AP Physics Summer Packet - Squarespace

1 AP PhysicsAP Physics Summer PacketThe science of Physics was developed to help explain the Physics environment around us. Many ofthe subjects covered in this class will help you understand the physical world around you. The topicsto be covered are:1D & 2D MotionTemperature & HeatForces and MotionThermodynamicsCircular MotionWaves & Sound & LightWork & EnergyElectrostaticsImpulse & MomentumCurrent ElectricityRotational TorqueMagnetism & InductionSimple Harmonic Motion & SpringsOpticsFluidsAtomic & Nuclear PhysicsBecause there is a lot of material to cover, this class will be fast-paced and rigorous. Be prepared towork long hours and do independent study. You must be committed to this class in order to do purpose of this Packet is for all students to have a firm foundation on the mathematical conceptsused in AP Physics .

2 You should be comfortable with the following materials since they will be usedthroughout the year, and this information will not be covered in the school be sure to understand the math concepts and do all assignments before the beginning of theschool year. There will be a quiz on the math concepts when you come to the :1. Math Review Worksheets (Sig Fig & Units Worksheet, Dimensional Analysis Worksheet, andMath Review & Vectors Worksheet): For all the worksheets, please show ALL work for yourcomputations and have units for all your final answers (if applicable).2. Read chapter 2 of the AP Physics textbook, Physics by Cutnell & Johnson. Fill out the NotesOrganizer (found at the end of the Packet ) for chapter you have any questions, feel free to email me: you re ready, let s get PhysicsScientific NotationIn science, very large and very small decimal numbers are conveniently expressed in terms of powersof ten.

3 Numbers expressed with the aid of powers of ten are said to be in scientific : Earth s radius = 6,380,000 m = x 106 mBohr radius of H atom = m = x 10 11 mAll scientific notations are composed of an integer (0< m 1) and powers of the calculator: you can punch in scientific notation on a scientific calculator using the followingbuttons, depending on your calculator: x 106 m : 6 = (the scientific notation on the calculator)NOTE: Do not punch 10 6, or your notation will be Figures (Sig Figs)The number of significant figures in a number is the number of digits whose value are known : a person s height: m, with the measurement error being in the third decimal place. All three digits are known with certainty, so the number contains 3 sig used in determining significant figures:1.

4 All non-zero numbers are significant. (Ex: 1, 2, etc)2. All zeros between 2 non-zero numbers are significant. (Ex: 4004, these 2 zeros count as sig figs)3. All final zeros after the decimal point are significant. (Ex: , these zeros count)4. Zeros that act as placeholders are not significant. (Ex: or 400, these don t count)Exception: 400. When a decimal point follows placeholders, they no longer act asplaceholders, but now are definite sig figs. So 400. has 3 sig and sig figs1. When adding/subtracting: round answer to the least number of decimal placesExample: m + m = m = m2. When multiplying/dividing: round answer to the least number of total sig figsExample: = = **Never write the entire number from the calculator as your answer. Always round answers to thecorrect sig 2 decimal placesHas 1 decimal placeHas 3 sig figsHas 4 sig figsAP PhysicsUnitsIn science, all numbers involve units, because all numbers are measurements of a quantity.

5 Numberswithout units mean nothing in Physics , unless they are referring to a this class, we emphasize the system of units known as SI units. By agreement of the scientificworld, a set of units are used as the standard. CGS, another system of units, may also be used: SI CGS LengthMeter (m)Centimeter (cm)MassKilogram (kg)Gram (g)TimeSecond (s)Second (s)The units for length, mass, and time, along with a few other units that will arise later, are regarded asbase SI units. The word base refers to the fact that these units are used along with various laws todefine additional units for other quantities. The units for these other quantities are referred to derivedunits, since they are a combination of the base units. We will discuss more about the derived units asthey come Prefixes: you need to memorize these:Prefix symbol Factortera T1012giga G109mega M106kilo k103deci d10 1centi c10 2milli m10 3micro 10 6nano n10 9pico p10 12femto f10 15 This prefixes can be used with any base : m = 1 cm -or- 1 m = 100 cmUnit ConversionMany quantities can be measured in several different units.

6 Therefore, it is important to know how toconvert from one unit to another.**Note: Only quantities with the same units can be added or subtracted. If not the same unit,convert them to the same units before doing the multiplying and dividing, units can be treated as algebraic : Express m in kilometers and in m x = m x = 3212 ftOther conversion factors you should know:1 h = 3600 s1 yr = days1 in = cm1 kg = lb1 m = ft1 m3 = 1000 L1 mile = 5280 ft = km1 km_103 ft_ 1 mAP PhysicsDimensional AnalysisThe term dimension is used to refer to the physical nature of a quantity and the type of unit used tospecify it. Distance has the dimension of length, which is symbolized as [L], while speed has thedimensions of length divided by time, or [L]/[T].

7 Many physical quantities can be expressed in termsof a combination of fundamental dimensions such as length [L], time [T], and mass [M].Dimensional analysis is used to check mathematical relations for the consistency of their : Is x = (1/2)vt2 correct or is x = (1/2)vt correct? Use dimensional analysis to = (1/2)vt2x = (1/2)vt[L] = [T]2 = [L][T][L] = [T] = [L]Dimensions cancel just like algebraic quantities, and pure numerical factors like 1/2 have nodimensions, so they can be ignored. The dimension on the right match, so this relation isdimensionally analysis can be used to derive equations by combining two or more equations ReviewSolving equationsIt is often necessary to solve the equation so that a variable whose value is unknown is expressed interms of known quantities.

8 In doing so, you will need to manipulate equations to solve for : Solve for t in the following equation: v = vo + = vo + atv vo = at(v vo)/a = tMake sure you are comfortable with manipulating the basic trig functions: sine, cosine, tangentsin = opposite/hypotenusecos = adjacent/hypotenusetan = opposite/adjacentKnow the Pythagorean Theorem: c2 = a2 + b2 VectorsSome quantities can be described with a single number (with units) giving its size or magnitude. Suchquantities are called scalar quantities. Examples of scalar quantities are time, temperature, and many quantities not only have a magnitude but also a direction. Such quantities are calledvectors. An example of a vector quantity is displacement. Displacement describes how far you veLTLTAP Physicstraveled and in which direction you have traveled.

9 For example, a car has traveled 2 km due vector quantities are velocity, acceleration, and arrow is used to represent a vector. 2 km due eastThe length of the arrow represents the magnitudeand the which way the arrow points is the direction of the ConventionsPositive and negative signs are typically used to indicate the direction of a vector mathematically. (InPhysics, positive and negative signs do NOT mean positive or negative numbers, as in a number line.)-positive sign: to the east or north (right or up)-negative sign: to the west or south (left or down)Adding VectorsA. Head-Tail Method-graphically adding vectors-place the tail of the 2nd vector at the head of the 1st vectorEx: Add the following 2 vectors:B. Adding Mathematically1. Vectors that are in the same directionEx: Add together Vector A: 275 m, due east and Vector B: 125 m, due = A + BR = +275 m + (+125 m) = +400 mEx: Add together Vector A: 275 m, due east and Vector C: 125 m, due westR = A + CR = +275 m + (-125 m) = +150 m2.

10 Vectors that are perpendicular to each other-Use Pythagorean Theorem and trigR2 = A2 + B2 SOHCAHTOA (sine, cosine, tangent)**Be sure your calculator is in DEGREE = 200 mB = 100 mThis vector is called the resultant vector (R), which isthe sum of all the vectors added = A + BABR = 400 m, due eastR = 150 m, due eastABRAP PhysicsEx: What is the magnitude and direction of R?R2 = A2 + B2R2 = (200. m)2 + (200. m)2R = 283 mtan = opp/adj = 200. m/200. m = 1 = 45 R = 283 m, 45 N of EHere is the directions of a compass, if you re not familiar Vectors That Are Not Perpendicular to Each Other-All vectors have an x-component and a adding vectors that are not going in the same direction or not perpendicular to each other,you must determine the x-component and y-component of each vector and add their : vector component that s parallel to x-axisAx = Acos y-component: vector component that s parallel to y-axis Ay = Asin Steps To Adding Non-Perpendicular Vectors:Ex: Add the following vectors: A = m/s, S of E B = m/s, S of WStep 1.