Module 2 Flashcards
Definition of density?
mass per unit volume
Units of density?
kg m^-3
Hookes Law?
Extension is proportional to the force applied, up to the limit of proportionality
What are the features of graph force against extension confirming Hooke’s Law?
There is a straight line through the origin of the graph.
Units of spring constant?
Nm^-1
Rules of springs in series
- Both springs experience the dame Force (F)
- The total extension (of both springs together) is the sum of the extension of each spring individually.
Rules of (identical) springs in parallel
- The Force (F) applied to the spring combination is shared across each of the springs individually (if there are two identical springs, each spring experiences a force of 1/2F).
- All the springs have the same extension (and equals the extension for the spring combination.
Definition of Elastic Limit?
The maximum amount a material can be stretched by a force and still return to its original length when the force is removed.
Definition of Limit of Proportionality
Point beyond which force is no longer proportional to extension
Definition of elastic behaviour?
Material will return to its original length (when force removed) with no permanent extension.
Definition of plastic behaviour?
Material will be permanently extended (when force is removed)
What does area under a force/extension graph show you?
- Area under a graph of force against extension is work done on spring and hence the energy stored, as it is loaded.
OR - Area under a graph of force against extension is the work done by the spring, and hence energy released, as it is unloaded.
What does the area between the loading and unloading curves of an elastic band?
Internal energy retained, e.g. as heat, within the elastic band.
Explain the derivation of energy stored = ½ FL?
- Energy stored in a stretched spring = work done stretching spring
- Work done = Force x distance (moved in the direction of the force)
- As spring is stretched, the force gets bigger (and so isn’t constant)
- Force is proportional to extension, so, the average force = F/2 which = 1/2F
- The work done = average force x distance moved
- energy stored = work done = ½ FL
- This is the area under the graph of Force against Extension (1/2base x height)
Explain the Derivation of energy stored = ½ FL from a graph of force against extesion
- W=Fs, so the area beneath the line from origin to L represents the work done to compress/extended spring.
- Work done (on spring) equals the energy it stores.
- Area under graph = area of triangle = 1/2base x height, therefore energy stored = ½ F x L.
What is the definition of tensile stress?
Tensile (stretching) force divided by its cross-sectional area
What are the units of stress?
Pa or Nm^-2
What is the definition of tensile strain?
It’s the extension of material divided by its original length
What are the units of strain?
None
What is the definition of breaking stress?
Stress needed to break a solid material.
What is the description of stiffness?
Requires a large force (or stress) for a small deformation (or extension)
What is the description of fracture?
- Non-brittle fracture: Material necks which reduces the cross-sectional area so increases stress at that point until the wire breaks.
- Brittle fracture
No plastic deformation, usually snaps suddenly without any noticeable yield.
What is the description of brittle?
A material that fractures without any plastic deformation.
What is the description of ductile?
When a material can be draw into a wire (exhibits a lot of plastic deformation)
Description of strength (or weakness)?
Material with a higher (or lower) breaking stress.
What is the definition of the Young Modulus?
It’s the ratio of tensile stress to tensile strain.
What is the unit of the Young Modulus?
Pa or Nm^-2
What is the use of stress/strain curves to find young modulus?
From a graph of stress against strain, Young Modulus is the gradient of the linear section of the graph (the region where the stress and strain are directly proportional).
What does the area under the graph of stress against strain show?
The energy stored per unit volume.
Explain one simple method of measuring Young Modulus
- Measurements to make
+ Original length of wire,L, with a ruler
+ Diameter of wire with a micrometer
+ Mass attached to end of wire
+ Length of stretched wire with a ruler - Reducing Uncertainty in each measurement
+ Repeat measurements of length
+ Repeat measurements of diameter of wire at different points
+ Check for zero error on electronic scales
+ Check for zero error on micrometer - How measurements are used to determine Young Modulus
+ F=weight=mg
+ Extension L = stretched length - original length
+ Cross sectional area of wire A = d2 / 4
+ Stress = F/A; Strain = L/L
+ Plot a graph of stress (y-axis) against strain (x-axis)
+ Young Modulus is gradient of linear section of the graph
What is the difference between a scalar and a vector?
Vector has magnitude and direction, whereas scalar only has magnitude.
What are some examples of scalar quantities?
- Speed
- Mass
- Time
- Energy
- Power
What are some examples of vector quantities?
- Displacement
- Velocity
- Acceleration
- Force
- Weight
How do you add perpendicular vectors by calculation?
- You draw the vectors a a right angled triangle.
- Then use the pythagoras theorem to find the magnitude of resultant vector
- Use trigonometry to calculate the angle of resultant vector.
How to add vectors by scale drawing?
- Write down scale eg 1cm=2N
- Draw the vectors to correct length and angle to each other “tip to tail”
- The add the resultant vector line
- Measure the length and angle of resultant vector
- Convert length into appropriate quantity to find magnitude of resultant vector.
`What are the conditions for equilibrium of two or three coplanar forces acting at a point?
- Total resultant equals zero
OR - If the vectors representing the forces are added together they will form a closed triangle.
What are the two conditions for a body to remain in equilibrium?
- Resultant force acting on body is zero
2. Resultant moment about any point is zero.
What is the definition of a moment?
Force multiplied by the perpendicular distance between the line of action of the force and the pivot.
What are the units of a moment?
Nm
What is the principle of a moment?
In equilibrium, the sum of the clockwise moments about a point equals the sum of the anticlockwise moments.
What is the definition of moment of a couple?
(one) force multiplies by the perpendicular distance between the lines of actions of the two forces.
What is the definition of centre of mass?
- The point in a body through which weight appears to act
OR - The point in a body where the resultant moment is zero.
What is a stable equilibrium?
When a body is displaced then released, it will return to its equilibrium position.
What is an unstable equilibrium?
When a body is displaced then released it will not return to its equilibrium position.
What is displacement defined as?
The distance in a given direction.
What is velocity defined as?
- The rate of change of displacement
OR - The change in displacement divided by the time taken
What is acceleration defined as?
- The rate of change of velocity
OR - The change in velocity divided by time taken
What does the gradient of displacement and velocity time graphs mean?
- Gradient of a displacement time graph = velocity
- Gradient of a velocity time graph = acceleration
What does the area under velocity and acceleration time graphs mean?
- Area under a velocity time graph = displacement
- Area under an acceleration time graph = velocity
What is the average velocity?
It is the total displacement divided by total time
What is the instantaneous velocity at a point?
- It is the rate of change of displacement at that point
- Gradient at a point on a displacement time graph.
What are the conditions for an object falling at terminal velocity?
- Resultant force on object is zero
- Acceleration is zero
- Object travels at a constant velocity
What are the factors affecting drag force on an object?
- The shape of the object
- It’s speed
- The viscosity of the fluid/gas
Explain why an object reaches terminal velocity falling through air?
- Initially only force acting is weight, so object accelerates at g.
- Drag force increases with increasing speed
- Therefore resultant force decreases
- Eventually drag force = weight, forces are balanced
- So resultant force is zero
- As F=ma, acceleration is zero so object falls at constant speed.
What is the horizontal and vertical motion of a projectile in absence of resistive forces?
- Horizontal motion: no force horizontally, no acceleration so constant velocity.
- Vertical motion: constant force due to weight, constant acceleration (equal to g)
What are Newton’s 3 laws of motion?
- 1st law: An object will continue at rest or uniform velocity unless acted on by a resultant force.
- 2nd law: The acceleration of an object id proportional to resultant force acting on it, i.e. F=ma (providing mass is constant)
- 3rd law: If object A exerts a force on a second object B, then object B will exert an equal and opposite force on object A.
What is the principle of conservation of energy?
Energy is neither created or destroyed, only converted from one form to another.
What are the energy conversions of an object falling in presence of resistive forces?
loss in g.p.e =gain in k.e. + work done against resistance work done typically appears as heat.
What is the definition of work done?
It means the force multiplied by distance moved in the direction of the force.
What is the unit of work done?
J
What is the definition of power?
- The rate at which energy is transferred
OR - Energy transferred (work done) divided by time taken
What are the units of power?
W (watts) or Js^-1
What is a longitudinal wave?
When a particle vibration is parallel to the direction of the wave propagation.
What are some example of a longitudinal wave?
Sound waves, seismic p-waves.
What is a transverse wave?
When a particle vibration is perpendicular to the direction of wave propagation.
What is particle displacement?
The distance of a particle from its equilibrium position in given direction
What is the definition of amplitude?
It is the maximum displacement of a particle (wave) from its equilibrium (or rest) position
What is the definition of frequency?
It is the number of oscillations (of a particle) per second
What is the definition of a time period?
The time for one complete oscillation
What is the definition of a wave length?
It is the shortest distance between two points in phase.
What is the definition of diffraction?
It is the the spreading out of a wave (when it passes through a gap or past the edge of an object)
What is the definition of refraction?
It is when the wave bends/changes direction when its speed changes
What is the definition of polarisation?
(transverse) wave oscillation is in one plane
Explain the application of polarisation in sunglasses?
- Light reflected from surfaces is (weakly) polarised in one plane (horizontal)
- Polaroid in sunglasses can be orientated to remove this reflected light
- Reducing glare
Explain the application of polarisation in tv transmitters and aerials?
- Signals from tv transmitter (radio waves) are polarised
- Aerials need to be orientated (rotated) so they are in the same plane as the transmitted signal
- For maximum signal strength
What is superposition?
Where two or more waves meet, the resultant displacement equals the vector sum of the individual displacements
What are the conditions for formation of stationary waves?
- Two waves travelling past each other in opposite directions
- With the same wavelength (frequency)
- Similar amplitude
What are nodes and anti-nodes?
Nodes- points of no oscillation/ zero amplitude
Anti-nodes - points of maximum amplitude.
What are coherent sources?
Waves (from two sources) that have:
- a constant phase difference
- same wavelength (or frequency)
What does monochromatic?
Single wavelength
What are the rules of safety with a laser?
- Avoid looking along the beam of a laser
- Wear laser safety goggles
- Avoid reflections
- Put up a warning sign that a laser is in use.
What are the properties of laser light?
- Monochromatic - only a single wavelength
- Coherent - waves have a constant phase difference
- Collimated - produces an approximately parallel beam.
Explain the formation of fringes with Young’s slits?
- Interference fringes formed
- Where light from two slits overlaps
- The light from the two slit is coherent
- Bright fringes formed where constructive interference
- Because light from the two slits is in phase (path difference equals a whole number of wavelengths)
- Dark fringed formed where destructive interference
- Because light from the two slits in anti-phase (path difference equals a whole number +0.5 wavelengths)
Explain the appearance of white light through Young’s slits?
- Central fringe would be white
- Side fringes are (continuous) spectra
- Bright fringe would be blue on the side nearest the central fringe
- Bright fringes merge further away from the centre
Explain the appearance of diffraction pattern from a single slit?
- Central bright fringe has twice width of other bright fringes
- The other bright fringes have a much lower intensity
- and are equally spaced
What are the applications of gratings to spectral analysis of light from stars?
- Dark lines in spectrum from a star (absorption spectrum)
- Reveal the composition of (elements present in) the star’s atmosphere
How does light change moving from air to glass?
- speed - decreases
- wavelength - decreases
- frequency - remains constant
What are the conditions for total intolerant reflection?
- Angle of incidence is greater than the critical angle
- The refractive index of the material light is going from is greater than the refractive index of the material the light is going to.
What is total internal reflection?
Where all the light is reflected back into the material
What is the critical angle?
Angle of incidence which produces an angle of refraction of 90 degrees.
What is the structure of an optical fibre?
- Central core, surrounded by cladding.
- Refractive index of core must be greater than the refractive index of cladding (to ensure total internal reflection)
What is the purpose of cladding?
- prevents crossover of signal/data to other fibres
- prevents scratching of the core
- reduces pulse broadening/dispersion
What are the uses of optical fibres?
- Communication - improve transmission of data/high speed internet
- Endoscopes - improved medical diagnosis
How do pulses of light change travelling down optical fibres?
- reduced amplitude due to absorption/energy loss and scattering within fibre
- pulse broadening due to multipath dispersion from rays taking different paths and different times to travel down same fibre
How is multipath dispersion reduced?
Core of fibre is made very narrow/thin
