Download 1_Physics_1_ReKaps

Dear Future Doctor:
Welcome to your Kaplan MCAT “ReKaps”. These ReKaps will be sent out after each
classroom session to help you review the material from class and fill in any information
you may have missed or that was not covered originally. These ReKaps are not
designed to stand alone but rather are to be used in conjunction with your Kaplan
Lesson Book as an additional resource after already attending class. Inside, you will find
passage maps, answers and strategies for questions, and additional content notes. You
can read these documents all the way through, but they are best used by picking and
choosing which specific topics or questions you would like to revisit. If anything is still
unclear in the lesson after reviewing these ReKaps, please remember you do have
access to Lessons-on-Demand for each session via your online syllabus at
http://www.kaptest.com.
Note that this is an interactive document best viewed in “Web Layout” in Microsoft®
Word. Any links may be followed by holding CTRL while clicking, including the links in
the table of contents, which will take you directly to that section. The homework is colorcoded to match your online syllabus, with red meaning “Required”, green meaning
“Strongly Recommended”, and purple meaning “Optional”.
Please do not hesistate to contact me with any questions or concerns regarding this
document or otherwise.
Best of luck studying!
Brannon Altenhofen
[email protected]
1-800-KAP-TEST
Physics 1 ReKaps
Lesson Book Pages 33-54
Review Homework for Physics 1
Translational Motion Test 1
Force, Motion, Gravitation, and Equilibrium Test 1
Work, Energy, and Momentum Test 1
Physics Subjects Tests 1-3
Preview Homework for General Chemistry 1
General Chemistry Review Notes Chapters 1-3, 7
Quantum Numbers and Electron Configuration Workshop and Quiz
General Chemistry Foundation Review Unit 1
Contents
Science ReKap ............................................................................................................... 2
Passage I: P-36 ............................................................................................................... 3
Newtonian Mechanics: P-38............................................................................................ 3
Passage II: P-42 .............................................................................................................. 5
Work, Energy, and Momentum: P-45 .............................................................................. 6
Passage III: P-50 ............................................................................................................. 9
Science ReKap
Newtonian Mechanics: Forces are vectors required to change velocity and can be
caused by any push or pull, such as gravity, friction, or rotation
Rotational Motion: Torques, like forces, are vectors that can cause a change in
velocity, so there must be no net torque to maintain equilibrium
Work: Forces applied over a distance represent a change in energy
Energy: Kinetic energy can be converted to potential energy and back, but the total
energy of a system must always be conserved
Collisions: Even if some energy is lost to the environment, momentum is always
conserved in collisions
Kinematic Equations: memorize these!
VAT: v f  vo  a  t
VAX: v f  vo  2ax
2
2
1
TAX: x  vo t  at 2
2
1
(v o  v f )t
2
When PE is converted to KE completely: v  (2 gh) 2
Uniform Acceleration: x 
Choose which kinematic equation to use based on the 4 variables you have and want
 if one equation does not have the correct 4 variables, you can combine equations
(but this will take a long time)
o instead, try to simplify the problem or use a different set of equations
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Passage I: P-36
Type: Informational: skim quickly, looking for new info and relationships
P1: 3 factors for accidents
P2: rxn time  min. safe stop distance
Eqn: min. safe distance
P3: safety innovations
Physics “Think” Step Strategy:
Write down what you want.
Write down what you know, such as variables
Draw a picture, free body diagram, or graph if possible
Question 1
Stop: acceleration as number with direction
Think: vo = 25 m/s, vf = 0 m/s, t = 10 s, a = ?
Predict: deceleration = negative acceleration = south; a = Δv/t = (25-0)/10 = 2.5 m/s
Match: B
Question 2
Stop: time in seconds
Think: vo = 10 m/s, vf = 0 m/s, x = 0.5 m, t = ?
Predict: won't be extreme (not A, D); d = vavg* t = (vo+vf)/2 * t
Match: B
Question 3
Stop: unsolved expressions for distance in meters
Think: vo = 15 m/s, a = 1 m/s2, t = 45x10-3, x = ?
Predict: must match TAX equation (eliminate B,C); must have correct signs (eliminate
A,C)
Match: D
Return to Top
Newtonian Mechanics: P-38
Newton's First Law (Inertia): objects keep doing what they are already doing until a net
force acts on them
Newton's Second Law: to change velocity, you need a force, which produces
acceleration
 Force (F), velocity (v) and acceleration (a) are vectors, so you must keep track of
magnitude and direction
 Speed is the scalar version of velocity with no direction
 Force is in Newtons = kg*m/(s2)
o Fnet is vector sum of all forces acting on object
 Acceleration (a): change in velocity
o a = 0 when not moving or when velocity is constant
P-38 Critical Thinking:
A falling object accelerating due to gravity will encounter air resistance proportional to
its increasing velocity
At terminal velocity, the force of air resistance equals the force of gravity, resulting in
Fnet and no acceleration
Newton's Third Law: every action has an equal and opposite reaction
 Force pairs must be the same TYPE of force, e.g. gravity, normal force
o This law only applies to gravity if you enlarge the system to include the
source of gravity, the Earth itself
Normal force (N): force exerted by a surface that opposes gravity
 If Fnet=0 and the only other force acting is gravity, then the magnitude of N = Fg =
mg
 If in an elevator is accelerating upward, N also includes opposition to the
additional force of upward acceleration (ma), so N = ma + mg
o For downward acceleration, change the equation to N = mg - ma
o Since a weight scale measures normal force, this is also how you
calculate apparent weight for accelerating upward in an elevator.
Friction: tendency of objects to stick together, opposing new forces (movement)
Static friction: friction between objects sitting still
 Varies based on force applied
 Has an absolute maximum, after which motion occurs and static friction is zero
Kinetic friction: friction between objects in motion
 Proportional only to N (not F applied)
Gravity: tendency of masses to attract other masses
Memorize the first equation since you will see similar equations for electrostatics:
Gm 1m 2
F=
 mg
r2
GM
g  2 earth
R 2 earth
g: acceleration due to gravity
G: gravitational constant
M: mass of earth
R: radius of earth from center to surface
 There is little need to memorize values for most constants, including G, M, and R
 The MCAT emphasis will be on relationships and changes, not plugging in
numbers
Do memorize sin and cos of 0°, 30°, 45°, 60°, 90°, 180°, 270°, 360°:
Free Body Diagrams include every force acting on the defined system to find net F
 May need to break up forces into components when applied at angles
o e.g. on inclined plane, gravity is separated into mgsin(θ) [opposed by
tension] and mgcos(θ) [opposed by normal force]
Centripetal Force
mv 2
Fc =
2
 For a satellite around earth, Fc is caused by gravity, so F = ma, thus a = (v2)/r
 No matter the source, Fc points straight in from the object to the center of the
object’s circular path
o e.g. gravity of Earth on satellite, external magnetic field acting on proton,
tension from string acting on tetherball
o Initial velocity is what keeps the object from getting pulled into the center
of the circle.
Rotational Equilibrium
Torque: rotational analogue of force
 In equilibrium, torques are equal: d1 m1 g sin(θ1) = d2 m2 g sin(θ2)
 Often, in these problems, the angle will be 90°, so sin(θ) = 1
 With torques, counterclockwise is defined as positive, clockwise is negative
P-41 Critical Thinking
Rotational equilibrium means there is no net torque, so: d1 m1 g sin(90°) = d2 m2 g
sin(90°)
 Since both sin(θ) and both g are equal, they cancel out from the equation,
leaving: d1 m1 = d2 m2
o d1 and m1 are inversely proportional because they are being multiplied
together on the same side of the equation
o Therefore, since d1 > d2 then m1 < m2
Return to Top
Passage II: P-42
Type: Experimental: focus on why, how, results
P1: measuring g
Exp 1: drop and record vfinal and change in momentum (known mass, height, initial
velocity – highlight these)
Exp 2: projectile motion
Roman numeral question strategy:
Evaluate the roman numeral that shows up most often in the answer choices first
Eliminate answer choices that do not fit that roman numeral
Evaluate roman numeral that appears most often in remaining answer choices
Continue until 3 wrong answer choices are eliminated
Question 4
Stop: roman numerals
Think: g = GM/R2
Predict: g only depends on the gravitational constant and the mass and radius of the
Earth
Match: A
Question 5
Stop: mass, velocity, volume
Think: ρ = mv
Predict: momentum depends on mass and velocity; final velocity is dependent on g
Match: D
Question 6
Stop: wordy, greater/less with reasoning
Think: free body diagram shows air resistance opposes Fg
Predict: a decreases, so v decreases
Match: C
Question 7
Stop: distance in cm
Think: projectile motion and kinematics;
h = ?, g = 10 m/s2, vf = 0 m/s, vo = 4 sin(30°) = 2 m/s
Predict: VAX
Match: B
Return to Top
Work, Energy, and Momentum: P-45
Force: push or pull (vector) in a direction
Work: transfer of E by a force acting over a distance: change in energy
 Units: Joules = J = N*m = (kg*m2)/(s2)
 Does NOT correspond with perceived energy expenditure


o If the force applied to a system is perpendicular to its motion, no work is
done because cos(90°) = 0
LOSS of E to the surroundings is + work being done BY the system and - work
being done ON the system
GAIN of E from the surrounds is - work being done BY the system and + work
being done ON the system
Energy: ability to do work (scalar Joules)
 Energy is what needs to be added to a system to make it do something it
normally would not want to do
o e.g. everything normally wants to sit still, bring all mass together because
of gravity, and have all positive and negative charges together to be
neutral
 Work and energy share the same units
Kinetic Energy (KE):
1
KE  mv 2
2
Gravitational Potential Energy (PE or U):
U  mgh
Work-Energy Theorem:
Work net  KE
 So: Fd = ½ mv2
KNOW all three energy equations!
P-45 Critical Thinking 1
W = ΔKE = Fd = ½ mv2
For a satellite, no work is being done:
 After one full orbit, no change in position, so d = 0, so W = 0
 Force applied is perpendicular to velocity: cos(90°) = 0, so W = 0
P-45 Critical Thinking 2
Must expand system to include person and Earth to account for all energy
 Work is done by person, who contributes chemical energy, which becomes
kinetic energy and is then turned into gravitational potential energy
 Gravity counters work so no NET work total (and therefore no loss in energy for
the entire system)
P-46 Question 8
Stop: wordy, contrasting ideas (so need good prediction)
Think: work-energy theorem; friction
Predict: work by person > work by friction since Fnet exists
Match: B
Mechanical Energy (ME) = KE + PE
 If moving down from a height > 0, PE is converted into KE if energy is conserved
 If moved to a height = 0, PE = 0 and all energy becomes KE if energy is
conserved
Mechanical Energy is conserved if only conservative forces are present
 Conservative forces are path independent (state functions that only depend on
initial state and final state), such as gravity, electrostatic, and spring forces
Energy is not conserved if non-conservative forces are present
 Non-conservative forces are path dependent (vary depending on what happens
between states), such as air resistance, turbulence, friction, and viscosity.
Power (P): measures energy expenditure over time. Being able to output more energy
in a shorter amount of time corresponds to higher power.
Units = W = J/s
Momentum
(ρ): tendency to keep going


p  mv
 Remember to use vectors with directions
Collisions: two objects hitting one another;
For all types of collisions, momentum is ALWAYS conserved, so:
m1v1i + m2v2i = m1v1f + m2v2f
Elastic collision: E is also conserved, so:
½ m1v1i2 + ½ m2v2i2 = ½ m1v1f2 + ½ m2v2f2
Inelastic: E is lost, such as due to friction, sound, light, or configuration changes, so:
½ m1v1i2 + ½ m2v2i2 > ½ m1v1f2 + ½ m2v2f2
Totally Inelastic: E is lost and objects stick together, so above equation for inelastic is
true and equation for momentum can be simplified as:
m1v1i + m2v2i = (m1+m2) vf
P-48 Critical Thinking
i) Elastic collision leads to equal and final velocities of same magnitude and opposite
direction as initial velocities
ii) Totally inelastic collision leads to sticking and zero final velocity
Impulse: how fast momentum of an object changes
 Increasing t decreases F
Return to Top
Passage III: P-50
Type: Experimental
P1: Rutherford backscattering spectrometry
Fig 1: beamed particles collide with sample, collect at detector
P2: exp description; collision is elastic
P3: K measures particle's energy retention
Fig. 2: K proportional to m2 (target/sample/foil), inverse to m1 (high-energy incident
particle)
Question 9
Stop: time, similar numbers, different powers
Think: KE = ½ mv2; d = vt
Predict: 108
Match: A
KE = 2 MeV * 1.6X10-19 J/MeV = 3.6x10-13 J
m = 4 amu * 1.7x10-27 kg/amu = 6x10-27 kg
KE = ½ mv2
v2 = 2KE/m
v2 = 2 * 3.6x10-13/6x10-27 = 1014
v = 107m/s
d = vt
t = d/v = 0.15 m / 107m/s = 1.5x10-8 s
Note: This full math for this question takes more work than a question on the MCAT
would but served as a great reminder to TRIAGE
Any problem with a lot of work should be marked, answered as an educated guess, and
saved until the end of a section.
 For an educated guess, notice there is a value of 15 cm given, so look for an
answer choice with “15” in it (A or C)
 Also notice you can manipulate the exponents of 1.66*10^-27 and 1.60*10^-19
by subtracting: 27-19 = 8 (A)
 Note that these are both NOT mathematically accurate assumptions, but using
clues like these can help you decide what to guess if you must do so
Question 10
Stop: wordy, similar: need a good prediction
Think: experiment says m1 incident particles hit the m2 sample and recoil to the detector
Predict: If m2 changes, m1 stays the same mass but will have different E depending on
which m2 is hit
Match: B
Question 11
Stop: elements
Think: sample mass m2 directly proportional to kinematic factor
Predict: want lowest m2
*However, m2 must be larger than incident particle m1 or m2 will be scattered instead*
Match: C
Question 12
Stop: distance relative to edge
Think: rotational equilibrium, torques cancel
Predict: fulcrum must be between blocks (eliminate A, B); fulcrum must be closer to
heavier block (increasing m decreases d)
Match: D
Question 13
Stop: velocity with direction
Think: puck 2 initially heading south will bounce off to head north (eliminate A, C)
Predict: conservation of momentum
mv1i + mv2i = mv1f + mv2f
v1i + v2i = v1f + v2f
2 - 4 = -3 + v2f
v2f = +1 m/s
Match: B
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