models Flashcards
equation for number of undecayed nuclei remaining (N)? (N0, λ, t)
N = N0(e^-λt)
where N0 = initial number of undecayed nuclei, λ = decay constant, t = time
equation for number of nuclei in sample (n)?
here n = number of nuclei present, in ideal gases n = number of moles and N = number of particles (kind of like number of nuclei)
n = (mass/molar mass) x avogadro’s constant
equation for activity of radioactive sample (A)? (λ, N)
A = λN
(dN/dt = -λN, whereas activity = rate of decay of radioactive sample (so A is +))
equation for activity of sample at certain point in time (A)? (A0, λ, t)
A = A0(e^-λt)
A0 = initial activity, λ = decay constant, t = time
equation for half-life (t 1/2)? (λ)
t 1/2 = ln(2)/λ
equation for capacitance (C)? (Q, V)
C = Q/V
equation for total work done in charging capacitor (E or W)? (Q, V)
E = 0.5QV
where Q = total charge and V = voltage (energy per unit charge)
equation for total work done in charging capacitor (E or W)? (C, V)
E = 0.5CV^2
equation for total work done in charging capacitor (E or W)? (Q, C)
E = (Q^2)/2C
equation for charge remaining on a discharging capacitor (Q)? (Q0, t, R, C)
Q = Q0(e^-t/RC)
equation for current remaining on a discharging/currently on charging capacitor (I)? (I0, t, R, C)
I = I0(e^-t/RC)
equation for pd remaining on a discharging capacitor (V)? (V0, t, R, C)
V = V0(e^-t/RC)
equation for charge on a charging capacitor (Q)? (Q0, t, R, C)
Q = Q0(1 - e^-t/RC)
equation for pd (V) on a charging capacitor? (V0, t, R, C)
V = V0(1 - e^-t/RC)
equation for restoring force (F) acting during SHM? (x)
F = -kx
where k = spring constant (when spring is oscillating, it might be smth else sometimes), x = displacement from quilibrium
(also minus bc restoring force acts in opposite direction to displacement)
equation for acceleration (a) of pendulum during SHM?
a = (-k/m)x
equation for angular frequency (ω)? (T)
ω = 2π/T
where T = time period (time taken for one complete oscillation)
(for ω, treat 1 oscillation as whole circle of 2π radians)
equation for angular frequency (ω)? (f)
ω = 2πf
equation for displacement (x) in SHM (when starting from the side)? (ω, A, f, t)
x = Acos(ωt)
or
x = Acos(2πft)
equation for displacement (x) in SHM (when starting from the midpoint)? (ω, A, f, t)
x = Asin(ωt)
or
x = Asin(2πft)
equation for velocity (v) in SHM (when starting from side)? (ω, A, f, t)
v = -ωAsin(ωt)
equation for velocity (v) in SHM (when starting from midpoint)? (ω, A, f, t)
v = ωAcos(ωt)
equation for v max (when starting from side)? (ω, A)
v max = ωA
what is the equation for acceleration (a) in SHM (when starting from the side)? (ω, A, t)
a = -(ω^2)Acos(ωt)
what is the equation for acceleration (a) in SHM (when starting from the midpoint)? (ω, A, t)
a = -(ω^2)Asin(ωt)
equation for a (a) in SHM (when starting from the side)? (ω, x)
a = -(ω^2)x
where ω = angular frequency and x = displacement
equation for maximum kinetic energy (KE max) for SHM pendulum? (m, ω, A)
KE max = 0.5m(ω^2)(A^2)
OR
KE max = 0.5k(A^2)
maximum elastic potential energy (EPE max) for SHM? (x, A)
EPE max = 0.5k(x max^2)
OR
EPE max = 0.5k(A^2)
equation for time period (T) of mass-spring system in SHM? (m, k)
T = 2π√(m/k)
where m = mass and k = spring constant of spring
equation for time period (T) of oscillation of pendulum in SHM? (L, g)
T = 2π√(L/g)
where L = length of string and g = g
equation to show decrease of SHM displacement due to damping is exponential? (ratios basically)
x1:x2 = x2:x3 = x3:x4
(ratios of decreasing displacements must all be same if exponential)
equation for number of nuclei remaining (N) after certain number of half lives? (N0, no. of half lives passed)
N = N0 x (0.5)^no. of half lives passed
equation for mass of radioactive sample after time t?
m = m0(e^-λt)
equation for count rate of radioactive sample after time t has passed?
C = C0(e^-λt)
