Book Three Flashcards
work, energy, power - deformation of solids - waves - superposition
what is work? + formula, SI unit
the product of a force of a body and its displacement in the direction of the force
work = force x displacement
Joule (equivalent to Nm)
what is the joule?
the work done when a force of 1 newton moves its point of application by one metre in its direction
what is efficiency? + formula, SI unit
the ratio of the useful work done by a machine or in a process to the total energy or heat taken in.
efficiency = useful energy output / useful energy input
what is energy? + formula, SI unit
the ability to do work
power x time
Joule
what is energy conversion?
change of energy from one form to another
principle of conservation of energy
it states that energy can neither be created nor destroyed , but can be transformed from one form to another
forms of energy
potential - energy due to position or condition
kinetic - energy due to motion
elastic/strain - energy due to stretching of a body
electrical - energy due to moving electric charge
sound - energy due to particles in a wave
wind - energy due to wind
light - energy due to electromagnetic waves
solar - energy from the sun
chemical - energy released during chemical reaction
nuclear - energy associated with particles in atomic nucleus
thermal - also known as heat energy
*chemical & electrical are high grade, everything else is low grade
what is potential energy? + formula, SI unit
this is energy due to position or condition
Ep = mgΔh
Joule
forms of potential energy
- gravitational potential energy (gpe) - energy due to position in the earths gravitational field
- elastic potential energy - energy stored in a body that has had its shape changed elastically
- electrical potential energy - energy due to attraction and repulsion of charges
what is kinetic energy? + formula, SI unit
this is energy due to motion
Ek = 1/2mv^2
Joule
what is gravitational potential energy? + formula, SI unit
energy due to position in the earths gravitational field
what is power? + formula, SI unit
this is the rate or energy transfer/ doing work
power = energy / time or work done / time
Watt
deformation of a solid + types
this is change in the shape of a solid when a force is applied on it
- tensile (when it stretches)
- compressive (when its squashed)
what does extension of a solid depend on?
- nature of the material
- size of the stretching force
- area of cross-section of the sample
- original length of the sample
what is stress? + formula, SI unit
this is force acting normally per unit area of cross-section of a material
stress = force / area
Pa
differences in pressure and stress
p. is the external force applied at a point
s. is the resistive force developed at a point
p. always acts normal to the surface
s. acts normal or parallel to the surface
p. at a point, is the same in all directions
s. at a point, isn’t the same in all directions
p. causes stress
s. doesn’t cause pressure
p. has measuring devices
s. has no measuring device
p. is a scalar quantity
s. is a tensor quantity
what is strain? + formula, SI unit
extension per unit length of a material
strain = extension / original length
its a ratio so it has no unit
what is hooke’s law? + formula
it states that extension of an elastic material is directly proportional to the stretching force applied to it given the elastic limit is not exceeded
F = kx
where k is spring constant
what is spring constant? + SI unit
is defined as force per unit extension of a material
Nm^-1
what is young modulus? + formula, SI unit
is stress divided by strain on a material
E = σ / ε
Pa
state the mechanical properties of materials
strength - a measure of applied force a material can withstand before breaking
stiffness - a measure of the opposition a material sets up to being distorted by having its shape/size changed
ductility - the ability of a material to be hammered, bent, pressed, rolled or drawn into shaped
toughness - on that is not brittle
*steel has all four properties
what is strain energy? + formula
energy stored up in a body due to its change of shape
1/2kx^2
what is a wave?
repeated vibration which transfers energy from one point to another without transferring matter
what is displacement, x ? + SI unit
the distance of a point on the wave from its rest position
metre
what is amplitude, a ? +SI unit
maximum displacement of a particle from its rest position
metre
what is wavelength, λ ? + SI unit
the distance between 2 adjacent crests or troughs
metre
what is frequency, f ? + SI unit
number of complete waves passing any point per second
unit - s^-1
SI unit - Hertz, Hz
*f = 1/T
what is wave speed, v ? + SI unit
the speed with which energy is transmitted by the wave
ms^-1
what is a wave front?
a line joining points at the same position along a wave
what is in phase?
when a crest is aligned with a crest
what is out of phase?
when a crest is aligned with a trough for example
what is phase difference, Φ ? + formula, SI unit
the amount by which one oscillation leads or lags behind another
Φ = x / λ x 360° or Φ = t / T x 360°
Φ = x / λ x 2π or Φ = t / T x 2π
degrees, ° or radians, rads
wave equation
speed = distance / time
v = f
what is intensity? + formula, SI unit
the amount of energy passing through unit area per unit time
I = P / A
watts per square metre , Wm^-2
what is the relationship between intensity, amplitude and frequency?
- intensity is directly proportional to the square of the amplitude of a wave
- intensity is directly proportional to the square of the frequency of a wave
- for a wave of amplitude a and frequency f, I ∝ a^2f^2
what is the intensity of spherical waves?
I = P / 4πr^2
where
- 4πr^2 is the surface area of the sphere
- P power of the source
I ∝ 1 / r^2
where
- r is the distance from the source
so
- I decreases with increase in r
what are transverse waves? +example
waves in which the particles vibrate perpendicular to the direction of energy transfer
- light
- radio
what are longitudinal waves? +example
waves in which the particles vibrate parallel to the direction of energy transfer
- sound
what is the doppler effect?
the apparent change in frequency of a wave when there is relative motion between a source and an observer
types of doppler effect {equations}
- source moving towards observer
λs = v / fs
λo = v - vs / fs
fo = v / λo
∴ fo = v / v - vs fs - when source is moving away from observer
λo = v + vs / fs
∴ fo = v / v ± vs fs
what is a red-shift?
looking for meaning
what are electromagnetic waves?
a disturbance in the electric and magnetic fields space
speed of light in a vacuum
c = 3.0 x 10^8 ms^-1
electromagnetic spectrum
- radio waves
- microwaves
- infrared
- visible
- ultraviolet
- x-rays
- gamma rays
[this is in order of ROYGBIV]
gamma to radio is increasing wavelength
radio to gamma is increasing frequency
similarities of electromagnetic waves
- travel at a speed of 3.0 x 10^8 ms^-1 in free space
- are transverse
- are progressive (they transmit energy)
what is polarisation?
this is when vibrations of a transverse wave are restricted to a single plane it doesn’t occur to longitudinal waves
how can we polarise light?
by using a polaroid filter
what is malus’ law?
states that the intensity of plane polarised light that passes through an analyser varies as the square of the cosine of the angle between the plane of the polariser and the transmission axis of the analyser
I = Io cos^2x
what is superposition?
occurs when 2 or more waves of the same type meet
principle of superposition
states that when 2 or more waves meet at a point, the resultant displacement is the algebraic sum of the displacements of the individual waves at the point
constructive + in phase wave?
destructive + out of phase wave?
- amplitude double
- amplitude zero
what is a stationary wave?
when 2 waves, which have the same speed, frequency and approx. the same amplitude, but travelling in opposite directions meet
what is a node?
points on a stationary wave where particle displacement is zero
what is an antinode?
points on a stationary wave where particle displacement is maximum. marks the amplitude of a stationary wave
fundamental frequency for
first harmonic
second harmonic (first overtone)
third harmonic (second overtone)
- fo = v / 2L
- f1 = 2fo
- f2 = 3fo
nth harmonic for (n-1)th overtone
fn = n v / 2L
formula for stationary waves in a closed pipe
- first harmonic
- third harmonic ( 1st overtone)
- fifth harmonic ( 2nd overtone)
- gen. formula
first harmonic - fo = v / 4L
third harmonic (1st overtone) - f1 = 3Fo
fifth harmonic (2nd overtone) - f2 = 5fo
general formula is,
fn = (2n - 1) v/4L
formula for stationary waves in an open pipe
- 2nd harmonic (1st overtone)
- 3rd harmonic (2nd overtone)
- gen. formula
first harmonic - fo = v / 2L
2nd harmonic (1st overtone) - f1 = 2fo
3rd harmonic (2nd overtone) - f2 = 3fo
general formula is,
fn = n v / 2L
comparison of progressive and stationary waves
p -crests and troughs move along the string
s - nodes and antinodes do not move along the string
p - all points have the same amplitude
s - amplitude of vibration varies with position along the string. its zero at a node, maximum at antinode
p - phase varies continuously along the wave
s - between adjacent nodes, all points of stationary wave vibrate in phase
formula for end correction, c
fo = v/4 (L+c) [closed pipe]
fo = v/2 (L+2c) [open pipe]
what is diffraction? +formulas
the spreading of a wave as it passes past an obstacle or gap
λ = a sinx
sinx = λ / a
sinx = nλ / a
conditions for interference of light
- the sources must be very close together
- the screen / eyepiece must be as far away from the source as possible
- must meet and cross
interference of light
occurs when similar waves from 2 coherent sources cross
what is coherent?
sources produce waves having the same frequency
what is monochromatic?
light of a single frequency
where does superposition occur during a double slit?
where the beams overlap
nb:
look at fringes and their conditions
what is a diffraction grating?
a number or fine, equidistant closely spaced parallel lines of equal widths ruled on glass or polished metal by a diamond point
types of diffraction grating
transmission - glass is used with ruled lines scattering incident light and are more or less opaque, spaces in between them transmit light and act as slits
reflection - lines are ruled on a polished metal and are opaque, while spaces in between them reflect light regularly and act as slits
diffraction of light by diffraction grating formula
dsinx = nλ
