MCAT Physics Review. Grant Hart

Transcription

1 MCAT Physics Review Grant Hart

2 Historical areas of emphasis -- probably similar in the future Mechanics 25% Fluid Mechanics 20% Waves, Optics, Sound 20% Electricity & Magnetism 10% Nuclear & Atomic Physics 15% Tools 10%

3 Important Ideas about the Chemical and Physical Foundations 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 as well. The majority of what you read is probably not going to be relevant to the questions.

4 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.

5 Important Ideas about the MCAT 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.

6 Suggestions for doing well 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.

7 If you aren t familiar with a 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.

8 If you are familiar with the topic: 1. Simplify. 2. Round your numbers to one significant figure. 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. This is often a very good way to eliminate answers!

9 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. The context may be complicated, but the problem itself is not.

10 How to Prepare Know the important equations. They are generally closely related to the basic concepts. Memorize the ones that are related to basic concepts. Secondary equations won t help you! Often they are used as ratio-type problems. For example, some quantity is known to be inversely proportional to the temperature, so when you increase the temperature by a factor of 1.5, that quantity decreases by a factor of 1.5.

11 How to Prepare You should know (to 1 significant figure) some important physical constants: J s 7 10 J s C 2 10 C m/s 3 10 m/s 9.8m/s 2 10 m/s 2 Know how to read graphs and tables. There will be a number of them on the exam!

12 From the MCAT instructions: 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.

13 Format of the Chemical and Physical Foundations Section 95 Minutes 59 questions. About 1/4 will be on physics and 3/4 on chemistry, biochemistry and biology. They may be mixed together in the same reading. 10 readings of about 250 words each with 4-7 questions about each one. All will be in the context of biology (defined loosely!) 15 questions unrelated to any reading.

14 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. This means working lots of sample problems!

15 Paradigms A paradigm is a model or typical pattern that can be followed, particularly to solve problems. I will talk about several paradigms that can be used to solve various classes of problems in physics.

16 Notes on the Web A printout of these notes can be found at the following url:

17 Paradigms we will use Block on Inclined Plane (Energy Conservation) Porsche (Power) Braking Car (Kinematics) Lifting a box (Equilibrium) Circuit (Resistance, Current, Capacitance 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) 14 C (Radioactivity and Half-life)

18 Paradigms we will use Block on Inclined Plane (Energy Conservation) Porsche (Power) Braking Car (Kinematics) Lifting a box (Equilibrium) 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) 14 C (Radioactivity and Half-life)

19 Block on Inclined Plane Paradigm This is a paradigm for conservation of energy. This is the easiest way to work a problem if it works. Energy and work: E initial E final E KE PE PE mgh KE 1 mv 2 2

20 Block on Inclined Plane Paradigm h There is no friction.

21 Block on Inclined Plane Paradigm initial E initial 0 mgh h final E final 1 2 mv 2 f mv 2 f mgh v f 2gh

22 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. You can use this in place of, or in addition to the gravitational PE.

23 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.

24 Possible biologically related systems A spring-loaded lancet is used to pierce a fingertip. How fast is it going when it hits the end of the finger? A person is injured by falling off of a wall. How fast where they going when they hit?

25 Diver vs. Slider Two people are on the top of a tower in a water park. One dives off the tower into the pool and the other takes a slide in the frictionless slide from the top of the tower into the same pool. Which one arrives first? Which one is moving faster when they arrive? Arrives First? Going Faster? (A) Diver Diver (B) Both at the same time Both have the same speed (C) Slider Slider (D) Diver Slider (E) Diver Both have the same speed

26 Paradigms we will use Block on Inclined Plane (Energy Conservation) Porsche (Power) Braking Car (Kinematics) Lifting a box (Equilibrium) Circuit (Resistance, Current, Capacitance 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) 14 C (Radioactivity and Half-life)

27 Porsche Paradigm Power: P E t W t (Porsche speeding up)

28 Porsche Paradigm It can go from 0 to 60 in 3 seconds, what is the power? P E t K f t K i 1 2 mv t 2 ~ 1500 kg, ~ 25 m/s, so ~ 210 HP ~150,000 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.

29 Work done Important ideas: Work-Kinetic Energy relation: Δ Σ Definition of Work (units: Joules): cos If you have a conservative force, then Δ

30 Power expended Important ideas: Power is the rate of doing work (units: Joules/sec or Watts) Since, then the work done is Δ. If an object is moving at speed, then the power acting on it instantaneously is

31 Possible biologically related systems How many Calories do you burn climbing to the top of a tall tower? How many horsepower can a person exert if they run up a short flight of stairs? How deeply will a biopsy needle penetrate, given the compression of the spring shooting it?

32 A box is pushed across the floor by applying a constant force to it. The box is pushed across the floor to the east in 30 seconds and pushed back to the starting point (to the west) in 15 seconds. Which is true of the work done by friction and the power expended? Work Power (A) East > West East > West (B) East = West East < West (C) East = West East = West (D) East < West East = West (E) East < West East > West

33 Paradigms we will use Block on Inclined Plane (Energy Conservation) Porsche (Power) Braking Car (Kinematics) Lifting a box (Equilibrium) Circuit (Resistance, Current, Capacitance 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) 14 C (Radioactivity and Half-life)

34 Braking Car Paradigm This paradigm is for kinematics description of motion. This is used when the following quantities are involved: - Position - Time - Velocity - Acceleration -Force

35 Braking Car Paradigm Basic Equations: N F mg W ma F m x x a v v at t v x x at v v f a F

36 Braking Car Paradigm Typical Problem: v 0 x t = 0 v = 0 t = t f d

37 Possible questions: What is the acceleration? What is the coefficient of friction? d v a ad v x x a v v g a ma mg F ma F f

38 Possible questions: How big is the frictional force? Given μ and d, what was v 0? ma F t v t t v v a f f gd v ad v a g ma mg

39 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.

40 Biologically related problems How long does it take a nerve impulse to travel the length of a neuron? A person blacks out at an acceleration higher than 7 g. How long would it take a car to go from 0-60 mph with that acceleration? How far would it travel? (0.4 sec, 5 m) A person lands after a fall high. Their legs bend when they land. How much force do their legs have to exert when they stop? Will they break their legs?

41 Conceptual question Which diagram best represents the velocity as function of the time of a ball thrown vertically upward?

42 Conceptual question Referring to the data plotted in the figure, what is the acceleration between time 0 and 5 s? a. +2 m/s 2 b. +25 m/s 2 c. 0 m/s 2 d. -2 m/s 2 e. -25 m/s 2

43 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 because it violates our intuition. 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!

44 Newton s Second and Third Second Law: Laws This means that we look at the acceleration and know what the net force is, both magnitude and direction. Third Law: Whatever force is exerted by object 1 on object 2, object 2 exerts and equal and opposite force on object 1.

45 An 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? Greater than mg. Equal to mg. Less than mg.

46 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 after he reaches terminal velocity? Greater than mg. Equal to mg. Less than mg.

47 Still Another Example: A monkey slides down a vine. At the time he reaches velocity v, he starts to tighten his grip on the vine. The frictional force increases with time. At the time that the force of friction equals his weight, He moves with constant speed down the vine. He stops. He starts to move upward.

48 Paradigms we will use Block on Inclined Plane (Energy Conservation) Porsche (Power) Braking Car (Kinematics) Lifting a box (Equilibrium) Circuit (Resistance, Current, Capacitance 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) 14 C (Radioactivity and Half-life)

49 Equilibrium When an object is at rest, then all the forces add to zero. This is a vector sum! You break all the forces into components and add all the x-components and set that to zero and do the same with the y-components. Occasionally they may ask a problem where the torques need to sum to zero as well.

50 Torque Torque is the effectiveness of a force at causing angular motion. It depends on both the size of the force and how it is applied.

51 Opening a Door Looking down on a door: Which force will be most effective in causing the door to rotate? Direction of the force matters Which of these forces will be most effective in causing the door to rotate? Distance from the rotation axis matters

52 Torque Defined The torque is defined as where F is the magnitude of the force and d is the lever arm, r is the distance from the axis to the point of application and θ is the angle between the distance and the force. A torque is positive if it wants to cause a counterclockwise rotation, negative if it wants to cause a clockwise rotation.

53 Torque, cont The moment arm, d, is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force. d = r sin Φ The horizontal component of the force (F cos ) has no tendency to produce a rotation.

54 Torque Units The SI units of torque are N. m. Although torque is a force multiplied by a distance, it is very different from work and energy. The units for torque are reported in N. m and not changed to Joules.

55 Picking up a Box A person bends to pick up a box. 45º 10º W box W torso T back Hip pivot

56 Are any forces missing? Yes, at the hip pivot 45º R y 10º W box W torso R x T back Hip pivot

57 What are the torques? The R forces exert no torque about the 45º pivot. 10º W box W torso Hip pivot T back If the length is L then we can calculate the torques

58 Sum torques to zero Three torques: 45º W box W torso Hip pivot 10º T back So

59 Sum torques to zero Three torques 45º 10º W box W torso sin 10 sin 45 Hip pivot T back 2 8.1

60 Possible Biological Applications Movement of joints Forces on tendons & ligaments Sports medicine Joints and limbs in traction

61 Conceptual Question A massless rod in the figure is free to rotate about an axis through point 0, at the right end of the rod. To maintain equilibrium, which of the following must force F, in Newtons, equal? a. 20 b. 40 c. 60 d. 100 e. 120

62 Sample MCAT physics problems These sample questions are from an old-style MCAT, but they illustrate many of the principles above. sampleitems.pdf