Physics and Math Flashcards
Vectors
Physical quantities with both magnitude and direction
Ex: force, velocity
Scalars
Physical quantities that have magnitude, but no direction
Ex: mass, speed
Average velocity
‘v’ = Δx / Δt
Acceleration
The rate of change of and object’s velocity
a = Δv / Δt
Linear motion equations
v = vo + at
x = vo(t) + 1/2a(t^2)
v^2 = (vo)^2 + 2ax
‘v’ = (vo + v) / 2
x = ‘v’t = ( (vo + v) / 2)t
Vertical component of velocity
v = vsinθ
Horizontal component of velocity
v = vcosθ
Static friction
The force that must be overcome to set an object in motion
0 ≤ fs ≤ (µs)N
Kinetic friction
Opposes the motion of objects moving relative to each other
fk = (µk)N
Newton’s first law
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.
F = ma
N =
kg(m) / s^2
Work
For a constant force F, acting on an object that moves a displacement of d, the work is W = Fdcosθ
For a force perpendicular to the displacement, W = 0
Joule =
N(m)
Power
P = W / Δt
Kinetic energy
1/2mv^2
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 and opposite in direction
Fb = -Fa
Newton’s law of gravitation
All forms of matter experience an attractive force to other forms of matter in the universe
F = G(m1)(m2) / r^2
Mass vs weight
Mass: a scalar quantity that measures a body’s inertia
Weight (Fg): a vector quantity that measures a body’s gravitational attraction to the earth
Fg = mg
Uniform circular motion
ac = v^2 / r
Fc = mv^2 / r
Potential energy
U = mgh
Total mechanical energy
E = Pe + Ke
E = U + K
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 = ΔE
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
Linear expansion
The increase in length by most solids when heated
*When temperature increases, the length of a solid increases “a Lot”
ΔL = αLΔT
Volume expansion
ΔV = βVΔT
Conduction
The direct transfer of energy via molecular collisions
Convection
The transfer of heat by the physical motion of a fluid
Radiation
The transfer of energy by electromagnetic waves
Specific heat
Q = mcΔT
- Can only be used when the object does not change phase
Q > 0 means heat is gained, and vise versa
Heat of transformation
The quantity of heat required to change the phase of 1g of a substance
Q = mL
First law of thermodynamics
ΔU = Q - W
Adiabatic
(Q = 0)
ΔU = -W
Constant volume
(W = 0)
ΔU = Q
Isothermal
(ΔU = 0)
Q = W
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 either increase or remain unchanged
Density
(p) = m / V
Specific gravity
(p)substance / (p)water (no units)
(p)water = 10^3 kg / m^3
Weight
(p)gV
Pressure
P = F / A
- For static fluids of uniform density in a sealed vessel, pressure = (p)gz
- Absolute pressure in a fluid due to gravity somewhere below the surface is given by the equation P = Po + (p)gz
- Gauge pressure:
Pg = P - Patm
Continuity equation
A1v1 = A2v2
Bernoulli’s equation
P + 1/2(p)v^2 + (p)gh = constant
Archimedes’ principle
F(body) = (p)fluid (g) (Vsubmerged)
Buoyant force
Equal to the weight of the displaced fluid
- If the weight of the fluid displaced is less than the object’s weight, the object will sink
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
P = F1 / A1 = F2 / A2
A1d1 = A2d2, so
W = F1d1 = F2d2
Coulomb’s law
F = kq1q2 / r^2
Electric field
E = Fe / q = kQ / r^2
- A positive point charge will move the same direction as the electric field vector; a negative charge will move in the opposite direction
Electrical potential energy (U)
U = qΔV = qEd = kQq / r
Electric dipoles
p is the dipole moment
(p = qd)
Electrical potential
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
Potential difference (voltage)
ΔV = W / q = kQ / r
- When two oppositely charged parallel plates are separated by a distance d, an electric field is created, and a potnetial difference exists between the plates, given by: V = Ed
Current
The flow of electric charge
I = Q / Δt
- The direction of current is in the direction positive charge would flow, or from high to low potential
Ohm’s law
V = IR (can be applied to circuit or individual resistors)
Resistance
R = (p)L / A
- Resistance increases with increasing temperatures for most materials
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
Power dissipated by resistors
P = IV = V^2 / R = I^2(R)
Capacitors
Capacitance: the ability to store charge per unit voltage
C = Q / V
C’ = (k) ((ε0)(A) / d)
Series vs parallel C
Parallel = C + C
Series = 1/C + 1/C
Energy stored by capacitors
U = 1/2QV = 1/2CV^2 = 1/2 Q^2 / C
Wave formulas
f = 1 / T
v = f λ
Standing waves (strings)
λ = 2L / n
f = nv / 2L
λ = 2L, λ = L, λ = 2L/3
*The ends of the strings are always nodes; nodes occur where the displacement is zero
Open pipes
λ = 2L / n
f = nv / 2L
L = λ/2, L = λ, L = 3λ/2
*The open ends of the pipes are always antinodes (max amplitude
Closed pipes
λ = 4L/n (n = odd 1, 3, 5)
f = nv / 4L
L = λ/4, L = 3λ/4, L = 5λ/4
*The closed end of a pipe is always a node, and the open end is always an antinode
Sound
Propagates through deformable medium by the oscillation of particles parallel to the direction of the wave’s propagation
Intensity
I = P / A
Sound level
β = 10 log (I / I0)
Note: An increase of 10 dB is an increase in intensity by a factor of 10. An increase of 20 dB is an increase in intensity by a factor of 100
Doppler effect
When a source and a detector move relative to one another, the perceived frequency of the sound recieved differs from the actual frequency emitted
f’ = f (v +- vD) / (v +- Vs)
Vs source
Vs dectector
Refraction
n = c/v
c = 3.0 x 10^8 m/s
Snell’s law
n1sinθ1 = n2sinθ2
- When n2 > n1, light bends toward the normal; when n2 < n1, light bends away from the normal
Focal length
Mirrors:
(+) concave/converging
(-) convex/diverging
Lens:
(+) convex/converging
(-) concave/diverging
Object distance (o)
Mirrors:
(+) real object (in front of mirror)
(-) virtual object (behind)
Lens:
(+) real object (in front of lens)
(-) virtual object (behind)
Image distance (i)
Mirrors:
(+) real image (in front of mirror)
(-) virtual image (behind)
Lens:
(+) real image (behind lens)
(-) virtual image (in front of lens)
Magnification (m)
Mirrors:
(+) upright image
(-) inverted image
Lens:
(+) upright image
(-) inverted image
Converging systems
- o > 2f
Real, inverted, reduced - o = 2f
Real, inverted, same - 2f > o > f
Real, inverted, magnified - o = f
No image - o < f
Virtual, upright, magnified
Diverging systems
All o distances
Virtual, upright, reduced
(concave lens, convex mirro)
1/f = 1/o + 1/i
Magnification
m = -i/o
P = 1/f (D = m^-1)
Observer and detector moving closer:
+ sign in numerator
- sign in denominator
Observer and detector moving apart:
- sign in numerator
+ sign in denominator
Photoelectric effect
E = hf = hc/λ
K = hf - W
K is the maximum kinetic energy of an ejected electron; W is the minimum energy required to eject an electron, called the work function
Mass defect
Results from the conversion of matter to energy, embodied by:
E = mc^2 (this is the binding energy that holds nucleons within the nucleus)
Half-life
n = noe^-λt
Alpha decay
238/92 –> 234/90 + 4/2
Beta-minus decay
137/55 –> 137/56 + 0/-1 + ‘v’e
Beta-plus decay
22/11 –> 22/10 + 0/+1 + ve
Gamma decay
12/6 –> 12/6 + 0/0Y
Logarithmic identities
- log A x log B = log A + log B
- log A/B = log A = log B
- log A^B = Blog A
- log 1/A = -log A
Converting logs
log x = ln x / 2.303
log (n x 10^m) ~ m + 0.n
Scientific method
Determine whether sufficient background exists and whether the question is testable
FINER method
Feasible, interesting, novel, ethical, and relevant
Hill’s criteria
Help determine the strength of causal relationships; only temporality is necessary
Error sources
Small sample size, defects in precision and accuracy, bias, confounding variables
Ethics
- Beneficence: the requirement to do good
- Nonmaleficence: “do no harm”
- Autonomy: the right of individuals to make decisions for themselves
- Justice: the need to consider only morally relevant differences between patients and to distribute healthcare resources fairly
Probability
Mutually exclusive: two events that cannot occur together
Independent: the probability of either event is not affected by the occurrence of the other
Null hypothesis
A hypothesis of no difference; always the comparator
p-value
The probability that results were obtained by chance given that the null hypothesis is true
Confidence interval
A range of values believed to contain the true value with a given level of certainty
Generalizability
Statistical significance and causality do not make something generalizable or a good intervention. Clinical significance and the target population must also be considered
