Physics
Energy, Work and Power
Work
Work is done when energy is used as a force to move an object through a distance
Work done against friction
Thermal energy lost due to friction
Work against friction = Frictional F x d
Energy
Forms of Energy
Kinetic energy
Energy possessed by object in motion
Gravitational potential energy
Energy possessed by object due to relative position from the ground
GPE = mgh
Legend (E,W,P):
GPE: Gravitational Potential Energy
KE: Kinetic Energy
W: Work done
v: Velocity
h: Height above ground
d: distance
t: time
Total amount of energy in a closed system is always constant
Mechanical energy
Mechanical energy = KE+GPE
Total mechanical energy of an object is constant (ignoring friction)
Efficiency of a machine is the percentage of its input energy that becomes useful output energy
Power
The rate of work done
P=E/t or P=W/t
KE = ½mv²
SI unit is joules (J)
Also rate of energy change
Pressure
In liquids
W=Fd
In solids
P=F/A
Also written as P=W/A, as weight is a force
Caused by the weight of liquid above
- Pressure increases with depth
- Pressure is not reliant on the container
Pressure exerted by liquid = hpg
Legend:
g: Gravitational pull (N/kg or m/s²kg)
F: Force
m: Mass
Legend (Pressure):
P: Pressure/Difference in pressure [manometer] (Pa)
W: Weight
A: Contact area (m^2)
h: Depth [liquid pressure]/Difference in level [manometer] (cm)
p: Density of liquid
In gases
Measured with manometer
Atmospheric pressure alternatively measured with barometer
Atmospheric pressure pushes down on liquid in a dish, which pushes some liquid into a tube with a vacuum
Mercury is most commonly used for its density
Atmospheric pressure decreases with altitude due to fewer air molecules
Accounts for additional pressure in liquids in open containers
A U-shaped tube filled with mercury or water
Uses liquid levels to measure unknown pressures and differences in pressure
P=hpg
General Wave Properties
A phenomenon in which energy is transferred through vibrations
Energy is carried from the source without transferring matter
Terms
High points are crests, low points are troughes
Amplitude (a) is the max displacement from rest
Amplitude indicates the energy of a wave
Energy increases with amplitude
Wavelength (λ) is the length of a complete wave
Measured by the distances between similar points on the wave
Frequency is the number of complete waves in a second
Equal to the number of crests/troughs that pass a point per second
Period (T) is the time taken to generate a complete wave
SI unit: Hertz (Hz)
f=1/T
Speed of a wave (v) is the distance moved by a wave in a second
v=λ/T
v=fλ
The wavefront of a wave is a surface containing points affected in the same way by a wave at a given time
The direction of travel of waves is perpendicular to the wavefront
Graphical Representation of Waves
Displacement-Position
Displacement-Time
Can obtain amplitude and wavelength of the wave
Can obtain amplitude and period of the wave
Types of waves
Transverse
Travels perpendicular to vibrations of the particles
Example: Electromagnetic waves
Longitudinal
Travels parallel to vibrations of the particles
Creates a series of compressions and rarefactions in the medium
Compression: Compressed region of particles
Rarefaction: Stretched region of particles
Examples: Sound waves, ultrasound waves
Properties of waves
The wavelength and velocity of waves change with different mediums and depths while the frequency remains unchanged
All waves obey the wave speed equation
Wavelength increases with depth
Waves travel faster in deeper regions and vice versa
Amplitude remains constant throughout path of the wave
Waves will bounce off barriers in the medium
All properties of the wave remain the same, only direction of travel changes
Movement of waves between depths
Waves are refracted moving between regions of different depth
Wavelength and velocity decrease when depth decreases and vice versa
Dynamics
Forces
A vector with magnitude and direction
Balanced forces acting on an object give no resultant force
If the forces are unbalanced, there is a resultant/net force
Measured using extension spring balances
Newton’s laws of motion
First law: In absence of resultant forces, objects at rest remain at rest, objects in motion maintain speed and direction
Second law: Resultant force of an object is equal to the product of its mass and acceleration
F=ma
Direction of net force is the same as the acceleration
Third law: Every action has an equal and opposite reaction
Forces appear in pairs
Action and reaction forces act on different bodies
Legend (Dynamics):
a: Acceleration
Contact forces
Non-contact forces
Legend (GWP)
f: Frequency (Hz)
T: Period (s)
V: Speed (m/s)
λ: Wavelength (m)
Forces that act at point of contact between bodies
Forces that act on bodies without contact
Free-body diagram
Diagram showing all forces acting on a body
Friction
Force that resists the relative motion of objects in contact
Air resistance is friction against air
Reducing friction
Smoothening of surfaces
Materials with low friction
Ball and roller bearings between parts
Surfaces separated by lubricant
Surfaces separated by air
Vector diagram
System of force vectors acting on an object
Balanced forces form a closed loop
Free-fall
When the only acting force is gravity
Will fall with constant acceleration g
g on Earth is ~10m/s²
g on Moon is 1/6 of Earth
Without air resistance, acceleration is constant
With air resistance, acceleration decreases with time
Speed approaches a constant velocity
(terminal velocity)
Object thrown upwards and downwards
Constant downwards acceleration/ upwards deceleration
Magnetism
Magnetisation
Magnetising
Direct current
Electromagnetism
Magnetic effect of a current
Straight wire
Direction and amplitude of current changes magnetic field
Higher amplitude, stronger field strength
Direction follows Right Thumb Rule
Solenoids
Field lines are almost straight and parallel near the centre
Direction of field follows Right-Hand Grip Rule
Magnetic strength can be increased by:
- Larger current
- More coils
- Inserting soft magnetic core
Magnetic field lines form concentric circles around wire
Combined magnetic fields
Current is defined as conventional current
Two fields acting in same direction create stronger field
Two fields acting in opposite directions create weaker field
Unbalanced fields around wire in magnetic field produces a catapult force
Direction can be found with Fleming's Left Hand Rule
Forces between two wires
Opposing directions currents repel
Same directions currents attract
Current carrying coil
Catapult field generates pair of equal and opposite forces
DC motor
Force pair rotates coil
- Current flows from P and X to Y and Q
- Coil turns anticlockwise
- Y will touch P while X touches Q
- Direction of current reverses every half rotation, coil keeps turning
Increasing turning effect
Increasing turns of coil
Increasing current
Inserting soft iron core
Soft iron cylinder will create a radial field which ensures that the pair of forces is almost constant
Unlike poles attract
Like poles repel
Attraction suggests either magnet or magnetic
Repel concludes as magnet
Only steel, iron, nickel and cobalt can be magnetised (SINC)
Made up of magnetic domains
Unmagnetised means randomly aligned domains
Magnetisation aligns the domains in one direction
Circles get closer together nearer to the wire
Field lines are closed loops along coil circumference
Stroke with permanent magnet
Stroke bar several times in same direction with same polarity
End of bar always has opposite polarity to magnet used
Field strength stronger
Induced magnetism
Electromagnetic induction
In a coil
Current is induced when magnet moves in coil
Current is induced by constant cutting of magnetic field lines, specifically due to relative motion
Current induced follows a direction that opposes the magnet's motion via Right-Hand Grip Rule
Imagine the direction the current would take to produce an electromagnet repelling the magnet
Galvanometer deflects in direction and with amplitude of current induced
When Force+Field=Current
In a wire
Follows Fleming's Right-Hand Rule
A strong magnet aligns the domains of a nearby magnetic material without direct contact
Demagnetising
Heating and hammering on poles
Process misaligns domains
AC solenoid
- Place magnet in solenoid
- Close switch and remove magnet slowly
Periodic changes in current misaligns the domains
Magnetic fields
A region where magnetic materials and wires experience magnetic force
Field lines start from North and end at South
Field lines never intersect
Proximity of lines determines field strength (closer is stronger and vice versa)
Properties of iron and steel
AC generators
Current is induced when the coil rotates
Cutting of field lines also known as magnetic flux
- Current flows from A to B and C to D
- After turning, current flows from B to A and D to C
Every half turn, the current reverses its direction, hence an alternating current
Changing output
Doubling turns in coil
Frequency is same
Output voltage doubled
Doubling rotation speed
Frequency doubled
Maximum output voltage doubles
Increasing EMF
Increase speed of rotation
Increase number of turns
Wind coil around soft iron core
Use stronger magnets
Dynamo
Magnet rotates, coil stationary
Transformers
Uses
Transformers step up or down mains supply (240V) to required voltage for different appliacnces
Contains two coils of insulated wire wound around an iron core
Coils known as primary and secondary coils
AC current is induced in secondary when power is supplied to primary
Primary coil induces magnetism in iron core, which induces emf in secondary coil
Transformer only works with AC, as AC current induces magnetic flux that DC cannot
Step up: Primary<Secondary Step down: Primary>Secondary
Ratios of voltage and current equal the ratio of the number of coil turns
Reduced line loss along power cables with less current but same power
Improving efficiency
Effective soft magnetic core
Low resistance wires
Special core design ensuring that magnetic field is linked completely
Primary coil is wound on top of secondary coil in a closed iron core
Laminated core reducing flow of eddy currents
Current may be induced in the core itself, called eddy currents
Cathode Ray Oscilloscope (CRO)
Uses
Measuring DC and AC voltages
Displaying waveforms
Measuring time and frequency
The larger the voltage, the greater the displacement
Reflection and Refraction
of Light
Reflection
The bouncing of light off a surface
Types of reflection
Regular
Diffused
Smooth surface
Reflected in one direction
Clear distinct image
Rough surface
Reflected in different directions
Unclear image
Images formed in a plane mirror
The image is upright, laterally inverted, virtual, of the same size as the object and lies as far behind the mirror as the object is in front of it
Refraction
Laws of refraction
Incident ray, refracted ray and normal lie in the same plane
Snell's Law: sini/sinr=n, where i is the angle of incidence, r is the angle of refractions and n is the refractive index
The change in direction of light as it passes between different mediums
n also found by c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium
Occurs because the speed of light changes
Light bends away from the normal when going into a denser medium, and bends away when going into a less dense medium
Practical electricity
Uses of electricity
Heating
Heating elements use nichrome wire
High resistivity: Much electrical energy is converted to thermal energy
High temperature tolerance: Heating element will not melt
Energy released as heat when charge flows from a higher potential to a lower potential
Lighting
Filament lamps use a tungsten coil
Tungsten: High melting point
Coiled: Increased length, more resistance, more light
Bulb filled with argon: Inert gases prevent oxidation of filament
Energy through a component
E=VQ
Power
Rate at which energy is released
P=E/t
Electricity consumption
Measured in kilowatt-hours
Consumption=Pt
Hazards
Overheated cables
Damaged insulation
Damp conditions
Damaged PVC or rubber covering exposes live wire to users
Water conducts electricity, providing a low-resistance path through the body of a person
When too much current flows through conducting wires due to short circuit or overloading
Short circuit: Live wire touches neutral wire
Overloading: Too many appliances on one socket
The large amount of current generated can melt insulation and start an electric fire
Safety features
3-pin plug
Circuit breakers