Equations - Paper 1 explained

Question 1

What is the equation for the first harmonic of a wave and what do all symbols mean?

Answer 1

f₁ = (1/2L) * (T / u)^½

L - length of the string (m)

T - Tension in the string (N)

u - Mass per unit length of the string (kg/m)

Question 2

What is the formula for fringe spacing and what do the symbols mean?

Answer 2

w= λD/s

ONLY USE FOR DOUBLE SLIT

w - fringe spacing (m)

λ - wavelength of light (m)

D - distance between slits and the screen (m)

s - separation of slits (m) from centre to centre

Question 3

What is the diffraction grating equation and what do the symbols mean?

Answer 3

dsinθ = nλ

d - distance between slits (m) - use unit/number
θ - the angle between the central and nth maxima (°)
n - maxima order number
λ - wavelength of the diffracted source (m)

Question 4

What is the equation for phase difference between two points on a (progressive wave or stationary wave ask dan)?

Answer 4

φ = 2πd/λ = 360d/λ

φ - phase difference (degrees or radians)
d - horizontal distance between points (m)
λ - wavelength of the wave (m)

This isn’t on the formula sheet

Question 5

What is the equation for the wavelength of the nth harmonic?

Answer 5

λ_n = λ₁/n

λ₁ - wavelenth of the first harmonic (m)

This isn’t on the formula sheet

Question 6

What is the equation for the frequency of the nth harmonic?

Answer 6

f_n = f₁ * n

f₁ - frequency of the first harmonic (Hz)

This isn’t on the formula sheet

Question 7

What is the formula for the law of refraction?

Answer 7

n₁sinθ₁ = n₂sinθ₂

n - the refractive index of the medium
θ₁ - angle of incidence
θ₂ - angle of refraction

Question 8

What is the equation for the number of maximums that can seen from a diffraction grating?

Answer 8

n_max = d/λ
Make sure to round down
d - speration of slits from centre to centre (m)
λ - wavelength of the wave (m)

This isn’t on the formula sheet

Question 9

What is the formula for the work done on an object?

Answer 9

W = Fs
W - work done (J)
F - parallel component of force applied (N)
s - parallel component of displacement(m)

Question 10

What is the equation for power in terms of energy and time?

Answer 10

P = ΔE/Δt

P - power (W)
E - energy transfered (J)
t - time (s)

Question 11

What is the equation for power in terms of work done and time?

Answer 11

P = ΔW/Δt

P - power (W)
W - work done (J)
t - time (s)

Question 12

What is difference about the v in kinetic energy compared to other formulas?

Answer 12

v in 1/2mv² represents speed not velocity
Therefore, KE cannot be negative as it is a scalar just as speed is

Question 13

What is the equation for power in terms of force and velocity?

Answer 13

P = Fv
Make sure to use driving force not resultant force
P - power (W)
F - driving force (F)
v - velocity (ms^-1)

Question 14

What are the two formulas for the energy stored in a spring?

Answer 14

E = 1/2FΔL
ΔL - extension of the spring (m)
F - force applied to the spring (N)

E = 1/2kΔL²
This one isn’t on the formula sheet
k - spring constant n/m

Question 15

What is the formula for resistivity and what do the symbols mean?

Answer 15

p = RA / L

p - resistivity (Ωm)
R - resistance (Ω)
A - cross-sectional area of the wire (m²)
L - length of the wire (m)

Question 16

What is the equation for work function in quantum?

Answer 16

φ = hf₀

φ - work function (J)
H - Planck’s constant (Js)
f₀ - threshold frequency (Hz)

This isn’t on the formula sheet

Question 17

What is the equation for angular velocity in terms of θ and t?

Answer 17

ω = Δθ/Δt

ω - angular velocity (rads.s^-1)
Δθ - angle the object has turned through (radians)
Δt - the time objects been turning (s)

Question 18

What is the formula for the difference in frequency between energy levels?

Answer 18

E₁ - E₂ = hf
h - planck’s constant
f - frequency (Hz)
Can also sub in hc/λ if asked what wavelength of light will be emitted following a de-excitation between energy levels

Question 19

What is the equation relating maximum kinetic energy and stopping potential in quantum?

Answer 19

KE_max = ev_s

KE_max - maximum ke of emited electrons (J)
e - magnitude of the charge of an electron
v_s - stopping potential of a photoelectric circuit (V)

This isn’t on the formula sheet

Question 20

What is the formula relating emf and energy in a circuit and what do the symbols mean?

Answer 20

ϵ = E / Q

ϵ - emf of the battery (V)
E - energy in the circuit (J)
Q - charge in the circuit (C)
From the definition, emf is the energy given to each unit of charge

Question 21

What is the equation for angular velocity in terms of time period?

Answer 21

ω = 2π/Τ

ω - angular velocity (rads.s^-1)
Τ - time period (s)

This isn’t on the formula sheet

Question 22

What is the formula which links emf to V = IR?

Answer 22

ϵ = I(R + r)
r - internal resistance (Ω)

Total resistance is internal resistance + resistance in the circuit
Use for ‘imperfect’ circuits

Question 23

What is the equation relating linear velocity and angular velocity?

Answer 23

ω = v/r

ω - angular velocity (rads.s^-1)
r - radius of circular path (m)
v - linear velocity (ms^-1)

Question 24

What is the equation for the length of an arc of a circle?

Answer 24

s = rθ

s - arc length (m)
r - radius of the circle (m)
θ - angle of the arc (radians)

This isn’t on the formula sheet

Question 25

When do you use x = Acos(wt) and x = Asin(wt)?

Answer 25

Use Acos(wt) when displacement is the amplitude when t = 0 (cos graph starts at max)

Use Asin(wt) when displacement is 0 when t = 0 (sin graph starts at 0)

This one isn’t on the formula sheet

MUST BE IN RADIANS

Question 26

What is the equation relating max KE,PE and total energy in SHM?

Answer 26

KE_max = PE_max = E_total = 1/2 mω²A²

m - mass of object that’s oscillating (kg)
ω - angular velocity of oscillations (rads.s^-1)
A - amplitude of oscillations (m)
KE_max - maximum kinetic energy (J)
PE_max - maximum potential energy (J)
E_total - maximum energy (J)

This isn’t on the formula sheet

Question 27

What is the formula for the time period of a mass spring system and what do the symbols mean?

Answer 27

T = 2π (m/k)^1/2

m - mass on the spring
k - spring constant
T - time period

Question 28

What is the formula for the time period of a simple pendulum and what do the symbols mean?

Answer 28

T = 2π (l/g)^1/2

l - length of the pendulum (m)
g - gravitational field strength (ms^-2)
T - time period

Question 29

When can you use P = FV?

Answer 29

When there is no acceleration, and force and velocity and parallel