Cracking The Mcat: Physics

Front 1

Missing "a" (missing acceleration)

Back 1

d = (1/2) (v0 + vf) t
("d" equals the average of the "v's" times "t")

Front 2

Missing "d" (missing displacement)

Back 2

vf = v0 + at

Front 3

Missing "vf" (missing velocity final)

Back 3

d = v0*t + (1/2)at^2

Front 4

Missing "v0" (missing initial velocity)

Back 4

d = vf*t - (1/2)at^2

Front 5

Missing "t" (missing time)

Back 5

vf^2 = v0^2 + 2ad

Front 6

Info about "Scientific Reasoning: The Physical Sciences" (1)

Back 6

- 52 q's, 70 minutes
- 4 to 7 mult choice questions after each passage
- some MC not related to passages
- scored from 0 to 15

Front 7

Info about "Verbal Reasoning" (2)

Back 7

- 40 questions, 60 minutes
- similar to reading comprehension of other standardized exams
- tests ability to paraphrase passages, draw inferences, characterize themes, and follow lines of reasoning from the passage

Front 8

Info about "Writing Sample" (3)

Back 8

- 2 essays, 30 min each
- comment on a philosophy or point of view

Front 9

Info about "Scientific Reasoning: The Biological Sciences" (4)

Back 9

- 52 q's, 70 min
- biology and organic chemistry
- same structure as physical sciences

Front 10

slope (m) = ?

Back 10

(y1-y2) / (x1-x2) = Δy / Δx

Front 11

how to convert between degrees and radians in angles?

Back 11

use this conversion factor:
180 degrees = π radians

Front 12

Pythagorean theorem:

Back 12

a^2 + b^2 = c^2

Front 13

SOH-CAH-TOA

Back 13

sinx = opp/ hyp
cosx= adj / hyp
tanx = opp / adj = sinx / cosx

Front 14

30-60-90 right triangle: what is the ratio of the sides (from smallest leg to hypotenuse)?

Back 14

1 : sqrt(3) : 2

Front 15

45-45-90 right triangle: what is the ratio of the sides (from smallest leg to hypotenuse)?

Back 15

1 : 1 : sqrt(2)

Front 16

3:4:5 triangle

Back 16

this is a special ratio of side lengths of specific right triangles

Front 17

Def: displacement

Back 17

a vector quantity describing the "net change in position" (from start to end)

Front 18

average velocity = v-bar = ?

Back 18

displacement / change in time =
d / Δt

Front 19

average speed = ?

Back 19

total distance / change in time

Front 20

average acceleration = a-bar = ?

Back 20

change in velocity / change in time =
Δv / Δt =
(vf - vi) / Δt

Front 21

If velocity and acceleration are pointing in the same direction, the object is "________ _____"

Back 21

speeding up

Front 22

If velocity and acceleration are pointing in opposite directions, the object is "________ _____"

Back 22

slowing down (still could be moving in the direction opposite of acceleration)

Front 23

If velocity and acceleration are pointing perpendicularly to eachother, the object is "__________ ______"

Back 23

changing direction

Front 24

Velocity vs. Time graphs: what does the slope represent?

Back 24

acceleration

Front 25

Velocity vs. Time graphs: what does the area under the curve represent?

Back 25

displacement

Front 26

Velocity vs. Time graphs:

when does a change in direction of the object occur?

Back 26

when the graph crosses the horizontal axis

Front 27

Velocity vs. Time graphs:

what does area under the horizontal axis represent?

Back 27

negative displacement

Front 28

Kinematics proportion (from vf=v0 + at)

Back 28

vf is directly proportional to t

Front 29

Kinematics proportion (from d = v0t + 1/2at^2

Back 29

d is directly proportional to t^2

Front 30

Kinematics proportion (from vf^2=v0^2 + 2ad)

Back 30

vf^2 is directly proportional to d

Front 31

When an object is thrown upward, it ____ ______ by approximately 10 m/s every second

Back 31

slows down

Front 32

When an object falls downward, it ____ ______ by approximately 10 m/s every second

Back 32

speeds up

Front 33

Solving projectile motion problems:

Back 33

- separate x and y equations
- v_x = d_x/t is the only equation needed for the x equations
- time is the bridge between the two equation sets

Front 34

Def: centripetal acceleration
a_c = ?

Back 34

- acceleration directed toward the center of the circle
- a_c=v^2/r
- a_c is directly proportional to v^2

Front 35

formula for period of a circular revolution (time it takes to go around circle once)

Back 35

T = 2πr / v

Front 36

What's a simple definition of force?

Back 36

a "push" or a "pull"

Front 37

Newton's First Law:

Back 37

"A body--in motion or at rest--will remain in its initial state unless acted upon by a nonzero net external force."

Front 38

What is inertia?

Back 38

the natural tendency of objects not to accelerate.

- mass is a measure of inertia

Front 39

Newton's Second Law:

Back 39

F_net= m*a

(a net external force will produce acceleration)

Force is directly proportional to mass

Front 40

What are the units of force?

Back 40

Newtons (N)

- 1 N = 1 kg * m/s^2

Front 41

Net force

Back 41

the vector sum of all forces acting on an object

- F_net = F_1 + F_2 + ...

- split forces into x and y components when necessary

Front 42

Newton's Third Law:

Back 42

"when one body exerts a force on another, the second body will exert an equal and opposite force on the first" (think of normal force)

Front 43

Formula for force of gravity for objects near earth's surface (aka "weight")

Back 43

F_g = m * g

m = mass
g = 10 m/s^2

Front 44

Newton's Law of Universal Gravitation:

Back 44

F_g = (G * m_1 * m_2) / r^2

- F_g is directly proportional to mass of each object
- F_g is inversely proportional to the square of the distance between the centers of the two objects (r)

Front 45

What is "normal force"

Back 45

force exerted by a surface perpendicularly to the surface

Front 46

___________ is always a pulling force on the MCAT.

Back 46

Tension

Front 47

The 2 types of Friction and their notation:

Back 47

- Kinetic Friction (sliding) = F_f,k'
- Static Friction (not sliding) = F_f,s'

Front 48

Equation for Kinetic Friction

Back 48

F_f,k' = μ_k * F_N

μ_k = coefficient of kinetic friction
F_N = normal force

Front 49

Inequality for Static Friction

Back 49

F_f,s' ≤ μ_s * F_N

μ_s = coefficient of static friction
F_N = normal force

- μ_s * F_N is the maximum value for force of static friction before an object begins to move

- static friction equals the magnitude of the applied force

Front 50

Centripetal force equation

Back 50

F_c = m*a_c = m * v^2/r

- centripetal force is not a new force, but a general term for any centerseeking force like gravity or tension

Front 51

center of mass equation

Back 51

x_cm = (m_1*x_1 + m_2*x_2 + m_3*x_3 + .....) / (m1 + m2 + m3 + ...)

Front 52

What is "rotational inertia" or "moment of inertia" (hint: related to rotational motion)

Back 52

the property that makes rotational acceleration difficult

Front 53

Info about Moment of Inertia

Back 53

- denoted by "I"
- measured in kg * m^2
- increases with mass
- increases with how far away the mass is from the axis of rotation (think of figure skater with arms out and with arms in while spinning)

Front 54

Torque (definition)

Back 54

- torque is created by a force that produces rotation
- required for rotational acceleration to occur just like force is required for translational acceleration to occur
- denoted by "τ"; measured in N * m

Front 55

Torque (equation)

Back 55

τ = r*F*sinθ

τ = torque
r = distance from pivot to point of applied force
F = applied force
θ = angle between r and F

Front 56

Torque (equation with lever arm)

Back 56

τ = L * F

τ = torque
L = lever arm = shortest distance from pivot to line of action (line of action is the line of the force)
F = applied force magnitude

Front 57

Statics: Translational equilibrium

Back 57

When no net force is acting on an object (object is still)

Front 58

Statics: Rotational equilibrium

Back 58

When no net torque is acting on a body (object is not rotating)

- set counterclockwise (CCW) torques equal to clockwise (CW) torques in rotational equilibrium

Front 59

sin (60 degrees)

Back 59

sqrt(3) / 2 = 0.87

Front 60

cos (45 degrees) and sin(45 degrees)

Back 60

sqrt(2) / 2 = 0.71

Front 61

sin(30 degrees)

Back 61

1/2 = 0.5

Front 62

Definition and Formula for Work (units as well)

Back 62

- Work is a measure of how much a force succeeds in moving an object in the direction of the displacement
- W = F*d*cosθ where d = displacement and Fcosθ = the component of the force in line with the displacement
- measured in Joules (N*m); work is a scalar

Front 63

The Signs of Work

Back 63

- Work is positive when cosθ is positive;
- work is neg when cosθ is neg (between 90 degrees and 180 degrees)
- work is 0 when cosθ = 0 (which means θ= 90)

Front 64

Total Work formula

Back 64

W_total = W_1 + W_2 + W_3...

total work is a scalar sum

Front 65

Work done by Changing Forces

Back 65

- if force is not constant, then the formula for work (W=Fdcosθ) cannot be used
- Calculate the area under the curve in a Force (N) vs. Position (m) graph

Front 66

Work done by Gravity

Back 66

- the work done by gravity is independent from it's path since gravity is a conservative force
- the vertical displacement is "d"
- use the formula W_g = mgΔh

Front 67

Kinetic Energy Formula

Back 67

KE = (1/2) mv^2

- measured in Joules (N*m)

Front 68

Work-Kinetic Energy Theorem

Back 68

W_total = ΔKE = KE_f - KE_0

- if a force does positive work, there is an increase in KE
- if a force does negative work, there is a decrease in KE

Front 69

Gravitational Potential Energy

Back 69

PE_g = mgh

Front 70

Work due to Gravity

Back 70

- the Work due to gravity can be seen as:
W_g = -ΔPE

Front 71

Law of Conservation of Energy

Back 71

"The energy of an isolated system remains constant"
- in such a system, energy can neither be created or destroyed, only converted to different forms

Front 72

Mechanical Energy Equation

Back 72

E = KE + PE

KE = kinetic energy
PE = potential energy

Front 73

Law of Conservation of Mechanical Energy

Back 73

E_0 = E_f
KE_0 + PE_0 = KE_f + PE_f

Front 74

Nonconservative forces and Conservation of Energy

Back 74

- there are 3 conservative forces: gravity, electrostatic force, and spring force
- If F is a nonconservative force (like friction or all applied forces), then:
KE_0 + PE_0 + W_F = KE_f + PE_f

Front 75

Mechanical Advantage

Back 75

applied force (F) is inversely proportional to displacement (d) according to W=F*d*cos(theta)
- simple machines like pulleys, levers, and inclined planes create mechanical advantage by **reducing required applied force and increasing displacement**

Front 76

Power formula and units

Back 76

- power is the quantity of work performed over time
- Power = W / ΔT
- measured in Watts (W) = 1 J/s

Front 77

Alternate formula for Power

Back 77

P = F*v*cosθ where v = velocity and F*cosθ = component of F that is pointing in the direction of the velocity

Front 78

Linear momentum (p)

- Formula
- Units
- Vector or scalar?

Back 78

p = m*v
m = mass
v = velocity

- Units: kg*m/s
- p is a vector since v (velocity) is a vector

Front 79

Impulse (J)

- Definition
- 2 formulas
- proportion

Back 79

- Impulse: the change in momentum

- Formula #1: J = Δp = p_f - p_0
- Formula #2: J = F_avg * Δt

- Proportion: F_avg is inversely proportional to Δt

Front 80

In which type of graph does the area under the curve correspond to impulse?

Back 80

in a Force (N) vs. time (s) graph

Front 81

Conservation of Linear Momentum Definition and Equation

Back 81

"If 2 objects hit eachother without any other external forces, total momentum of the system is conserved"

P_A0 + P_B0 = P_Af + P_Bf

Front 82

Elastic Collisions

Back 82

In elastic collisions and inelastic collisions, momentum is conserved. However, in elastic collisions, KE is also conserved

Front 83

Inelastic Collisions

Back 83

In elastic collisions and inelastic collisions, momentum is conserved. However, in inelastic collisions, KE is NOT conserved.

Front 84

Perfectly Inelastic Collisions

Back 84

When during a collision, the KE is not conserved and the objects stick together and move together after collision
- combine masses when finding the final momentum: (m_1 + m_2) * v_f

Front 85

Collisions in Two Dimensions

Back 85

since momentum is a vector, the components of momentum are also conserved during a collision

Front 86

Recoil or Explosion and Conservation of Momentum

Back 86

Total momentum is also conserved when two objects begin as one and then separate (verb) from each other

Front 87

How are solids different than liquids?

Back 87

Solids don't flow

Front 88

Density (ρ)

Back 88

Density = Mass / Volume (in kg/m^3)

- density is a conversion factor to/from volume from/to mass

Front 89

Specific Gravity

Back 89

S.G. = ρ_fluid / ρ_water

* ρ_water = 1000 kg/m^3
* S.G. is unitless since its a ratio of densities

Front 90

What are the two characteristics of tensile stress?

Back 90

- tensile stress refers to a force that is equally applied to both ends of a solid
- tensile stress refers to a force that tends to compress or stretch a solid

Front 91

What is the equation for Tensile Stress (T_ss)?

Back 91

T_ss = F / A_c

A_c = cross sectional area
F = applied force

- units = N/m^2 = 1 Pascal = Pa

Front 92

Define Tensile Strain:
What's the equation for Tensile Strain (T_sn)?

Back 92

Tensile Strain refers to the degree that tensile stress changes the length of an object

- T_sn = ΔL / L_0
* ΔL = change in length
* L_0 = initial length

- T_sn is unitless since it's a ratio of lengths

Front 93

What is Young's modulus a ratio of?

Back 93

YM = T_ss / T_sn

Front 94

Density of liquids and density of gases

Back 94

- density of liquids is fairly constant
- density of a gas will change at varying temperatures and pressures

Front 95

Formula for pressure:

Back 95

Pressure = Force / Area (units: N/m^2 = 1 Pascal)

Front 96

Fluid pressure definition

Back 96

- Fluid pressure is the pressure exerted by a fluid on a real or hypothetical body

Front 97

What is the formula for gauge pressure (a type of fluid pressure)?

Back 97

P = ρ*g*h

- gauge pressure does not include atmospheric pressure
- ρ = density of fluid
- g = 10 m/s^2
- h = height of fluid above a specific point

Front 98

What is equation for absolute pressure?

Back 98

Absolute pressure = gauge pressure + atmospheric pressure
= ρgh + atmospheric pressure

Front 99

Pascal's principle:

Back 99

- "pressure exerted on an enclosed fluid it equally transmitted to every part of the fluid and also on the walls of the container"
- "fluid pressure at any given depth in a resting fluid is unrelated to the shape of the fluid's container"

Front 100

Proportions in the fluid pressure equations (P = ρgh)

Back 100

P is directly proportional to ρ (density) and to h (depth)

Front 101

Define buoyancy:

Back 101

Buoyancy refers to a fluid's tendency to propel submerged or partially submerged objects up towards the surface

Front 102

Description and Equation of Bouyant Force (Archemides' Principle):

Back 102

- the buoyancy force is an upward force exerted by a fluid on another body or fluid.

- Buoyancy (F_b) = V * ρ * g = weight of displaced fluid
* V = volume of displace fluid
* ρ = density of fluid
* g = acceleration due to gravity (10 m/s^2)

Front 103

Flow (Q): description and equation

Back 103

the volume of fluid that passes a given point in a given period of time

- Flow (Q) = A*v
(A = cross sectional area of pipe; v = velocity of pipe; units = m^3/sec

Front 104

Characteristics of Ideal Flow

Back 104

1) flow is constant at all points
2) ideal flow has no viscosity
3) Ideal flow has no turbulence
4) ideal flow has no fluid friction (drag)
5) flow = velocity * area

Front 105

The Bernoulli Equation: description and implications

Back 105

Bernoulli's equation implies that at high velocities, fluid pressure decreases, and at low velocity, fluid pressure increases

- v = sqrt(2gh)

Front 106

Laminar flow

Back 106

smooth flow of liquid in layers with no whirpools

Front 107

Turbulent flow

Back 107

flow that contains whirpools and eddies

Front 108

Fluids flowing through a pipe with changing caliber: proportions

Back 108

velocity is inversely proportional to cross-sectional area

pressure increases with cross-sectional area

Front 109

What are qualities of conductors?

Back 109

- they are usually metals
- they have high electron mobility

Front 110

What are qualities of insulators

Back 110

- low electron mobility
- nonmetals like rubber and glass

Front 111

What is Coulomb's Law?

Back 111

F_e = k * q_1 * q_2
--------------------
r^2
where k = 9*10^9 = 1/(4πε_0)

Front 112

What is Electric Field Strength (E)?
What direction does Electric Field point in?
What are the units of Electric Field?

Back 112

- the hypothetical force on a +1 charge at a specific distance
- electric field extends from a charge in all directions and points in the direction a test charge would move in
- Units: N/C

Front 113

Describe a capacitor:

Back 113

- two closely spaced plates parallel to each other with equal area
- each plate has equal and opposite charge

Front 114

What's the formula for Electric Field within a Capacitor?:

Proportions?

Back 114

E=Q/(ε_0 * A)

(units: N/C)
Electric field is proportional to charge and inversely proportional to area

Front 115

What is the definition of Electrostatic potential of a capacitor?

Back 115

Electrostatic potential refers to the potential energy possessed by a massless particle with |q| = 1 situated on the like-charged plate of the capacitor

Front 116

What is the equation for Electrostatic Potential of a Capacitor?

Back 116

V = E*d

V = electrostatic potential (J/C)
E = electric field strength (N/C)
d = distance between capacitor's plates

Front 117

How is Electrostatic Potential within a Capacitor similar to Gravitational Potential energy/Work?

Back 117

in the formula V=Ed, E represents the force repelling the test charge, d represents the "height" the charge will move, and V represents the "gravitational potential energy"

Front 118

What is capacitance (definition)?

Back 118

Capacitance is the ability of a capacitor to store electric charge.

Front 119

What 2 things is Capacitance (C) proportional to?

Back 119

Capacitance is proportional to (Q/V)
Capacitance is also proportional to Area of the plate

Front 120

What is the equation of capacitance and what are its inherent proportions?

Back 120

C = (k * ε_0 * A) / d

k= dielectric constant
A = area of capacitor's plates
d = distance between plates

- C is directly proportional to Area and inversely proportional to distance btw plates

Front 121

Explain what dielectric breaking point is.

Back 121

At high values of Electric Field (E), stored charge in a capacitor will be discharged. This E value corresponds to the dielectric's "breaking point."

Front 122

How is electromotive force (emf) produced in a circuit?

Back 122

by the difference in electric potential at each terminal

Front 123

From which terminal of the voltage source do electrons flow in a circuit?

Back 123

Electrons flow from the negative terminal to the positive terminal

Front 124

What is the definition of current in a circuit?

Back 124

Current is the flow of positive charge; current flows from the positive terminal of the battery in a circuit

Front 125

What is the definition of voltage in a circuit?

Back 125

Voltage is the difference in elec. potential btw the cathode and the anode measured in Volts

Front 126

What is Ohm's Law for circuits? What are it's inherent proportions and other algebraic forms?

Back 126

V = IR
(V = voltage (Volts); I = current (A); R = resistance (Ω - ohms)

Front 127

What is the formula for Power in a circuit?
When combining this formula with Ohm's Law, what other versions of the formula exist?

Back 127

P = I*V
P = I^2 * R
P = V^2/R

Front 128

What are resistors?

Back 128

Objects that conduct electricity poorly (like lightbulbs)

Front 129

What is the formula for total resistance when resistors are connected in series?

Back 129

R_total = R_1 + R_2 + R_3...

Front 130

What is the formula for total resistance when resistors are connected in parallel?

Back 130

1/R_total = 1/R_1 + 1/R_2 + 1/R_3...

Front 131

What formula should you use to calculate voltage drop at each resistor in a circuit?

Back 131

V = IR (Ohm's Law)

Front 132

How are magnetic fields produced? What direction does the vector (magnetic field) have at all points in a circular path?

Back 132

By flowing electrons; when magnetic field is rotating around a wire, the magnetic field points as a vector tangential to the circle.

Front 133

How does magnetic field strength around a wire change when distance from the wire changes?

Back 133

Magnetic field strength is greater near the wire and less from the wire.

Front 134

What is the symbol and unit for magnetic field strength?

Back 134

B; in Teslas

Front 135

How do you determine the direction of magnetic field (B) around a wire?

Back 135

Use the right hand rule where your thumb points in the direction of the current (flow of positive charge) and your fingers curve in the direction of magnetic field.

Front 136

How do you determine the direction and magnitude of the force produced by a magnetic field?

Back 136

- to determine direction of the force, put your right hand flat and point fingers in direction of field (B), thumb in direction of velocity (v), and then the palm will point in the direction of force (F) on a positive charge.

- magnitude of force: F = q*v*B

Front 137

In the context of transverse waves, what do cycle, period, wavelength, amplitude, and frequency mean?

Back 137

Cycle = one crest and one trough
Period (T)= time for one cycle to occur
Wavelength (λ) = distance traveled by one cycle
Amplitude (A) = height from middle line of a wave and crest of the wave
Frequency (f)= amount of cycles per second

Front 138

How are period and frequency related in the context of transverse waves?

Back 138

F = 1/T
T = 1/f

T = period in seconds/cycle
f = frequency in cycles/second (aka Hertz (Hz))

Front 139

How are velocity of a wave, frequency and wavelength related in the context of waves?

Back 139

v = f * λ

Front 140

In longitudinal compressional waves, what parts of the waves are analogous to crest and troughs?

Back 140

crest = compression
trough = rarefraction

Front 141

How do density of a medium and resistance to compression affect the speed of sound?

Back 141

The speed of sound decreases when the density of a medium increases;
- the speed of sound increases when resistance to compression increases

Front 142

How are loudness (β) and Intensity (I) of sound related? What are the units of loudness (β) and intensity (I)?

Back 142

β = 10 * log (I / I_0)

β = loudness (in decibels)
I = intensity of the sound (W/m^2)
I_0 = lowest intensity that is dectectable by humans (10^-12 W/m^2)

- when intensity is multiplied by 10^x, β increases by 10(x)

Front 143

In an oscillating spring or pendulum, where is the point of highest velocity?

Back 143

At the point when the spring/pendulum is in it's relaxed position

Front 144

In an oscillating spring, what happens to the kinetic energy and potential energy of the spring?

Back 144

Kinetic energy and potential energy are converting into eachother back and forth.

mgh_max = 1/2mv^2_max

Front 145

What is Hooke's law in the context of springs?

Back 145

F = - k * x where k is the spring constant and x is the displacement from the relaxed position

Front 146

How can one approximate the spring constant of a pendulum

Back 146

k for pendulums ≈ wt of pendulum / length of pendulum

Front 147

Is the total energy of a oscillating system constant or changing?

Back 147

Total energy is constant in a oscillating system (spring or pendulum)

Front 148

What is the range of sound frequencies that are detectable by human ears?

Back 148

10 Hz - 20,000 Hz

- sound below the lower threshold is called infrasonic
- sound above the top threshold is called ultrasonic

Front 149

Describe the Doppler Effect in the context of sound and pitch:

Back 149

As the source of sound approaches an observer, the pitch (apparent frequency) increases and then suddenly decreases once the source begins to move away from the observer.

Front 150

What is the equation for Doppler effect?

Back 150

f_0 = f_s [(v ± v_0)/(v ± v_s)]

f_0 = apparent pitch (not true frequency)
f_s = frequency of source's sound
v = velocity of sound in that medium
v_0 = velocity of the observer
v_s = velocity of the source

Note: assign positive and negative by this rule - if the observer is moving towards the source, then the fraction would need to get bigger so numerator's sign would be positive; if the source is moving towards the observer, then the fraction would need to bigger so the denominator's sign would be smaller.