source of error comes from the angle at which an instrument is read. Scales should be read with one’s eye directly above the measure. The difference in the readings is caused by parallax, which is the apparent shift in the position of an object when it is viewed from different angles. All measurements are subject to some uncertainty GRAPHING DATA - - A variable is any factor that might affect the behavior of an experimental setup [x] Independent variable is the factor that is changed or manipulated during the experiment (mass) [y] Dependent variable is the factor that depends on the independent variable (the amount that the spring stretched) The line of best fit is a better model for predictions than any one point that helps determine the line. (it is drawn as close to all the data points as possible) Linear Relationship Between Two Variables: y = mx + b; slope = rise/run = Δy/Δx o If slope is going down = negative sign Ellipse Predicting values: substitute value for “x” after finding slope and y-intercept Data are plotted in graphical form to show the relationship between two variables. ROUNDING 1. When the leftmost digit to be dropped is less than 5, that digit and any digits that follow are dropped. Then the last digit in the rounded number remains unchanged. 2. When the leftmost digit to be dropped is greater than 5, that digit and any digits that follow are dropped, and the last digit in the rounded number is increased by one. 3. When the leftmost digit to be dropped is 5 followed by a nonzero number, that digit and any digits that follow are dropped. The last digit in the rounded number increases by one. 4. If the digit to the right of the last significant digit is equal to 5, and 5 is followed by a zero or no other digits, look at the last significant digit. If it is odd, increase it by one; if it is even, do not round up. Examples: Round the following numbers to the stated number of significant digits. 8.7645 rounded to 3 significant digits is 8.76. 8.7676 rounded to 3 significant digits is 8.77. 8.7519 rounded to 2 significant digits is 8.8. 92.350 rounded to 3 significant digits is 92.4. 92.25 rounded to 3 significant digits is 92.2. Acceleration = Change in velocity/speed Time elapsed Velocity: determines acceleration (displacement/time) Constant velocity = zero acceleration Straight line = constant acceleration Curved = variable velocity, variable acceleration, displacement is area under curve Parallel to x-axis = constant velocity, 0 acceleration, displacement can be found by finding area of graph Displacement: determines velocity Speed: distance/time Straight line = constant velocity Force = mass * acceleration (Units = kg . m/s2) - Derived units: units that can be broken down into base units (m3 → m) Two-point calibration: the method of checking the accuracy of an instrument. An instrument is check for zero error and for the correctness of a reading, while measuring accepted standard. Parallax: phenomenon that states that measurement readings read from different angles will result in different recorded values o Parallax only affects accuracy, not precision α - proportional Boyle’s Law – inverse relation (PV) Charles’ Law – direct/straight line (V/T) Gay-Lussac's Law – direct/straight line (P/T) RATIOS - A ratio is a comparison between two numbers by division. RATES - A rate is a ratio that compares two quantities with different measurement units. A unit rate is a rate that has been simplified so that the denominator is 1. V α (1/P) VαT PαT
