Download PHYSICAL SCIENCE PAPER 1:PHYSICS

PHYSICAL SCIENCE PAPER 1: PHYSICS
Electricity and Magnetism ................................................................................................................................................ 2
Fields ............................................................................................................................................................................. 2
Electric Circuits .............................................................................................................................................................. 2
Resistance ..................................................................................................................................................................... 2
Work done or energy transferred.............................................................................................................................. 3
Power dissipated ....................................................................................................................................................... 3
Capacitance ................................................................................................................................................................... 3
Electrodynamics ................................................................................................................................................................ 4
L-H Motor and R-H Dynamo Rule .............................................................................................................................. 4
Dynamo ...................................................................................................................................................................... 4
Alternating Current .................................................................................................................................................... 4
Electromagnetic Radiation ............................................................................................................................................ 5
Nature of an EM wave ............................................................................................................................................... 5
EM Spectrum ............................................................................................................................................................. 5
Photoelectric Effect ................................................................................................................................................... 5
Mechanics ......................................................................................................................................................................... 6
Force, Momentum and Impulse ................................................................................................................................... 6
Momentum ................................................................................................................................................................ 6
Vertical Projectile Motion .......................................................................................................................................... 6
Work, Energy and Power .............................................................................................................................................. 7
Waves, Sound and Light .................................................................................................................................................... 7
The Doppler Effect ........................................................................................................................................................ 7
Mach Numbers .......................................................................................................................................................... 8
Mach Cone ................................................................................................................................................................. 8
2D and 3D Wave Fronts ................................................................................................................................................ 8
Interference ............................................................................................................................................................... 8
Diffraction .................................................................................................................................................................. 8
© Samir Daniels
Physical Science Paper 1
Page 1
ELECTRICITY AND MAGNETISM
FIELDS



A field is a region of space in which an object experiences a force
o Force is equal to the product of electric field strength and the charge in the field.
o 𝐹 = 𝐸𝑞
A point charge goes from positive to negative
o Field lines are drawn to describe what a positive charge will do.
An electric field (𝐸) exists due to the presence of just one charge.
o

𝑣
𝐸=𝑑
 Measured in 𝑁𝐶 −1
 𝑘 = 9 × 109
 𝑟 is the distance
 𝑄 is the charge on the charge sphere
Adding another charge in the field will experience a force
o

𝑘𝑄
𝑟2
𝐸=
𝑘𝑄1 𝑄2
𝑟2
𝐹=
Coulomb’s Law: the force of an electric force is directly proportional to the product of two charged particles
and inversely proportional to the square of the distance between the two of them.
ELECTRIC CIRCUITS

Current is the push of electrons
o

𝐼=
𝑞
Δ𝑡
Electric Current Strength is the number of coulombs passed in a second
𝑉 = 𝐼𝑅
o 𝑒𝑚𝑓 = 𝐼(𝑅 + 𝑟)
𝑅𝑡𝑜𝑡 = 𝑅 + 𝑟
RESISTANCE





Ohm’s Law: The resistance in a circuit is directly proportional to the potential difference and inversely
proportional to the current flowing through the circuit, provided that the temperature is constant.
Ohmic Conductors are those which follow Ohm’s Law (𝑉 = 𝐼𝑅)
o Copper wire
Non-ohmic conductors are those which don’t obey Ohm’s Law
o Transistors
𝑅𝑠𝑒𝑟𝑖𝑒𝑠 = 𝑅1 + 𝑅2 + 𝑅3 + ⋯
1
𝑅𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙
=
1
𝑅1
1
+𝑅
2
+
1
𝑅3
+⋯
Remove Resistor
Voltage
Current
Parallel
Series
Voltage
Same
Voltage
Splits
Current
Splits
Current
Same
Add Resistor
Voltage
Current
Series
Parallel
© Samir Daniels
Physical Science Paper 1
Page 2
WORK DONE OR ENERGY TRANSFERRED
o
𝑊 = 𝑉𝑞 = 𝑉𝐼𝛥𝑡 = 𝐼 2 𝑅𝛥𝑡 =
𝑉 2 𝛥𝑡
𝑅
POWER DISSIPATED
o
𝑃 =
𝑊
𝛥𝑡
= 𝑉𝐼 = 𝐼 2 𝑅 =
𝑉2
𝑅
measured in W
CAPACITANCE

Measured in Farads

𝐶=

𝜀0 𝐴
𝑑
o
o
o
𝜀0 = 8.85 × 10−12 Permittivity of free space
𝐴 is the area of the plates
𝑑 is the distance between the plates
o
o
A dielectric (insulator) is in between the plates
o
Capacitance in Series
o
o
1
𝐶𝑡𝑜𝑡
1
1
1
2
=𝐶 +𝐶 +⋯

Capacitance in Parallel

o
o 𝐶𝑡𝑜𝑡 = 𝐶1 + 𝐶2 + ⋯
Charge (𝑄)
o
𝐶=
𝑄
𝑉
© Samir Daniels
Physical Science Paper 1
Page 3
ELECTRODYNAMICS
L-H MOTOR AND R-H DYNAMO RULE

Left Hand Motor

o
Right Hand Dynamo
o Flemming


o
AC produced → generator uses a SLIP RING
DC produces → generator uses a SPLIT RING
DYNAMO
ALTERNATING CURRENT



𝐼𝑚𝑎𝑥
√2
𝑉
𝑉𝑟𝑚𝑠 = 𝑚𝑎𝑥
√2
𝐼𝑟𝑚𝑠 =
Average power in an AC Circuit
o
2
𝑃𝑎𝑣𝑒𝑟𝑎𝑔𝑒 = 𝑉𝑟𝑚𝑠 × 𝐼𝑟𝑚𝑠 = 𝐼𝑟𝑚𝑠
×𝑅 =
2
𝑉𝑟𝑚𝑠
𝑅
© Samir Daniels
Physical Science Paper 1
Page 4
ELECTROMAGNETIC RADIATION
NATURE OF AN EM WAVE



The source of electromagnetic waves →
accelerating charge
The EM wave propagates1 when an electric field
produces a magnetic field oscillating in a pale at
right angles to oscillating electric field.
Speed of EMR = 3 × 108 ms-1 = c
EM SPECTRUM

𝑐 = 𝑓𝜆
Big wavelength
Small frequency
Radio Waves
Microwaves
Infrared
Visible Light
Red
Orange
Yellow
Green
Blue
Indigo
Violet
Ultraviolet
X-ray
Small Wavelength
High frequency
Gamma
PHOTOELECTRIC EFFECT

The process that occurs when light shines on a metal and it ejects an electron
o
Energy of a photon = 𝐸 = ℎ𝑓 =



ℎ𝑓 = 𝑊0 +
ℎ𝑐
𝜆
Planck’s Constant (ℎ) = 6.63 × 10−34 𝐽𝑠
Speed of light (𝑐) = 3 × 108 𝑚𝑠 −1
1
𝑚𝑣 2
2


1
Spreads
© Samir Daniels
Physical Science Paper 1
Page 5
MECHANICS
FORCE, MOMENTUM AND IMPULSE
MOMENTUM



Motion of a moving body is measured by the product of its mass and velocity
o 𝒑 = 𝒎𝒗
o kg∙m∙s-1
The momentum of a system is conserves when no external forces act upon it
External forces cause momentum to change (Impulse) 𝜟𝒑 = 𝑭𝒏𝒆𝒕 𝜟𝒕
o

𝐹𝑛𝑒𝑡 =
Δ𝑝
Δ𝑡
o The longer something takes to happen, the less force it has
Momentum is conserved in a closed system
o Kinetic energy is transferred from one to the other
o Inelastic collisions occur when two objects collide and do not bounce away from each other.
Momentum is conserved. Kinetic energy is not conserved.
 𝑝𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑝𝑎𝑓𝑡𝑒𝑟
 𝑚𝑎 𝑣𝑖𝑎 + 𝑚𝑏 𝑣𝑖𝑏 = 𝑚𝑎+𝑏 𝑣𝑓
o
 𝑚𝑎 – mass of 𝑎
 𝑣𝑖𝑎 – initial velocity of 𝑎
 𝑚𝑎+𝑏 – mass of 𝑎 and 𝑏 (combined mass)
 𝑣𝑓 – final velocity of combined mass
Elastic collisions occur when the objects bounce off each other after the collision. Both momentum
and kinetic energy are conserved
 𝑝𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑝𝑎𝑓𝑡𝑒𝑟

 𝑚𝑎 𝑣𝑖𝑎 + 𝑚𝑏 𝑣𝑖𝑏 = 𝑚𝑎 𝑣𝑓𝑎 + 𝑚𝑏 𝑣𝑓𝑏
Kinetic energy is also conserved, so
𝐾𝐸𝑖 = 𝐾𝐸𝑓

1
𝑚 𝑣2
2 𝑎 𝑖𝑎
1
1
1
2
+ 2 𝑚𝑏 𝑣𝑖𝑏
= 2 𝑚𝑎 𝑣𝑓2 + 2 𝑚𝑏 𝑣𝑓2
VERTICAL PROJECTILE MOTION



Draw a Diagram!
𝑔 = 9.8ms-2 (decide whether up or down is positive)
Write down what you know / what information is given and what you need to find out.
o 𝑣𝑓 = 𝑣𝑖 + 𝑎Δ𝑡
1
2
o
Δ𝑥 or Δ𝑦 = 𝑣𝑖 Δ𝑡 + 𝑎Δ𝑡 2
o
𝑣𝑓2 = 𝑣𝑖2 + 2𝑎Δ𝑥 or Δ𝑦
o
Δ𝑥 or Δ𝑦 = (
𝑣𝑓 +𝑣𝑖


2
) Δ𝑡
Use Δ𝑥 for horizontal motion
Use Δ𝑦 for vertical motion
© Samir Daniels
Physical Science Paper 1
Page 6
Newton’s First Law: An object will remain at rest or at a constant speed unless an external force acts upon it.
Newton’s Second Law: The net force acting on an object is equal to the rate of change in momentum 𝐹𝑛𝑒𝑡 =
Δ𝑝
Δ𝑡
Newton’s Third Law: when objects interact with each other, the exert forces that are equal in size but opposite in
direction to each other.
F ORCE F ORMULAE
𝐹𝑛𝑒𝑡 = 𝑚𝑎
𝐹𝑛𝑒𝑡 = 𝛥𝑝 = 𝑚𝑣𝑓 − 𝑚𝑣𝑖
𝑝 = 𝑚𝑣
𝑤 = 𝑚𝑔
WORK, ENERGY AND POWER


𝑊 = 𝐹Δ𝑥 cos 𝜃
o Work done on an object when a force is applied at an angle will cause the object to move a distance.
𝑾𝒏𝒆𝒕 = 𝚫𝑬𝒌 = 𝑬𝒌𝒇𝒊𝒏𝒂𝒍 − 𝑬𝒌𝒊𝒏𝒊𝒕𝒊𝒂𝒍

𝑀𝐸 = 𝐸𝑝 + 𝐸𝑘

𝟏
𝑴𝑬 = 𝒎𝒈𝒉 + 𝒎𝒗𝟐
𝟐
Power is the rate at which work is done
o 𝑃 = 𝐹𝑣
WAVES, SOUND AND LIGHT
THE DOPPLER EFFECT
The apparent change in frequency and wavelength of a wave when the observer and the source of the wave more
relative to each other
𝒇𝑳 =


𝒗 + 𝒗𝑳
× 𝒇𝑺
𝒗 + 𝒗𝑺
o 𝑓𝐿 – the frequency of the sound heard by the listener
o 𝑣 – velocity of the waves
o 𝑣𝐿 – velocity of the listener
o 𝑣𝑆 – velocity of the source
o 𝑓𝑆 – frequency of the source
IMPORTANT
o Source moves toward listener
𝑣𝑆 negative
o Source moves away from listener
𝑣𝑆 positive
o Listener moves toward source
𝑣𝐿 positive
o Listener moves away from source
𝑣𝐿 negative
o Source coming toward you – higher sound, increased pitch
o Source moving away from you – lower sound, decreased pitch
Frequency is measured in Hz
© Samir Daniels
Physical Science Paper 1
Page 7
MACH NUMBERS
The ratio between the speed of an object and the speed of sound
𝑴𝒂𝒄𝒉 𝑵𝒖𝒎𝒃𝒆𝒓 =
𝒗𝒐𝒃𝒋𝒆𝒄𝒕
𝒗𝒔𝒐𝒖𝒏𝒅
MACH CONE
𝐬𝐢𝐧 𝜽 =
𝒗𝒔𝒐𝒖𝒏𝒅
𝒗𝒐𝒃𝒋𝒆𝒄𝒕
2D AND 3D WAVE FRONTS
Huygen’s Principle – each wavefront acts like appoint source of circular waves. They interfere to form another
wavefront
A Wave front is an imaginary line that connects waves that are in phase.
INTERFERENCE
Constructive Interference when both waves have displacement in the same direction
Deconstructive interference when waves have displacement in opposite directions
DIFFRACTION

1 Slit
o
© Samir Daniels
Physical Science Paper 1
Page 8

2 Slits

o
2 sources
o

Slit diffraction pattern

𝐬𝐢𝐧 𝜽 =
o
o
o
o
𝒎𝝀
𝒂
𝜃 is the angle to the minimum
𝑚 is the order of the minimum (e.g. ±
1, ±2, ±3)
𝜆 is the wavelength of the waves
𝑎 is the width of the slit (in meters)
© Samir Daniels
Physical Science Paper 1
Page 9