Physics and General Chemistry MCAT

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physical quantities with both magnitude and direction

vectors
examples: velocity, force

physical quantities that have magnitude but no direction

scalars
examples: speed, mass

finding resultant using component method

1. resolve vectors into x and y components
2. sum all the vectors in the x direction to get the resultant for the x direction, and sum all the vectors in the y direction to get the resultant for the y direction
3. the magnitude of the resultant is R= √(Rx^2 + Ry^2)

the change in position that goes in a straight-line path from the initial position to the final; it is independent of the path taken

displacement (Δx)

SI UNIT: m (meters)

Δx/Δt
displacement/time

average velocity

SI UNITS: m/s (meters/second squared)

the rate of change of an object's velocity; it is a vector quantity;
Δv/Δt
velocity/time

acceleration

SI UNITS:SI UNITS: m/s^2 (meters/second squared)

linear motion equations (5)

1. Vf= Vo + at
2. Vf^2= Vo^2 + 2a⋅(Δx)
3. Δx= Vot + 1/2at^2
4. Vaverage= (Vo + Vf)/2
5. Δx= vt= ((Vo + Vf)/2)⋅t

vertical component of projectile motion problem

= v⋅sin(theta)

horizontal component of projectile motion problem

= v⋅cos(theta)

When solving for time, there will be two values for t in projectile motion problem which are:

1. when the projectile is initially launched and
2. when it impacts the ground

to find max height:

remember: that the vertical velocity of the projectile is 0 at the highest point of the path

force that must be overcome to set an object in motion.
it has the formula:

static friction (fs)

formula: 0 ≤ fs ≤ µs⋅N

opposes the motion of objects moving relative to each other.
it has the formula:

kinetic friction (fk)

formula: fk= µk⋅N

a body in a state of motion or at rest will remain in that state unless acted upon by a net force

Newton's First Law (Law of Inertia)

when a net force is applied to a body of mass (m), the body will be accelerated in the same direction as the force applied to the mass.

this is expressed by the formula:

Newton's Second Law

F=ma
Force=mass x acceleration

SI UNIT: NEWTON (N)=kg⋅m/s^2
Newton= kilograms x meters/second squared

Fgravity (Fg or Fw) > Fparachute

person accelerates downward

Fgravity (Fg or Fw) = Fparachute

terminal velocity is reached (person travels at constant velocity)

if body A exerts a force on body B, then body B will exert a force back onto body A that is equal in magnitude but opposite in direction.

this can be expressed by the formula:

Newton's Third Law

formula: Fb = -Fa

All forms of matter experience an attractive force to other forms of matter in the universe.

The magnitude of the force is represented by:

Newton's Law of Gravitation

F= G⋅m1⋅m2/ r^2

a scalar quantity that measures a body's inertia

mass (m)

a vector quantity that measures a body's gravitational attraction to the earth

weight (W)

W= m⋅g
Weight= mass x gravity

Uniform circular motion (2)

1. ac= v^2/r
2. Fc= m⋅v^2/r

An object is in translational equilibrium when the sum of forces pushing it one direction is counterbalanced by the sum of forces acting in the opposite direction.

it can be expressed as:

First condition of equilibrium

ΣF=0

Fn up, Fw⋅cos(theta) down (vertically)
Fw⋅sin(theta) and Ff side to side (horizontally)

ΣF=0 must be true for translational equilibrium; therefore,

Resolve forces into x and y components
ΣFx=0 and ΣFy=0

Only forces in the x direction affect motion of the object: ΣFx=m⋅a

For a constant force (F) acting on an object that moves through a distance (d), what is the work?

Work (W) = F⋅d⋅cos(theta)
Work=force x distance x cos(theta)

SI UNIT: JOULE= N⋅m
Joule=Newton x meters

For a force perpendicular to the displacement, what is the work?

Work (W)=0

SI UNIT: JOULE= N⋅m
Joule=Newton x meters

the rate at which work is performed, and is given by:

Power (P) = W/t
Power= work/time

SI UNIT: JOULE/SEC or J/s or N⋅m/s

is energy a scalar or vector quantity?

Energy is a scalar quantity

SI UNIT: JOULE or N⋅m

the energy associated with moving objects

formula:

Kinetic energy (mechanical energy)

KE= 1/2m⋅v^2

the energy associated with a body's position.
__ of an object is due to the force of gravity acting on it and it is expressed as:

Potential energy (mechanical energy)

Gravitational potential energy (U)
U= mgh
GPE= mass x gravity x height

This is conserved when the sum of kinetic and potential energies remains constant.

Total Mechanical energy (E)

E= U + K
Total Mechanical energy= potential energy + kinetic energy

SI UNIT: JOULE or N⋅m

Relates the work performed by all forces acting on a body in a particular time interval to the change in kinetic energy at that time.

the expression is:

Work-Energy Theorem

W=ΔKE
Work= change in kinetic energy

When there are no nonconservative forces (e.g., __) acting on a system, the total mechanical energy remains constant.

Conservation of Energy

e.g., friction, air resistance

ΔE= ΔK + ΔU= 0
change in energy= change in kinetic energy + change in potential energy

is momentum a scalar or a vector quantity?

momentum is a vector quantity.

p=m⋅v
momentum (p)= mass x velocity

Elastic Collisions--Target at Rest
Conservation of momentum:
Conservation of kinetic energy:

Elastic Collisions (no loss of KE, both p and KE conserved)--Target at Rest
Conservation of momentum:
m1i⋅v1i = m1f⋅v1f + m2f⋅v2f

Conservation of kinetic energy:
1/2m1i⋅v1i^2 = 1/2m1f⋅v1f^2 + 1/2m2f⋅v2f^2

Completely Inelastic Collisions--Target at Rest
Before
Momentum:
Kinetic energy:
Conservation of momentum:

After
Momentum:
Kinetic energy:
Conservation of momentum:

Completely Inelastic Collisions (part of the KE is changed to some other form of energy, so KE is not conserved, but do obey conservation of momentum)--Target at Rest

Before
Momentum: m1⋅vi
Kinetic energy: 1/2m1⋅vi^2
Conservation of momentum:
m1⋅vi = (m1 + m2)⋅vf

After
Momentum: (m1 + m2)⋅vf
Kinetic energy:1/2(m1 + m2)⋅vf^2
Conservation of momentum:
m1⋅vi = (m1 + m2)⋅vf

Impulse (J)=

Impulse (J)= F⋅t = ΔP
impulse= force x time = change in momentum

the increase in length by most solids when heated

linear expansion (thermal expansion)

mnemonic: when temperature increases, the length of a solid increases "a Lot" (α⋅LΔT)

ΔL = α⋅LΔT

the increase in volume of fluids when heated

volume expansion (thermal expansion)

ΔV = Β⋅VΔT

Heat Transfers (3)

1. Conduction
2. Convection
3. Radiation

the direct transfer of energy via molecular collisions

Conduction (Heat spontaneously flows from higher temp to lower temp)

the transfer of heat by the physical motion of the heated material (only liquids and gases)

Convection

the transfer of energy by electromagnetic waves

Radiation

the amount of heat per unit mass required to raise the temperature by one degree Celsius
-can only be used to find heat added (Q) when the object does not change phase
Q > 0 means:
Q < 0 means:

specific heat (c)
The specific heat of water is 1 calorie/gram °C = 4.186 joule/gram °C which is higher than any other common substance

Q=mcΔT (Mnemonic: looks like MCAT)
Q=heat added, m=mass, c=specific heat, Δt=change in temperature

Q > 0 means: heat is gained
Q < 0 means: heat is lost

SI UNITS: JOULES OR cALORIES

the quantity of heat required to change the phase of 1 kg of a substance

formula:

Heat of Transformation

Q = m⋅L (phase changes are isothermal processes)
Q=amount of energy released or absorbed during the phase change
m=mass
L=latent heat for a particular substance

When the piston expands...

work is done BY the system ( W > 0)

When the piston compresses the gas...

work is done ON the system ( W < 0)

The area under a P vs. V curve is...

the amount of work done in a system

energy cannot be created or destroyed; change in internal energy= heat added TO the system - work done BY the system

First Law of Thermodynamics

ΔU= Q - W
change in internal energy= heat added TO the system - work done BY the system
or
ΔU= Q + W
change in internal energy = change in heat transferred to it + work done ON it

SI UNITS: all Joules or calories

First Law of Thermodynamics

Process: First Law becomes:
Adiabatic
Constant Volume
Closed Cycle

First Law of Thermodynamics

Process: First Law becomes:
Adiabatic (Q=0) ΔU = - W
Constant Volume ( W=0) ΔU = Q
Closed Cycle (ΔU=0) Q = W

no heat is added or removed from the system

adiabatic process (Q=0), so ΔU = - W
occurs when work is done fast

the heat given off or absorbed by the reaction is equal to the change in the internal energy that occurs during the reaction.

constant volume process (W = 0)

example: breakfast in a bomb calorimeter

in any thermodynamic process that moves from one state of equilibrium to another, the entropy (S) of the system and environment together will either increase or remain unchanged

Second Law of Thermodynamics

ratio of shear stress to shear strain

Shear Modulus (S) = (F/A)/(x/h) or modulus of rigidity
force/area
displacement/height

always positive

can be used to predict the elongation or compression of an object as long as the stress is less than the yield strength of the material

Young's Modulus (Y) = (F/A)/(Δl/lo)
stress/strain

l=length

law of physics describing the electrostatic interaction between electrically charged particles

formula:

Coulomb's Law

formula: F= (kq1q2)/r^2

SI UNITS: NEWTONS (N)

the electric force per unit charge

a positive (+) point charge will move...
a negative (-) charge will move...

Electric field

E= F/q = k⋅q/r^2

SI UNITS: N/C or V/m
C=coulombs; V=volts

in the same direction as the electric field
in the opposite direction

amount of work required to move a charge (q) from infinity to the point in space

Electric Potential Energy (U)

U= qΔV = qEd= (kq1⋅Q)/r

SI UNITS: JOULE

with electric dipoles, p is the...

the dipole feels no translational force, but experiences a ___ about the center causing it to rotate, so that...

dipole moment and p=qd

the dipole feels no translational force, but experiences a TORQUE about the center causing it to rotate, so that the dipole moment aligns with the electric field

the amount of work required to move a positive test charge (qo) from infinity to a particular point divided by the test charge

Electric Potential (V)

V= W/ qo
Work/ positive test charge

SI UNITS: VOLT= JOULE/coulombs

when two oppositely charge parallel plates are separated by a distance (d), an electric field is created, and a ___ exists between the plates, given by:

Potential Difference (Voltage)

Voltage (V)= W/q = kq/r
V=Ed

SI UNITS: VOLT = Joule/Coulomb

density (ρ)=

ρ (rho)=m/v
ρ=mass/volume

SI UNITS: kg/m^3
kilogram per cubic meter

specific gravity=

ρsubstance/ρwater

NO UNITS

ρwater=

10^3 kg/m^3

ρgV=

Weight (W) in fluids and solids
Weight (W)= ρ⋅g⋅V

scalar quantity defined as force per unit area

Pressure (P) = F/A

SI UNITS: PASCAL = N/m^2

For static fluids of uniform density in a sealed vessel, pressure (P)=

P= ρgh

Absolute pressure in a fluid due to gravity somewhere below the surface is given by the equation:

P= Po + ρgh

Gauge pressure=

reads the excess of pressure over atmospheric pressure and this excess

Pg= Pabs - Penviornment

If steady flow exists in a channel and the principle of conservation of mass is applied to the system, this exists and is defined as: "The mean velocities at all cross sections having equal areas are then equal, and if the areas are not equal, the velocities are inversely proportional to the areas of the respective cross sections." Thus if the flow is constant in a reach of channel the product of the area and velocity will be the same for any two cross sections within that reach.

Continuity Equation: v1A1=v2A2

v=the mean velocity
a=cross sectional area of flow

points 1 and 2 lie on a streamline,
the fluid has constant density,
the flow is steady, and
there is no friction.

Bernoulli's Equation:
P + 1/2ρv^2 + ρgh = constant
P=pressure, ρ=density, v=velocity, g=gravitational acceleration, h=elevation

the buoyant force is equal to the weight of the displaced fluid.
--if the weight of the fluid displaced is < than the object's weight, then...

--if the weight of the fluid displaced by the object is ≥ to object's weight, then...

Fbuoyant= ρfluid⋅g⋅Vsubmerged
density x g x volume

Archimedes's Principle

the object will sink
the object will float

a change in the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessels

Pascal's Principle

ΔP= F1/A1 = F2/A2 and A1d1 = A2d2, so
W= F1d1 = F2d2

created by permanent magnets and moving charges; their lines depict the direction a compass needle would point if placed in the field from the North Pole(away from) to the South Pole (towards)

Magnetic Fields (B)

SI UNITS: Tesla (T) - N⋅s/m⋅C

A charge moving in a magnetic field experiences a force exerted on it.

Magnetic Force

F=q⋅v⋅B⋅sin(theta)

When is the magnetic force (F=q⋅v⋅B⋅sin(theta))=0?

When charges move parallel or antiparallel to the magnetic field.

the flow of electric charge; and the direction is the direction positive charge would flow or from high to low potential

DC (Direct Current)
Current (I)

Current (I)= Δq/Δt

SI UNITS: Amp (A) = Coulombs/second or C/s

states that the current (I) through a conductor between two points is directly proportional to the potential difference across the two points, and inversely proportional to the resistance between them

Ohm's Law (can be applied to entire circuit or individual resistors)

V (potential difference)=I (current) ⋅R (resistance)

V=IR

opposition to the flow of charge; and it increases with increasing temperatures with most conductors

Resistance (R)= ρL/A

SI UNITS: Ohm (Ω)

1. At any junction within a circuit, the sum of current flowing into that point must equal the current leaving.
2. The sum of voltage sources equals the sum of voltage drops around a closed circuit loop

Kirchoff's Laws (Circuit Laws)

the movement of electric charge periodically reverses direction

Alternative Current (AC)

Series Circuits

Reff= R1 + R2 + R3...
Veff= V1 + V2 +V3...
Ieff= I1 = I2 = I3...

Parallel Circuits

1/Reff= 1/R1 + 1/R2 + 1/R3...
Veff= V1 = V2 =V3...
Ieff= I1 + I2 + I3...

Power dissipated by resistors

P=IV = V^2/R = I^2⋅R

the ability to store charge per unit voltage

capacitance (under capacitors)

C=Q/V = KεoA/d

Capacitors in parallel...
Capacitors in series...

ADD; Ceq= C1 + C2 + C3
ADD as RECIPROCALS; 1/Ceq= 1/C1 + 1/C2 + 1/C3

Energy stored by capacitors (U)

U=1/2QV = 1/2CV^2 = 1/2Q^2/C

Q=charge, V=voltage, C=capacitance

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