MCAT Physics and Math

What is the range of values for fs?

0 ≤ fs ≤ 𝝁s*N; 0 if the object is on a surface with NO STATIC FORCE, and 𝝁s*N is the maximum (note: do not assume its experiencing the max)

If you travel 2km E, then N, then W, then S, what is your displacement?

0km!

Atomic Energy: Electron Volts

1 eV = 1.6*10-19J

Ångstrom

1 Å = 10-10m

Vector Addition Methods (2)

1) tail-to-tip method, 2) component vectors

Nanometers

1nm = 10-9m

G (Gravitational Constant)

6.67*10^(-11) N*m^2/kg^2

g (Acceleration due to gravity)

9.8m/s^2 (usually rounded to 10); decreases with height above earth

1 eV is equal to...

= the amount of energy gained by an electron accelerating through a potential difference of one volt

Gravitational Force (equation)

Fg = G*m1*m2/r^2; G = gravitational constant, m1 and m2 are the masses of 2 objects, r is the distance between their centres of mass

Weight and mass equation

Fg-> = mg->

What is the direction [⨂] in vectors?

INTO page (like an arrow)

SI Derived Work/Energy

Joule (J) (kg*m2/s2)

Which vector multiplication is commutative (order-insensitive)? Which is not?

NEITHER are commutative because of the directions and angles between the vectors

Is vector subtraction commutative (order-insensitive) i.e. A-B = B-A?

NO

Is static friction constant?

NO, it exists in an interval

Does a rolling wheel experience kinetic friction? When would it? Explain the significance

NO; it IS NOT SLIDING on the floor, it has INSTANTANEOUS STATIC FRICTION at the points of contact of the wheel; only a wheel sliding on ice has fk; you must be careful about what is experiencing fk and fs

SI Derived Force

Newton (N) - 1 kg*m/s2

Do objects always experience maximum static friction force (𝝁s*N)?

No; do not assume this

What governs friction more, surface roughness (𝝁s) or Normal force (N)?

Normal force!

What is the direction [⨀] in vectors?

OUT of page (like an arrow)

Resultant equation (given the 2 added perpendicular component vectors)

Pythagorean Theorem; V = √(X^2 + Y^2)

Relationship between force of gravity exerted by each object on each other

SAME MAGNITUDE but OPPOSITE DIRECTION; note that in a = F/m, the more massive the object, the less it accelerates; that's why we accelerate faster towards earth than it accelerates towards us

SI Usage

Used in science/MCAT

SI Derived Power

Watt (W) (kg*m2/s3)

Is kinetic friction constant?

YES; there is an equals sign so it always stays the same for a combo of 𝝁k and N; DOES NOT MATTER HOW MUCH SURFACE IS IN CONTACT NOR VELOCITY

How are changes in velocity caused (acceleration)?

a FORCE (push or pull)

What is the only body that has a centre of gravity at its geometric centre?

a homogenous, spherical object with uniform mass and density

On what type of path is there a PRONOUNCED difference between vector and scalar quantities?

a non-linear path

Imperial System (British)

aka foot-pound-second (FPS)

SI Current Unit

ampere (coulomb/second) (A)

Atomic Measurements

angstroms, nanometers, eVs

Where does static friction occurs between objects? Why does it increase with Normal Force?

at their contact points; it increases with normal force because 2 objects squeezed closer together by the normal load have more contact points

2 Types of units in a unit system

base and derived

Derived Units

base units associated with each other (e.g., Newton, 1 kg*m/s2)

SI Luminous Intensity Unit

candela (cd)

Displacement (x-> or Δd->)

change in position; vector that connects initial and final position

Scalar notation

denoted as an italic usually

Vector notation

denoted with an ARROW ON TOP (A->) OR as BOLD

Arrow Vectors

direction symbolizes the direction of the vector, and the length is proportional to the magnitude of the vector

Examples of vectors (3)

displacement, velocity, acceleration

3 basic quantities of kinematics

displacement, velocity, and acceleration

Distance vs Displacement (the extreme difference between scalar vs vector) (and earth example)

distance is the ACTUAL DISTANCE TRAVELED vs displacement, which is the net change in position (e.g., earth travels a DISTANCE of a zillion km per year, but its displacement annually is 0!)

Distance (d)

distance of path traveled; scalar

Examples of scalars (5)

distance, speed, energy, pressure, mass

Multiplying a vector by a vector (2 types)

dot product or cross product; DO NOT FORGET UNITS (e.g., N x m = Nm)

Imperial Length Unit

foot (ft)

Friction Force

force that opposes the movement of objects; ALWAYS SLOWS DOWN THE OBJECT (never speeds up and slows like gravity would)

Kinetic Friction (fk) (+equation)

friction force that exists between a sliding object and the surface; fk = 𝝁k*N (𝝁k = coefficient of kinetic friction, N is the normal force)

Static Friction (fs) (+equation)

friction force that exists between a stationary object and the surface it rests upon; 0 ≤ fs ≤ 𝝁sN (𝝁s = coefficient of static friction, N = normal force); exerts equal and opposite force to pushing force of an object

Where Imperial System is used

in US, nowhere else (not Britain)

Centre of mass equations

in a system with 3D, the centre of mass requires 3 coordinates; note that 3 of these equations must be worked out following the same pattern (for x, y, z); m are the masses of the samples and x/y/z are the coordinates sampled

What is the purpose of finding the centre of gravity?

it is the point with which we actually can conceptualize physics with our equations

If a tennis racket is thrown into the air, does the entire thing fly in a pattern? What pattern? What parts of it?

its CENTRE OF MASS travels in a PARABOLIC PATH

SI Temperature Unit

kelvin (K)

SI unit of mass

kilogram

SI Mass Unit

kilogram (kg); NOT WEIGHT

Magnitude of a vector notation

lines around the vector; |A->| or no arrow; A

Multiplying a vector by a scalar

magnitude will change (factor of the |scalar|; e.g., x3) and the direction will stay the same or flip if (-); e.g., B-> = nA->; n = -3, |n| = 3 and its negative, therefore B-> = -3A->, a vector x3 as long in the opposite direction

SI Length Unit

meter (m)

SI System

meters-kilograms-seconds

7 Base SI Units

meters-kilograms-seconds (MKS) OR centimeters-grams-seconds (CGS) + ampere, mole, kelvin, candela

SI Amount of Substance Unit

mole (mol)

Does mass depend on gravity?

nope, but weight does; an object has the same mass anywhere in the entire universe

Scalars

numbers with just magnitude, no direction

Vectors

numbers with magnitude and direction

Proportionalities of Gravitational Force equation

often tested by saying "if you half distance, what happens to force" (it is X4 the strength! Just do the math and bring the fraction out in front)

What is direction notation for vectors?

placed in square brackets; e.g. [N]

Imperial Weight Unit

pound (lb)

Force (F->)

push or pull of an object (even if 2 objects are not touching; gravity or electrostatic); units Newton (N) (1 kg*m/s^2)

Velocity (v->)

rate of change of displacement (m/s); vector with direction the same as the displacement

Imperial Time Unit

second (s)

SI Time Unit

second (s)

Imperial Mass Unit

slug OR blob

If a suitcase does not roll when pushed with 50N but does with 100N, what is the fs?

somewhere between 50 and 100N; anything less than this threshold is not enough to make the bag move

Base Units

standard units around which the system is designed

2 types of friction

static and kinetic

Mass (m)

the amount of matter in an object; the measure of a body's inertia; scalar

Gravity

the attractive force between ALL objects; only noticeable on the planetary mass level

Instantaneous velocity & speed (+equation)

the average velocity/speed as time approaches 0; always the same magnitude as each other; lim(Δt→0) Δx/Δt

Normal Force (N)

the component of the force between 2 objects that is PERPENDICULAR to the plane of contact

If you flip the order of vectors in the cross product, what happens?

the magnitude is the same, BUT THE DIRECTION IS EXACTLY THE OPPOSITE

Weight (Fg->)

the measure of gravitational force exerted on an object's mass; a vector always

Vector Dot Product (+equation)

the multiplication of 2 vectors that results in a scalar (e.g., work = force•displacement); A->•B-> = |A->||B->|cosθ, where theta is the angle between the 2 vectors

Vector Cross Product (+equation)

the multiplication of 2 vectors that results in a third vector (e.g., torque); A->×B-> = |A->||B->|sinθ (this is the magnitude), where theta is the angle between the vectors; direction comes from RIGHT HAND RULE

Centre of Mass/Gravity

the point at which the weight of an object is applied; although all points in a moving object move differently, this point moves in a simple path

In the cross product, what is the direction of the product relative to the 2 crossed vectors?

the product is PERPENDICULAR to the plane created by those 2 vectors (and perpendicular to both vectors themselves)

Acceleration (a->)

the rate of change of velocity; occurs as a result of APPLIED FORCE; vector, units m/s^2

Vector Subtraction Methods

the same as vector addition (tip-to-tail or components), just change the (-) vector into SAME MAGNITUDE, OPPOSITE DIRECTION and add it; A-> -B-> = A-> + (-B->)

Resultant

the sum or difference of 2+ vectors

(average) Speed

the total distance over time; scalar; v = d/t

Coefficient of Static Friction (𝝁s)

unitless quantity specific to 2 materials in contact

Right Hand Rule

used to determine the direction of a vector when taking the cross product; in A-> × B-> = C->, your thumb points with A, your index points with B, and your palm points in the direction of C

Average velocity (equation)

v-> = Δd->/t

Tail-to-tip method

vector addition: add the tip of vector1 to the tail of vector 2; resultant is the tail of 1 to tip of 2;

Component vectors

vector addition: resolve & add all the x/y (or parallel/perpendicular) components of the vectors separately; add the x's to x's and y's to y's, get the total magnitude using V = √(X^2 + Y^2) and the direction with θ = tan^(-1)(Y/X)

Component vector equations

x = Vcosθ, y = Vsinθ

Is vector addition commutative (order-insensitive)?

yes!

Theta equation using the component vectors X and Y

θ = tan^(-1)(Y/X)

What is larger, 𝝁k or 𝝁s? fk or fs?

𝝁s; therefore fs will always be larger; it will always take more force to get an object to start moving (un-stick) than to keep it moving