Essential Formulae Flashcards
force (using acceleration)
F = m*a F = force (N) m = mass (kg) a = acceleration (m s-2)
Young’s modulus (using force and extension)
E = (F*L)/(A*x) E = Young's modulus (N m-2) F = force (N) L = original length (m) A = area (m2) x = extension (m)
potential difference (using current and resistance)
V = IR V = potential difference (V) I = current (A) R = resistance (Ω)
wavelength (using diffraction grating)
n*λ = d*sin(𝜃) n = order of the maximum (no unit) λ = wavelength (m) d = slit separation (m) 𝜃 = angle between normal to the grating and the beam of light (°)
force (using acceleration due to gravity)
F = m*g F = force (N) m = mass (kg) g = acceleration due to gravity (9.81 m s-2)
thinking distance
thinking distance (m) = reaction time (s) * velocity of the car (m s-1)
relationship between braking distance and velocity
braking distance ∝ (velocity)^2
stopping distance
stopping distance = thinking distance + braking distance
thermal energy
E = m*c*ΔT E = thermal energy (J) m = mass (kg) c = specific heat capacity (J kg °C-1) ΔT = change in temperature (K or °C)
nuclear energy
E = m*c^2 E = nuclear energy (J) m = mass (kg) c = speed of light in a vacuum (3.00 * 10^8 m s-1)
weight (using acceleration due to gravity)
w = m*g w = weight (N) m = mass (kg) g = acceleration due to gravity (m s-2)
gravitational potential energy
GPE = m*g*Δh m = mass (kg) g = acceleration due to gravity (m s-2) Δh = change in height (m)
relationship between gravitational potential energy and kinetic energy
kinetic energy (J) ↓ , gravitational potential energy (J) ↑ kinetic energy (J) ↑ , gravitational potential energy (J) ↓
relationship between intensity and amplitude
intensity (W m-2) ∝ (amplitude (m))^2
energy (using power)
E = P*t E = energy (J) P = power (W) t = time (s)
impulse
I = F*Δt I = impulse (N s) F = force (N) Δt = change in time (s)
power (using force and distance)
P = (F*d)/t P = power (W) F = force (N) d = distance (m) t = time (s)
work done (using force and distance)
W = F*d W = work done (J) F = force (N) d = distance (m) this is the same as W = F*d*cos(θ) but θ is 0° so cos(θ) = 1
work done (using acceleration due to gravity)
W = m*g*h W = work done (J) m = mass (kg) g = acceleration due to gravity (9.81 m s-1) h = height (m)
e.m.f (using energy transferred)
e.m.f (V) = energy transferred (J) / charge (C)
energy (using work done)
energy (J) = work done (J)
potential difference (using work done)
V = W/Q V = potential difference (V) W = work done (J) Q = charge (C)
relationship between resistivity and temperature
ρT = ρ0[1 + ∝(T - T0)] ρT = resistivity of material at temperature T (Ω m) ρ0 = resistivity of material at temperature T0 ∝ = the temperature coefficient T = temperature of the material (K or °C) T0 = reference temperature at which the resistivity of the material is quoted (K or °C)
percentage uncertainty from absolute uncertainty
percentage uncertainty = (absolute uncertainty / measured value)*100%
y = a*b
% uncertainty of y from % uncertainties of a and b
% uncertainty of y = % uncertainty of a + % uncertainty of b
y = a/b
% uncertainty of y from % uncertainties of a and b
% uncertainty of y = % uncertainty of a + % uncertainty of b
y = a^n
% uncertainty of y from % uncertainty of a
% uncertainty of y = % uncertainty of a * n
percentage uncertainty from a gradient
percentage uncertainty = (absolute uncertainty / gradient of line of best fit)*100%
percentage uncertainty from a y-intercept
percentage uncertainty = (absolute uncertainty / ‘best’ y-intercept)*100%
absolute uncertainty form gradients
absolute uncertainty = gradient of best fit line - gradient of worst fit line
absolute uncertainty form y-intercepts
absolute uncertainty = best y-intercept - worst y-intercept
average speed
average speed (m s-1) = distance (m) / time (s)
average velocity
average velocity (m s-1) = total displacement (m) / time (s)
acceleration (using change in velocity)
acceleration (m s-2) = change in velocity (m s-1) / time (s)
1 kilowatt-hour
1 kilowatt-hour = 1000 watts * 3600 seconds
1 kilowatt-hour = 3600 000 Joules
cost of energy
cost = number of kilowatt-hours * cost per kilowatt-hour
distance between nodes in a stationary wave
λ/2
λ = wavelength (m)
distance between anti-nodes in a stationary wave
λ/2
λ = wavelength (m)
distance between nodes and anti-nodes in a stationary wave
λ/4
λ = wavelength (m)
Kirchhoff’s first law
ΣIin = ΣIout
sum of currents entering a junction (A) = sum of currents exiting a junction (A)
Kirchhoff’s second law
Σε = ΣI*R
sum of the e.m.f (V) = sum of the products of current and resistance of each component in series (V)
maximum kinetic energy of electrons emitted as a result of the photoelectric effect
maximum kinetic energy (J) = charge of an electron (1.602 * 10^-19 C) * stopping potential (V)
Snell’s law
n1 * sin(θ1) = n2 * sin(θ2)
n1 = refractive index of material 1 (no units)
θ1 = angle between normal to material 1 and the beam of light in material 1 (°)
n2 = refractive index of material 2 (no units)
θ2 = angle between normal to material 2 and the beam of light in material 2 (°)
critical angle between two materials
sin(C) = n1/n2 C = critical angle (°) n1 = refractive index of material 1 (no units) n2 = refractive index of material 2 (no units)
Kinetic energy (using velocity)
KE = 1/2*m*v^2 KE = kinetic energy (J) m = mass (kg) v = velocity (m s-1)
Drag
Fd = 1/2*ρ*Cd*A*v Fd = drag (N) ρ = fluid density (kg m-3) Cd = coefficient of drag (no units) A = cross-sectional area of the moving object (m2) v = velocity of the moving object (m s-1)
force (using acceleration)
F = m*a F = force (N) m = mass (kg) g = acceleration (m s-2)
