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- MCAT 3

Jessica K.

Linear Motion equations

V=V_{o} + at

x= v_{o}t + 1/2 a t^{2}

V=V^2= Vo^2 + 2ax

Vavg = Vo + V / 2

x=vt= (vo + v)/2 t

Projectile Motion

Vertical component of velocity = vsin (theta)

Horizontal component of velocity = vcos (theta)

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Work

for a constant force F acting on an object that moves through a distance d, the work is W=Fd cos (theta)

For a force perpendicular to the displacement, W=0

Si unit: Joule = Nm

power

the rate at which work is performed: P=work/time

unit: watt (Joule/sec)

Kinetic energy

the energy associated with moving objects

KE= 1/2mv^2

Potential energy

the energy associated with a body's position. Gravitational potential energy of an object is due to the force of gravity acting on it, and it is expressed as U=mgh

Total Mechanic Energy

E= U + K

mechanical energy is conserved when the sum of kinetic and potential energies remains constant

Work-energy theorem

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:

w=change in kinetic energy

Conservation of energy

when there are no nonconservative forces (friction) acting on a system, the total mechanical energy remains constant:

change in energy= change in kinetic energy + change in internal energy= 0

Momentum

p= mv

Inelastic collision equations

momentum: m1vi = (m1+m2)Vf

kinetic energy 1/2m1vi^2 = 1/2 (m1+m2) Vf^2

conservation of momentum: m1vi = (m1+m2)Vf

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Newton's first law (Law of inertia)

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

Newton's second law

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 F=ma

Si unit: newton, kg*m/s^2

Parachute problem

Fgravity > Fparachute; person accelerated downward

Fgravity=Fparachute; terminal velocity is reached; person travels at constant velocity

Newton's third law

If body A exerts a force on body B, then B will exert a force back onto A that is equal in magnitude but opposite in direction. This can be expressed as Fb= -Fa

Newton's Law of Gravitation

All forms of matter experience an attractive force to other forms of matter in the universe. the magnitude of the force is represented by F=Gm1m2/r^2

Centripetal motion

Ac=V^2/r

Fc=mv^2/r

Specific heat

q= mc(change in)temp

can only be used to find q when the object does not change phase.

Q>0 means heat is gained; Q<0 means heat is lost (joules or calories)

Heat of transformation

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

Q=mL

System work

When the piston expands, work is done by the system

when the piston compresses the gas, work is done on the system

the area under a P vs. V curve is the amount of work done in a system

First Law of thermodynamics

change in internal energy = heat - work

constant volume (w=0); change in internal energy= heat

closed cycle (change in internal energy =0) heat=work

Second law of thermodynamics

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

Density

mass/volume

Units: kg/m^3

Specific gravity

density of the substance / density of water

density of water = 10^3 kg/m^3

Pressure

force/ area

Units: pascal, N/m^2

For static fluids of uniform density in a sealed vessel, P=density * g * height

Continuity equation

V1A1 = V2A2

Bernoulli's equation

P + 1/2 density*v^2 + density*g*h = constant

Pascal's Principle

(hydraulic cylinder)

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 vessel.

change in pressure= F1/A1=F2/A2 and W= F1d1= F2d2

Wave formulas

f=1/T v=f*l

Mirror equation (works for lenses too)

1/f ( or 2/r)= 1/ image + 1/ object

Refraction

n= c/v

speed of light (c) = 3 * 10^8 m/s

Snell's Law

n1 sin (theta)1 = n2 sin (theta)2

n2>n1; light bends toward normal

n1>n2 ; light bends away from normal

Strong Acids

Hydroiodic (HI)

hydrobromic (HBr)

hydrochloric (HCl)

nitric (HNO3)

perchloric (HClO4)

chloric (HClO3)

sulfuric (H2SO4)

Strong Bases

sodium hydroxide (NaOH)

potassium hydroxide (KOH)

amide ion (NH2-)

hydride ion (H-)

calcium hydroxide Ca(OH)2

sodium oxide (Na2O)

calcium oxide CaO

Acidity (Periodic Trend)

down and to the right. increasing acidity.

The larger the Ka and the smaller the pKa, the stronger the acid.

-when considering salts, remember all cations, except those of the alkali metals and the heavier alkaline Earth metals (Ca2+, Sr2+. Ba2+) act as weak Lewis acids in aqueous solution

Oxidation states

oxidation state atom

0 atoms in their elemental form

-1 Fluorine

+1 Hydrogen (except when bonded to a metal then: -1)

-2 Oxygen (except when in a peroxide like H2O2)

More oxidation states

+1, group 1 elements

+2, group 2 elements

-3, group 15

-2, group 16

-1, group 17

Reaction Quotient

Q= [products]^coeff / [reactants]^coeff

used to predict the direction a rxn will proceed (gases and partial pressures)

If Q=K equilibrium

If Q>K increase reactants, and decrease products. reverse rate > forward rate

If Q<K increase products, and decrease reactants. forward>reverse

Average Kinetic Energy of molecule in fluid

KE=3/2 KT

Rault's law of nonvolatile solutes

Pv=XaPa

for volatile solutes

Pv=XaPa + XbPb

Boiling point elevation due to addition of a nonvolatile solute

change in temperature=Kb * molality * i

Freezing point depression for an ideally dilute solution

change in temperature=Kf * molality * i

Osmotic Pressure

= i * molarity * R *T

Lower brain

medulla, hypothalamus, thalamus, cerebellum

integrates subconscious activities

Higher brain (cortical)

cerebrum/cerebral cortex

cant function without lower brain

stores memories and processes throughts

The eye

converging lens => object outside focal distance is real and inverted

flattening the eye makes the lens less powerful (relaxing ciliary muscles)

making the lens less powerful moves the focal point away from the lens

The Ear

cochlea detects sound

semicircular canals detect orientation and movement of the head

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