MCAT Physics
x = vt =
((v(o) + v)/2)*t
adiabatic (Q = 0)
(delta)U = -W
constant volume (w = 0)
(delta)U = Q
first law of thermodynamics
(delta)U = Q - W
weight =
(ro)gV
second law of thermo
In any thermodynamic process that moves from one state of equilibrium to another, the entropy of the system and environment together will either increase or remain unchanged.
bernoulli's equation
P + 1/2ρv2 + ρgh = constant
power dissipated by resistors
P = IV = V^2/R= I^2R
Intensity =
P/A (SI units: W/m^2)
gauge pressure
Pg = P - Patm
Absolute pressure in a fluid due to gravity somewhere below the surface is given by the equation P =
Po + ρgz
isothermal (delta)U = 0
Q = W
work-energy theorem
Relates the work performed by all forces acting on a body in a particular time interval to the change in energy at that time: W = (delta)E
energy stored by capacitors
U = 1/2QV = 1/2CV^2 = 1/2Q^2/C
When two oppositely charged parallel plates are separated by a distance d, an electric field is created, and a potential difference exists between the plates, given by:
V = Ed
ohm's law of resistance
V = IR (can be applied to entire circuit or individual resistors)
potential difference (Voltage)
Voltage (delta(V)) = W/q = kQ/r (si units: volt = J/C)
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 (N) = kg*m/s^2
system work
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.
conservation of energy
When there are no nonconservative forces (such as friction) acting on a system, the total mechanical energy remains constant: ΔE = ΔK + ΔU = 0
uniform circular motion
a = v^2/r F(c) = mv^2/r
pressure
a scalar quantity defined as force per unit area: P = F/A [SI units: pascal =N/m2 ]
mass (m)
a scalar quantity that measures a body's inertia
weight (F(g))
a vector quantity that measures a body's gravitational attraction to the earth F(g) = mg
The electrical potential energy of a charge q at a point in space is the
amount of work required to move it from infinity to that point. U = qΔV = qEd = kQq/r[SI units: J]
increase of 10 kB is
an increase in intensity by a factor of 10. inc of 20 dB is inc in intensity by factor of 100
for open pipes, open ends of pipes are always
antinodes (max amplitude)
Sound propagates through a
deformable medium by the oscillation of particles parallel to the direction of the wave's propagation
The direction of current is the
direction positive charge would flow, or from high to low potential
A positive point charge will move in the same direction as the
electric field vector; a negative charge will move in the opposite direction
The amount of work required to move a positive test charge q from infinity to a particular point divided by the test charge: V = U/q [SI units: volt = J/C]
electric potential
wave formulas
f = 1/T v = f*(lambda)
If the weight of the fluid displaced is greater than or equal to the object's weight, then it will
float.
static friction (fs)
force that must be overcome to set an object in motion O <= fs <= u(s)*N
denstiy (p) =
m/v (kg/m^3)
refraction
n = c/v (speed of light = 3 * 10^8 m/s)
snell's law
n1sinθ1 = n2 sin θ2. When n2 > n1, light bends toward the normal; when n2 < n1, light bends away from the normal. -calculates the angle at which our light will be refracted as it changes mediums
for closed pipes, closed end of the pipe is always a
node, and the open end is always an antinode
ends of the strings are always
nodes. Nodes occur where the displacement is zero.
kinetic friction f(k)
opposes the motion of objects moving relative to each other f(k) = u(k)*N
resistance
opposition to the flow of charge. R =(ro)L/A (Resistance increases with increasing temperatures with most conductors.) [SI Units: ohm (Ω)]
electric dipoles
p is the dipole moment p = qd
specific gravity
p(substance)/p(water) p(water) = 10^3 kg/m^3
F(gravity) > F(drag)
person accelerates downward
scalars
physical quantities that have magnitude, but no direction ex: mass, speed
vectors
physical quantities with both magnitude and direction ex: force, velocity
specific heat
q = mc(delta)T 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
energy
scalar quantity (joules)
If the weight of the fluid displaced is less than the object's weight, the object will
sink
F(g) = F(drag)
terminal velocity is reached (person travels at constant velocity)
capacitance
the ability to store charge per unit voltage. It is given by: C = Q/V C' = κ^(epsilon)*o^A/d
displacement
the change in position that goes in a straight-line path from the initial position to the final position; independent of the path taken (SI unit: m)
conduction
the direct transfer of energy via molecular collisions
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 is expressed as: U = mgh -conservative force that results in being able to store that energy -ex: gravitational p.e. and elastic p.e., and electric p.e. -the stored energy can be released later
kinetic energy
the energy associated with moving objects. It is given by: K = 1/2mv^2
current
the flow of electric charge. (positive charge) Current is given by: I = Q/(delta)t units: ampere = C/s
linear expansion
the increase in length by most solids when heated Mnemonic: when temperature increases, the length of a solid increases "a Lot"(αLΔT) (delta)L = alpha*L*(delta)T
volume expansion
the increase in volume of fluids when heated (delta)V = beta*V*(delta)T
When a source and a detector move relative to one another,
the perceived frequency of the sound received differs from the actual frequency emitted even though the source velocity and frequency is unchanged. f ′ = f(v +- v(d))/(v +- v(s))
Heat of transformation:
the quantity of heat required to change the phase of 1 g of a substance. Q = mL (phase changes are isothermal processes)
power
the rate at which work is performed; it is given by: P = W/(delta)t (SI unit: watt = J/S)
acceleration
the rate of change of an object's velocity; it is a vector quantity: a = (delta)v/(delta)t in m/s^2
buoyant force is equal to
the weight of the displaced fluid.
The dipole feels no net translational force, but experiences a
torque about the center causing it to rotate so that the dipole moment aligns with the electric field.
radiation
transfer of energy by electromagnetic waves
convection
transfer of heat by physical motion of a fluid
stationary detector
v(d) = 0
v =
v(o) + at; also = (v(o) + v)/2
v^2
v(o)^2 + 2ax
x =
v(o)t + 1/2a*t^2
stationary source
v(s) = 0
projectile motion
vertical component of velocity = v*sin(theta) horizontal component of velocity = v*cos(theta)
open pipes
λ = 2L/n (n = 1, 2, 3...) ƒ = nv/2L (n = 1, 2, 3...)
strings
λ = 2L/n (n = 1, 2, 3...) ƒ = nv/2L (n = 1, 2, 3...)
closed pipes
λ =4L/n (n = 1, 3, 5...) ƒ = nv/4L (n = 1, 3, 5...)
For static fluids of uniform density in a sealed vessel, pressure: P =
ρgz
avg velocity
= (delta)x/(delta)t in m/s
sound level (beta)
= 10log(I/I(o)) (unit: decibel = dB)
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.
pascal's principle
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. F1/A1 = F2/A2
continuity equation
A1v1 = A2v2
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
First condition of equilibrium:
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 ƩF = 0.
kirchhoff's laws
At any junction within a circuit, the sum of current flowing into that point must equal the sum of current leaving. The sum of voltage sources equals the sum of voltage drops around a closed-circuit loop.
electric field
E = F(e)/q = Q/r^2 (N/C or V/M)
total mechanical energy
E = U+K Mechanical energy is conserved when the sum of kinetic and potential energies remains constant
coulomb's law
F = kq1q2/r^2 (newtons)
archimedes' principle
F(buoy) = ρfluid*gVsubmerged
F = 0 must be true for equilibrium; therefore
F(x) = 0 and F(y) = 0
work
For a constant force F acting on an object that moves a displacement of d, the work is W = Fd cos θ. (For a force perpendicular to the displacement, W = 0.) d = displacement N*m multiplying two vectors by cosine of an angle yields a dot product...which yields a scalar
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 F(b) = -F(a)
