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Historical Areas of Emphasis MCAT Physics Review Grant Hart [email protected] Important Ideas about the Physical Science part of the MCAT • The problems are not complicated. They usually involve just one or two concepts, but you may have to dig a little in the reading material to find what you need. – You may also have to apply some common sense to what you read. – The majority of what you read is probably not going to be relevant to the questions. Mechanics 35% Fluid Mechanics 15% Waves, Optics, Sound 20% Electricity & Magnetism 10% Nuclear & Atomic Physics 10% Tools 10% Important Ideas about the MCAT • The problems are almost all conceptual and can be answered with fairly basic physics. The reading may involve more complicated ideas, but the questions are based evaluating based on simple physics. 1 Important Ideas about the MCAT Suggestions for doing well • Most of the time if you have to do more than add or multiply a couple of numbers together, you are probably on the wrong track. 1. Read everything carefully. 2. There is a lot of unused information in the reading. Don’t worry if you don’t use it. 3. If you are weak in a topic, don’t just pass it over. There are several techniques to improve your chances when you guess. If you aren’t familiar with a topic: If you are familiar with the topic: 1. Use your common sense. 2. Eliminate unreasonable answers. 3. Guess, but mark the problem number so that you can come back to it if you have time. 1. Simplify. 2. Round your numbers. 3. Calculate. You cannot use a calculator, so any calculations will necessarily be simple. You can use scratch paper if you need to. 4. Check for reasonableness. 2 How to Prepare • Study the prime areas: – Mechanics/E&M,circuits/Fluids/Radioactivity/ Waves/Optics • Understand the concepts – complicated problems are not the MCAT way. How to Prepare • Know the important equations. They are generally closely related to the basic concepts. – Don’t try to memorize everything, particularly equations. It will just confuse you and won’t help you. • Know how to read graphs and tables. There will be a number of them on the exam! From the MCAT instructions: Format of Physical Science Section • Neither the passage-based questions nor the independent questions test your ability to memorize scientific facts. Rather, both types of questions assess knowledge of basic physical and biological science concepts and your facility at problem solving at using these concepts. • 70 Minutes • 52 questions. About half will be on Physics and half on Chemistry. They may be mixed together in the same reading. • 7 readings of about 250 words each with 4-7 questions about each one. • 13 questions unrelated to any reading. 3 How to approach a Physics problem Exam Preparation • The purpose of this class is not to teach you physics – you should know most of what you need to know already. • The purpose of this class is to help you organize that material in your mind so you can get more points on the exam. • It is essential that you practice thinking physics, that is the only way to recognize when the principles come up in the reading. 1. Read • • • 2. Organize your thoughts • • • How to approach a Physics problem 3. Simplify the problem • Ignore extraneous information. The important principles in step 2 will help recognize this. 4. Solve • • Concepts used to select method. Equations • Equations are only useful in two ways: • • • • They organize the concepts – a good summary. This often shows up as ratio problems. You need them when you need a numerical answer. Be careful – make sure your units are compatible and watch the signs of things. Be quick – most of the time you can round to 1 figure and do a quick calculation. Passage Problems Answers – are they reasonable? Visualize and sketch it. Decide what physics principles are important. Note given any needed information. How to approach a Physics problem 5. Think • • Reasonable? Units match? 6. After about 1 minute • • • Eliminate the unlikely answers Guess Write down the problem number if there is hope. 4 What if the answer is bad? - Wrong units - Check multiply/divide, powers, bad equation - Wrong number Paradigms • A paradigm is a model or typical pattern that can be followed, particularly to solve problems. – Signs, algebra, bad equation, bad calculation ─ Quickly check your work – then make your best guess. • I will talk about several paradigms that can be used to solve various classes of problems in physics. Notes on the Web Paradigms we will use A printout of these notes can be found at the following url: http://www.physics.byu.edu/faculty/hart/MCAT/ • Block on Inclined Plane (Energy Conservation) • Porsche (Power) • Braking Car (Kinematics) • Ball on Inclined Plane (Rotation) • Colliding Blocks (Momentum Conservation) • Circuit (Resistance, Current and Voltage) • Charge in Capacitor (Electric Forces) • Water Tank (Fluids) • Wave (Waves and Sound) • Ball hitting wall (Optics – reflection) • Cart going into sand (Optics – refraction) • 14C (Radioactivity and Half-life) 5 Paradigms we will use • Block on Inclined Plane (Energy Conservation) • Porsche (Power) • Braking Car (Kinematics) • Ball on Inclined Plane (Rotation) • Colliding Blocks (Momentum Conservation) • Circuit (Resistance, Current and Voltage) Block on Inclined Plane Paradigm • Charge in Capacitor (Electric Forces) • Water Tank (Fluids) • Wave (Waves and Sound) • Ball hitting wall (Optics – reflection) • Cart going into sand (Optics – refraction) • 14C (Radioactivity and Half-life) • This is a paradigm for conservation of energy. This is the easiest way to work a problem – if it works. Einitial E final • Energy and work: E KE PE PE mgh 1 KE mv 2 2 Block on Inclined Plane Paradigm Block on Inclined Plane Paradigm Einitial 0 mgh initial final h • There is no friction. h E final 1 2 mv f 0 2 1 2 mv f mgh 2 v f 2 gh 6 Block on Inclined Plane Paradigm • As long as there is no friction, the path between start and finish doesn’t matter. – Free fall is the same as sliding down something without friction in terms of what the final velocity will be. • For springs the PE is ½ k x2 Block on Inclined Plane Paradigm • Use this technique whenever possible. Key things to look for: – Only conservative forces involved (usually gravity, electric forces, and springs.) – Time is not involved in the problem, you have just an initial state and a final state. – Usually just one object is moving. Paradigms we will use • Block on Inclined Plane (Energy Conservation) • Porsche (Power) • Braking Car (Kinematics) • Ball on Inclined Plane (Rotation) • Colliding Blocks (Momentum Conservation) • Circuit (Resistance, Current and Voltage) • Charge in Capacitor (Electric Forces) • Water Tank (Fluids) • Wave (Waves and Sound) • Ball hitting wall (Optics – reflection) • Cart going into sand (Optics – refraction) • 14C (Radioactivity and Half-life) Porsche Paradigm • Power: P E W t t (Porsche speeding up) 7 Porsche Paradigm • It can go from 0 to 60 in 3 seconds, what is the power? P E K f Ki t t 1 2 mv 2 t • Divide whatever change in energy you have by the time interval. That is the power, the rate at which energy changes. You don’t use this for electrical power in circuits, although it works at the microscopic level. Braking Car Paradigm • This paradigm is for kinematics – description of motion. • This is used when the following quantities are involved: - Position - Velocity - Force - Time - Acceleration Paradigms we will use • Block on Inclined Plane (Energy Conservation) • Porsche (Power) • Braking Car (Kinematics) • Ball on Inclined Plane (Rotation) • Colliding Blocks (Momentum Conservation) • Circuit (Resistance, Current and Voltage) • Charge in Capacitor (Electric Forces) • Water Tank (Fluids) • Wave (Waves and Sound) • Ball hitting wall (Optics – reflection) • Cart going into sand (Optics – refraction) • 14C (Radioactivity and Half-life) Braking Car Paradigm • Basic Equations: v v0 a t 1 x x0 v0t a t 2 2 2 2 v v0 2a x x0 F ma F ma W mg F f N 8 Braking Car Paradigm Possible questions: • What is the acceleration? v 2 v02 2a x x0 • Typical Problem: v0 t=0 x v02 2ad v02 2d • What is the coefficient of friction? a v=0 t = tf F f ma d F mg ma ag Possible questions: • How big is the frictional force? v v0 v0 a t f t0 tf F ma • Given μ and d, what was v0? mg ma g a v02 2ad v0 2 g d Braking Car Paradigm • Remember – this is for anything speeding up or slowing down, whether horizontally or vertically. • Use whichever equations have the right variables in them. • Make sure that conservation of energy is not the easier way to do it. 9 Aside – Newton’s Laws • A number of conceptual questions address Newton’s Laws directly, not in the context of kinematics. • In many ways Newton’s first law is conceptually the hardest. Example: • A car goes around a corner. The bag of groceries on the seat slides and hits the door. What force caused that? – None! The bag just traveled in a straight line and the car turned under it. – When an object has no net force acting on it, then it moves at a constant speed in a straight line. – It does not take a force to keep something moving! Another Example: Another Example: • A skydiver jumps out of a plane. His speed increases until he reaches terminal velocity. How big is the force of air resistance on him at first? • A skydiver jumps out of a plane. His speed increases until he reaches terminal velocity. How big is the force of air resistance on him after he reaches terminal velocity? – Greater than mg. – Equal to mg. – Less than mg. – Greater than mg. – Equal to mg. – Less than mg. 10 Circular Motion • Circular motion is the 2-D motion that you are most likely to see. • The a in F=ma is a vector acceleration – if the direction of the velocity changes but the magnitude does not, you still have an acceleration. • In circular motion the acceleration is toward the center (centripetal) and of magnitude v2 / r. Equilibrium • When an object is at rest, then all the forces add to zero. This is a vector sum! • Occasionally they may ask a problem where the torques need to sum to zero as well. Gravity and Orbital Motion • Newton’s law of gravity: – Only attractive – Inverse square law F Gm1m2 r2 • In orbit gravity supplies the centripetal force necessary to keep you tied to the Earth. Path without gravity Actual path Paradigms we will use • Block on Inclined Plane (Energy Conservation) • Porsche (Power) • Braking Car (Kinematics) • Ball on Inclined Plane (Rotation) • Colliding Blocks (Momentum Conservation) • Circuit (Resistance, Current and Voltage) • Charge in Capacitor (Electric Forces) • Water Tank (Fluids) • Wave (Waves and Sound) • Ball hitting wall (Optics – reflection) • Cart going into sand (Optics – refraction) • 14C (Radioactivity and Half-life) 11 Ball on an Inclined Plane Paradigm Ball on an Inclined Plane Paradigm • Rotation: – This is a lot like ordinary kinematics and energy conservation. Make substitutions for the variables and all the equations are the same: v a mI x F p mv L I KE 12 mv 2 KE 12 I 2 add the relationships v r and a r Ball on an Inclined Plane Paradigm initial h Ball has radius r final h • Equating the two: • At the bottom E 12 mv 2 12 I 2 v E 12 mv 2 12 I r I E 12 m 2 v 2 r • At the top E mgh 2 • No slipping or sliding. Notes on the Web (Week 2) A printout of these notes can be found at the following url: http://www.physics.byu.edu/faculty/hart/MCAT/ I mgh 12 m 2 v 2 r v 2 gh I 1 2 mr 12 Sample MCAT physics problems • sampleitems.pdf Paradigms we will use • Charge in Capacitor (Electric Forces) • Water Tank (Fluids) • Wave (Waves and Sound) • Ball hitting wall (Optics – reflection) • Cart going into sand (Optics – refraction) • 14C (Radioactivity and Half-life) • Block on Inclined Plane (Energy Conservation) • Porsche (Power) • Braking Car (Kinematics) • Ball on Inclined Plane (Rotation) • Colliding Blocks (Momentum Conservation) • Circuit (Resistance, Current and Voltage) Collisions • In collisions, momentum is always conserved! Colliding Blocks Paradigm Before: m1 • If kinetic energy is conserved, it is called elastic. • If kinetic energy is not conserved, it is inelastic. • If the two stick together it is called totally inelastic. (maximum energy loss) v1 v2 m2 Note: v2 < 0 x After: v1’ m1 m2 v2’ Note: now v1’ < 0 x 13 Colliding Blocks Paradigm • Momentum conservation: m1v1 m2v2 m1v1 m2v2 2 unknowns, 1 equation. Need more information… Colliding Blocks Paradigm • However, totally inelastic, v1’ = v2’ Before: m1 v1 x m1 m2 v x – KE conserved: m1v12 12 m2 v22 12 m1v12 12 m2v22 • Lots of nasty algebra, not likely to see on MCAT. Paradigms we will use • Block on Inclined Plane (Energy Conservation) • Porsche (Power) • Braking Car (Kinematics) • Ball on Inclined Plane (Rotation) • Colliding Blocks (Momentum Conservation) • Circuit (Resistance, Current and Voltage) m2 After: • Elastic Collision: 1 2 v2 • Charge in Capacitor (Electric Forces) • Water Tank (Fluids) • Wave (Waves and Sound) • Ball hitting wall (Optics – reflection) • Cart going into sand (Optics – refraction) • 14C (Radioactivity and Half-life) m1v1 m2v2 m1 m2 v v m1v1 m2v2 m1 m2 Electric Circuits • Definition of Current: I=∆q/ ∆t … flow of charge • Ohm’s Law: V=IR • Series and Parallel combinations of resistors: – Series: Req = R1 + R2 – Parallel: 1/Req = 1/R1 + 1/R2 • Electrical Power: P = I V • Kirchoff’s rules (only conceptually) – Loop rule: Sum of voltage changes around a loop = 0 – Junction rule: Current into a junction = current out of that junction 14 Circuit Paradigm Circuit Paradigm R1 = 2 Ω I2 2Ω R2 = 1 Ω 1Ω 1Ω I3 R3 = 1 Ω I1 6V 6V 1) V across R1 = 6V so I2 = V1 / R1 = 6 V / 2 Ω = 3 A 2) V across R2 and R3 = 6V, so 6 V = V2 + V3 = I3 R2 + I3 R3 = I3 ( R2 + R3 ) = I3 ( 2 Ω) I3 = 6 V / 2 Ω = 3 A 3) I1 = I2 + I3 = 3 A + 3 A = 6 A Circuit Paradigm Circuit Paradigm 2Ω I2 1Ω I3 • Power dissipated in R1 1Ω – P = I V = (3 A) (6 V) = 18 W – P = I2 R = (3 A)2 (2 Ω) = 18 W – P = V2 / R = (6 V)2 / (2 Ω) = 18 W I1 Quick solution: 2Ω 1Ω 6V 2Ω 1Ω 1Ω • Similar expressions for R2 and R3. 2Ω 6V 6V 6V I1 = 6 V / 1 Ω = 6 A. Because the equivalent resistance of I2 is the same as I3, I2 = I3 = 3 A. V2 = V3 = 3 V. – P2 = (3 A) (3 V) = 9 W – P3 = (3 A) (3 V) = 9 W 15 Paradigms we will use • Charge in Capacitor (Electric Forces) • Water Tank (Fluids) • Wave (Waves and Sound) • Ball hitting wall (Optics – reflection) • Cart going into sand (Optics – refraction) • 14C (Radioactivity and Half-life) • Block on Inclined Plane (Energy Conservation) • Porsche (Power) • Braking Car (Kinematics) • Ball on Inclined Plane (Rotation) • Colliding Blocks (Momentum Conservation) • Circuit (Resistance, Current and Voltage) Charge in Capacitor Paradigm Electric Forces • Coulomb’s Law: – Opposites attract, likes repel – Force proportional to charge – Inverse-square law, like gravity • Electric Field: – Force per unit charge • Electric Potential: – Work per unit charge d k q1q2 r2 F qE V E d Charge in Capacitor Paradigm • Possible questions: ∆V F ∆V d +q E – What is the force on the charge? + q E • F=qE • E = ∆V / d – How much work is done in moving a charge from one plate to the other? • W = q ∆V = q E d 16