AP PHYSICS 1 TOOLKIT

Transcription

1 AP PHYSICS 1 TOOLKIT Welcome to AP Physics 1! It is a college level physics course that is fun, interesting, and challenging on a level you ve not yet experienced. This toolkit will go through mathematical concepts that are prerequisites for this course. These may seem simple, but they are important concepts that will appear over and over again throughout this course. Most sections have example problems that you will have to complete before the first day of classes. Other sections just require you to read through them for now. You will have this packet as reference for the rest for the course. By taking the time to review and understand all parts of this packet, you will help yourself acclimate to the rigor and pacing of AP Physics 1. This packet will be due the first day of class. Good luck! 1. Scientific Notation Many numbers in physics will be provided in scientific notation. You need to be able read and simplify scientific notation. (This section is to be completed without calculators all work should be done by hand.) Express the following the numbers in scientific notation. Keep the same unit as provided. ALL answers in physics need their appropriate unit to be correct. a. 7,640,000 kg b s c m d km/s Often times multiple numbers in a problem contain scientific notation and will need to be reduced by hand. Before you practice, remember the rules for exponents by circling the appropriate term: When numbers are multiplied together, you (add / subtract) the exponents and (multiply / divide) the bases. When numbers are divided, you (add / subtract) the exponents and (multiply / divide) the bases. When an exponent is raised to another exponent, you (add / subtract / multiply / divide) the exponent.

2 Using the three rules for exponents, simplify the following numbers in proper scientific notation. Show all your work i.e. do not just plug these into the calculator: e. (3x10 6 ) (2x10 4 ) = f. (7x10 3 ) 2 = g. (1.2x10 4 ) / (6x10-2 ) = h. (2x10-3 ) 3 = 2. Dimensional Analysis (Unit Conversion) Dimension is a term used to refer to the physical nature of a quantity and the type of unit used to specify it. We will be using dimensional analysis in this course to convert units. Example: Convert 80m to km Firstly, you need to know the conversion factor: a ratio expressing how many of one unit are equal to another unit. For example, there are 100 centimeters in 1 meter, 60 seconds in 1 minute, and so on. You might already know how many meters are in a kilometer. What if you don t remember? Luckily, you have your AP equation sheet, which includes a prefix table (see right). Here we can see the symbol k, indicates 10 3, or This means there are 1000 m in 1 km. We have to multiply 80 m by the conversion factor to get km. We set it up as follows: 80 m & 1 km ) = 0.08 km 1000 m Note that we are left with the desired unit (km), while the original one is canceled out (m). What if we flipped the conversion factor by accident? 80 m, -... / /3 1 = 80,000-0/ 0/ Well, we can see that we get an answer that makes no sense!

3 Convert the following numbers into the specified unit using dimensional analysis. Show your work in the space provided. a. 20 m = cm b MHz = Hz c. 10 Gs = s d. 6 Gb = kb e. 24 g = kg f. 640 nm = m 3. Algebra You will be using these skills daily. Practice with the following problems. Don t forget units in your answer! a. K = - 5 mv5 = kg,5.5 / 5 : 15 = b. F = k < =< 3 > 3 =,9 N /3 B 31 CD -.EF BGCH -. EF BG (H -. EJ /) 3 = c. τ = rf sin θ = 1.2m 15N sin 25 = d. T = 2πV W X = 3 =

4 For the following problems, don t get confused with the letters, think of them as numbers and algebraically rearrange for the chosen variable. d. U X = mg y; solve for D y h. x = x.f v g. t a gt 5 ; solve for ax e. P = ` ; solve for D t a i. F = k < =< 3 > 3 ; solve for q2 g. a c = d3 ; solve for v > j. T = 2πV / ; solve for m 0 4. Uncertainty, Precision vs. Accuracy A measurement result is only complete if it is accompanied by a statement of the uncertainty in the measurement. Measurement uncertainties can come from the measuring instrument, from the item being measured, from the environment, from the operator, and from other sources. Measurement: It tells about a property of something and assigns a number to that property. Uncertainty: A state of having limited knowledge. It is impossible to exactly describe a property. Uncertainty in a tool comes from how small it can accurately measure. Most standard meter sticks have 1mm or 0.1cm minor ticks with 1cm major ticks. A general rule is you should be able to read to ½ the minor tick. E.g. A particular meter stick might yield a reading of 50.0 cm ± 0.05cm where 50.0 cm is the measurement and 0.05cm is the uncertainty.

5 Accuracy- How close your measurements are to the accepted value (how close are you to the bullseye ). Precision- How consistent your measurements are. A useful quantity to determine how accurate your result is by finding the percent error: % error = expected experimental expected 100 The expected is what the real value is supposed to be. For example the expected value for g=9.8 m/s 2. The experimental value is what the student has measured or calculated based on data. A quick note about significant digits: the AP exam doesn t require you to follow the rules for significant figures, but the general rule of thumb is to use a reasonable amount of significant figures. This is typically leaving answers to about 2 decimal places. Do NOT put all the digits that your calculator spits out e.g. write 2.25 if your calculator shows If you write all the digits that the calculator spit out then you are stating that you think your answer is very accurate, which is almost always not the case!!! 5. Scalars vs. Vectors Scalar quantities only have magnitude o E.g. distance, speed, time o You can add/subtract/multiply/divide scalar quantities as if they are ordinary numbers Vector quantities have magnitude and direction o E.g. displacement, velocity, acceleration o Denoted with an arrow (F) uuuu or in boldface (F) o Vectors are represented as arrows in diagrams, with the arrow pointing in the direction of the vector o The length of the arrow is proportional to the magnitude of the vector o Methods of manipulating vector quantities (e.g. adding/subtracting) will be introduced in the future

6 6. Variables Any factor that might affect the behavior of an experiment is called a variable The independent variable (IV) is the factor that is changed The dependent variable (DV) is the factor that depends on the independent variable For the following experiments, identify the independent variable and dependent variable: a. How much the spring stretches by the amount of mass b. How radioactivity varies with time c. How friction changes with weight d. How the strength of a magnetic field depends on the distance from a magnet 7. Conceptual Review of Graphs As creating and interpreting graphs is a very important skill in AP Physics 1, we will devote more time in class for graphs. For now, we will review interpreting graphs conceptually with the following problems: a. A student uses data from a table to make a graph as shown. What, if anything, is wrong with this graph? If something is wrong, identify and explain how to correct all errors. If the graph is correct, explain why.

7 b. Four points are labeled on a graph. Rank the slopes of the graph at the labeled points. Explain your reasoning. c. Shown are several lines on a graph: Rank the slope of the lines on the graph shown. Explain your reasoning.