The Berkeley Review MCAT Physics Part 1

284 Pages·2011·43.09 MB·English

Physics
Parti
Sections I-V
Section I
Translational Motion
Section II
Forces, Circular Motion,
and Gravitation
Section III
Work and Energy
Section IV
Momentum and Torque
Section V
Periodic Motion
and Waves
1RERKELEY
•*Kr
D R.E«V»I«E«l/ir
Specializing in MCAT Preparation
The
ERKELEY
®
R • E • V • I • E • W
P.O. Box 40140, Berkeley, California 94704-0140
Phone: [phone] (5 10) TH E-TEST
Internet:
October 2010-
So you plan to become a doctor! It is quite an admirable quest and sacrifice.
Before getting into the crux of this book, I'd like to thank you. First, I'd like to
thank you for choosing such a career path, and a life dedicated to serving
humanity. Second, I'd like to thank you for choosing us to help you achieve your
goal. My sincerest hope is that this book helps make your path into medical
school just a bit easier and more successful.
What we've set out to build here is the best physics MCAT preparation book ever.
And by best, that means a book that clearly reviews material, presents clever and
memorable mnemonics, provides unique test-taking strategies, offers plenty of
practice questions, presents thorough answer explanations, and ultimately serves
as a printed friend.
This book is the latest edition of a project that started in 1992. It has undergone
five previous revisions, although this sixth and latest one represents its biggest
change to date. This book is the collaborative work of seven different authors
who collectively have over 10,000hours teaching MCAT preparation to students
like yourself. Our goal was to write the book like a teacher would explain the
subject matter one-on-one to a student. We sought a diverse group of authors for
the practice questions and passages, so that you get exposed to a plethora of
different voices and styles. Your MCAT will be a compilation of passages by
different authors, so that is what we aimed to produce here.
As you prepare for the MCAT, you need to keep in mind that MCAT-level
physics is different than college-level physics. Most notably, it is in a multiple-
choice format and has a strict time limitation. To do well on MCAT physics, you
need to think quickly, have a good conceptual understanding of the material, and
not get hung up on the details. Pick a best answer quickly and then move on to
the next question. To help you to do this, we have included plenty of mnemonics
and visualization tricks. Even more importantly we present and emphasize what
we will call headstarts for saving time on questions. Because you don't have to
show your work on the MCAT, you arebetter off rewriting your equations into an
easier to use state. We rewrite many equations so that anyone can easily do the
math in their head. You'll notice that we do this in nearly every chapter.
To get the most out of these books, you should practice the methods, algorithms,
and techniques we present in the text on the practice questions at the end of each
chapter. You should emphasize doing as much in your head as possible, without
writing on scratch paper or this book. After taking the chapter exams, you should
spend a significant amount of time making sure you understand each and every
passage and question. Repeat any questions you miss until you get them right,
and then read and review the answer explanations.
If you are feeling driven, rewrite some of our questions by changing the numbers,
the terminology, or the conditions and see how you do on your own questions.
Doing such a thing has an amazing impact on your ability to take a multiple-
choice test. Even if you don't choose to do that, there are tons of questions to test
yourself with.
Each chapter has an average of 18 multiple-choice questions intertwined in the
text followed by a 25-question review exam and a 52-question practice test. Take
as much time as you need on the text questions and the 25-question review exams,
but do your best to finish the 52-question practice tests within 70 minutes each.
Developing speed is a vital part of your preparation, so make sure you do this at
least one time per chapter.
We wish you the best of luck staying motivated throughout your preparation.
Keep the following three things in mind as you go:
1) The MCAT is a thinking exam, so keep things simple.
2) Avoid careless mistakes; be fast but not rushed.
3) The answer is given; all you need to do is find it
Once again, thank you for sharing this stage of your pathway to medical school
with us.
Sincerely and with great respect,
The Berkeley Review
Table of Contents
1. Translational Motion
Units and Dimensions page5
Vectors page 10
Speed, Velocity, and Acceleration page 16
Free Falling Bodies page 20
Projectiles page 27
Translational Motion Review Questions page 35
Detailed Answer Explanations page 40
Translational Motion Practice Exam page 45
Detailed Answer Explanations page 56
2. Forces, Circular Motion, and Gravitation
Newton's Laws of Motion page 67
Law of Gravitation page 75
Uniform Circular Motion page 79
Centripetal Force page 86
Kepler's Laws of Orbital Motion page89
Friction page 91
Inclined Planes and Pulley Systems page 94
Forces, Circular Motion, and Gravitation Review Questions page 99
Detailed Answer Explanations page 104
Forces, Circular Motion, and Gravitation Practice Exam page 109
Detailed Answer Explanations page 120
3. Work and Energy
Work page 131
Kinetic Energy page 134
Gravitational Potential Energy page 139
Conservation of Energy page 141
Power page 144
Work and Energy Review Questions page 145
Detailed Answer Explanations page 150
Work and Energy Practice Exam page 155
Detailed Answer Explanations page 166
4. Momentum and Torque
Linear Momentum page 177
Impulse page 181
Torque and Equilibrium page 186
Momentum and Torque Review Questions page 191
Detailed Answer Explanations page 196
Momentum and Torque Practice Exam page 201
Detailed Answer Explanations page 212
5. Periodic Motion and Waves
Harmonic Oscillation page 223
Springs and Pendulums page 226
Wave Properties page 232
Periodic Motion and Waves Review Questions page 241
Detailed Answer Explanations page 246
Periodic Motion and Waves Practice Exam page 251
Detailed Answer Explanations page 262
Physics Chapter 1
86 100
by
Translational Motion
Selected equations, facts, concepts, and shortcuts from this section
O Important Equations
d =_ 1^-oat2r + v0t + d0 (if you're lacking vO vt = vo + aAt (if you're lacking d)
d do + V° t Vt t (if you're lacking a) vt2 = v02 + 2a(dt - do) (ifyou're lacking t)
© ImportantConcept
X-motion is independent of Y-motion, and flight time only depends on the y-component
All four launches start at the same height
Horizontal launches in all cases execpt vox = 0
All four objects hit at the same time
x-Displacement at collision Time depends only on h, and not on vx
© Quick Free-fall CalculationTrick
The distance traveled in the y-direction of freefall from rest is found using Ah = 4.9t2 = 5t2
The speed at impact in the y-direction whenfalling from rest is found using vt = 9.8t» lOt
By using the results when t = 1, t = 2, t = 3, t = 4, etc..., you can quickly estimate a best answer
Ah tfall Vf
How far... t=1.7s? How long... d = 114 m? How high... vinity = 42 m/s?
1.25 m 0.5 s 5m/s
O A. 5.8 m O A. 2.92 s O A. 21.8 m
5 m Is lOm/s
O B. 14.2 m O B. 3.36 s OB. 42.9 m
20 m 2s 20m/s
O C. 25.0 m O C. 4.82 s O C. 71.4 m
45 m 3s 30m/s O D. 36.9 m O D. 5.66 s O D. 90.6 m
80 m 4s 40m/s Given just under 2s Given just under 125m Given vimpact = 40+m/s
125 m 5s 50m/s .-. just under 20m /. just under 5s /. t = 4+s and /. d = 80+m
320 m 8s 80m/s B is the best choice C is the best choice D is the best choice
Physics Translational Motion Units and Dimensions
Translational Motion
The three basic types of motion that we will be considering are translational
motion, rotational motion, and vibrational motion. Translational motion
involves the movement of an object from one place to another place. As a result,
the center of mass changes its position when an object undergoes translational
motion. When this occurs, the center of mass is said to be displaced.
Translational motion looks at the change of position of an object as a function of
time. Rotational motion examines how an object rotates about an axis over time.
Vibrational motion examines how an object oscillates back and forth about some
central point or axis over time. In both vibrational and rotational motion, the
center of mass does not change over time. It is possible for an object to undergo
more than one type of motion at a time. In this section, we will primarily be
examining translational motion. However, there will be times when we will
discuss the combination of translational motion with both rotational and
vibrational motion. These studies fall within the realm of kinematics, which is the
study of motion without considering the various forces that cause it.
Units and Dimensions
Units
The system of units used on the MCAT is predominantly the metric system. The
units of length, mass, and time in the metric system are the meter (m), kilogram
(kg), and second (s).These metric units are referred to as the Systeme International
d'Unites or the SI units. The metric system is based on atomic standards. The
Englishsystem of units uses the foot (ft), pound (lb), and seconds (s).
Table 1.1
Multiples of the Meter Length Conversion Factors
gigameter 1 G = 109 m mile 1 mi = 1609.38 m
megameter lM = 106m yard 1 yd = 0.9144 m
kilometer lkm = 103m foot 1 ft = 0.3048 m
meter lm inch 1 in = 2.540 cm
centimeter 1 cm = 10"2 m
millimeter 1 mm = 10"3 m Mass Conversion Factors
micron 1 /im = 10'6 m kilogram 1 kg = 2.204 lb
nanometer 1 nm = 10~9 m gram 1 g = 10"3 kg
Angstrom 1 A = 10"10 m milligram 1 mg = 10"3 g = 10~6 kg
picometer 1 pm = 10"12 m
femptometer 1 fm = lO"15 m
Multiples of the Second Typical Masses
year lyr =3.16x!07s Sun 2.0 x1030 kg
day 1 day = 8.64 x104 s Earth 6.0xl024kg
hour 1 hr = 3600 s RedBlood Cell 9 x10"14 kg
minute 1 min = 60 s Proton 1.66 x10"27 kg
millisecond 1 ms = 10"3 s Electron 9.11 x10'31 kg
Copyright © by The Berkeley Review Exclusive MCAT Preparation
Physics Translational Motion Units and Dimensions
Note that the kilogram and the pound do not represent the same physical
quantity. The kilogramis a unit of mass, whereas the pound is a unit of force— a
distinction that will be addressed in Section II.
There will be occasions when a question will require conversion between
different sets of units. For example, you may need to convert a distance of 100
miles into meters. Table 1.1 shows that 1 mile is equal to 1609.38 meters. This is
the same as saying the following:
1609.38 m
1 mile
In order to convert 100 miles to meters, the conversion factor (shown above) is
multiplied by 100 miles. The miles will cancel out, leaving 160,938 m. This value
is commonly expressed in scientific notation as 1.61x 105 m.
(1609.38 m](100 miles) =160/938 m
V lmile I '
If you did not know the specific value for this conversion factor, do not worry.
Conversion factors for most units will usually be given on the MCAT. You
should, however, have at least an approximate idea of these factors (e.g., know
that therearearoundonethousand, or maybe abit more, meters in onemile.)
Example 1.1a
Table salt consists of sodium chloride. The approximate distance between the
nuclei of a sodium atom and a chlorine atom is 2.8 A. How far apart are these
nuclei in miles? (1 A= lO'10 m and 1 mile = 1609.38 m)
A. 1.74 x 10"13 miles
B. 4.51 x 10"7miles
C. 1.74 x 10-3 miles
D. 4.51 x 103 miles
Solution
This is a numeric answer, which traditionally involves multiplying and dividing
various numbers. This arithmetic can, however, become very time-consuming.
You should try to avoid doing full arithmetic on the MCAT whenever you can.
Magnitude Intuition: The numbers in questions with numeric answers
sometimes vary byorders ofmagnitude. As a first approach, use the magnitude
intuition technique. It can help to eliminate incorrect answers without doing
math. Simply cross outanswer choices that seem too big or too small. Here, we
are asked about the separation of two atoms in a molecule. Which of the choices
might you eliminate without resorting to math? Probably choice D. If you also
Test Tip thinkaboutchoice C,and happento knowthat thereare thousands of feet in one
Magnitude Estimation mile, you'll see that choice Cis also too big. Is there a way to differentiate fairly
easily between choices Aand B? Yes, use the magnitude estimation technique.
Magnitude Estimation: Simply write out the numbers in scientific notation and
estimatethe order ofmagnitude of the result. Here, the actualcalculation is
distance in miles =(2.8 A)|10~10ml/- 1 mile x 10"13m
1 1A Hi 60938 x 103m 1.6
To estimate the order ofmagnitude, look only at the powers often. Doing sowill
give 10-13 as the resulting order of magnitude. If another choice is within one
orderofmagnitude (e.g., lO'12 or 10'14), you will needto check theother numbers
in the calculation (i.e., 2.8/1.60938). This, too, is easy. Simply askyourself if these
Copyright©by The BerkeleyReview The Berkeley Review