SPH3U Physics Exam

Enduring ExpectationsKey Understandings

Waves

• Two types of waves: linear and longitudinal• Properties of all waves• Universal wave equation: v=fl• resonance

Waves can be classified as linear or longitudinal

Wave Properties

• 5 major wave properties exist– transmission– Reflection– Refraction– Diffraction– Interference

• Know what happens to v, f and l for each and know at least one real world example for each

frequency

• The frequency of a wave is created at the vibrating source– Once established it will not change– Frequency doesn’t change in transmission,

reflection, refraction, diffraction or interference.

speed

• The speed of the wave changes if the medium changes– Speed changes when a wave refracts. This means

the wavelength changes as well– If a wave enters a denser medium the speed

decreases and the wavelength decreases.

wavelength

• The measured distance from crest to crest• Changes in refraction• Straight waves spread out in diffraction

(wavelength doesn’t change … just direction)• Interference creates a new more complex

wave but original wavelengths still exist• When reflecting from a more dense material

waves undergo a l/2 phase shift

diffraction

• Waves spread out when either passing through a small opening or around a hard object– The larger the wave the larger the amount of

bending for an object– Ideal amount of bending when the width of the

opening equals the wavelength

Applications

• Transmission: how your voice carries across a room

• Reflection: an echo• Diffraction: noise barriers on sides of roads• Refraction: sonic mirage• Interference: using beat frequency to tune an

instrument

Resonance

• When an external vibrating source occurs at the natural vibrational frequency of an object the object will experience continual constructive interference --- resonance– Can be viewed as a feedback loop

• Applications: MRI, ultrasonic healing/heating/surgery, Wind tunnel testing

UWE- Universal Wave Equation

• v=fl– Explains why a medium change has an impact on

the wavelength of the wave

Sound

• Definition of sound• Human hearing• Air column theory• Air column lab

Definition of Sound

• Be prepared to pull definition apart– A LINEAR PRESSURE wave travelling through a

MEDIUM at a speed close to 330 m/s.

Human Hearing

• 3 Separate areas– Outer, middle, inner

• Physics of hearing more important than the biology of the ear … but you need the biology to understand the physics

Outer Ear

• External ear, auditory canal, ear drum• Allows for transmission of sound into the

inner ear without changing wavelength• External ear: concave reflector• Auditory canal: closed air column• Ear drum: thin easy to vibrate membrane

Middle Ear

• Ossicles/ossicular chain• Three tiny bones that work together to:– Transmit sound from ear drum to cochlea– Amplify vibrations because of lever action

Inner Ear

• Cochlea– Acts as an analog (vibration) to digital (electrical

pulses) converter– Hairs at different lengths resonate at different

frequencies– Each hair is embedded in a nerve cell converting

mechanical motion into electrical pulses

Air Column

• Air column resonance occurs because of reflection of sound off of the bottom surface of the air column

• Always has a predictable pattern– Fundamental always at l/4 then an increase of l/2

for successive patterns– Can you• Derive the patterns• Do the math

Two types of air column questions

• Given ONE specific point of resonance– A closed air column resonates at the second

harmonic ….• Given two successive points of resonance– A closed air column resonates at 17 cm and again

at 30 cm ….

One point of resonance

• Determine the point of resonance– Fundamental = L1, first harmonic = L2

• Apply the appropriate relationship– L1 = l/4, L2 = 3l/4, L3=5l/4 …

• A closed air column resonates at first harmonic with an overall length of 10 cm. The air inside the air column is 20°C. What is the produced frequency?

Two Points of resonance

• ALWAYS used in air column experiments• ALWAYS use the DL=l/2 relationship• A closed air column resonates at 10 cm and

then again at 27 cm when induced to vibrate by a 1000 Hz tuning fork. What is the temperature inside the column?

Motion/Kinematics

• 3 aspects of motion– Vectors– Graphical analysis– Freefall/accelerated motion

Vectors

• Magnitude with a direction• Collinear- motion in one dimension– Add/subtract as you would integer values– 100 m/s north plus 50 m/s south = (+100) + (-50)

• Orthogonal- forms a right angle triangle– Use trigonometry (SOH CAH TOA) and

Pythagorous

Sample Vector Question

• The little mermaid wants to swim due north across a stream with a current of 2 m/s. She is capable of maintaining a speed of 2.5 m/s relative to the water. Find:– Her resultant speed if she swims due north and

allows the current to push her around– The angle she would have to swim at if she wants

to swim due north

Graphical Motion

• The slope of the graph can give you the average rate of change or the instantaneous– Slope of a position-time graph = velocity– Slope of a velocity-time graph = acceleration

• To convert between graphs you need to calculate the instantaneous rate of change (IROC)

• Area under the curve is used to work backwards– Area under an acceleration-time graph = velocity– Area under a velocity-time graph = position

• Can you analyze ticker tape?– 6 dots = 0.1 seconds of motion– 60 dots = 1 second of motion– The instantenous rate of change at the centre of an

interval = the average on either side of the interval

Reading graphs

• Do you know the general shape of:– Constant uniform velocity– Constant acceleration

Constant velocity

• Position-time– Straight line … slope of the line = velocity

• Velocity-time– Horizontal line … y-value = velocity

• Acceleration-time– Straight line along x-axis

Accelerated Motion

• Position-time– Smooth curve – shape of curve determines

slowing down or speeding up• Velocity-time– Straight line … slope of line = acceleration

• Acceleration-time– Horizontal line. Y-intercept = acceleration

Freefall=accelerated motion

• If an object is not supported by a surface it will accelerate towards the ground because of gravity– Gravitational acceleration does not depend on

mass

• Dd=viDt + ½aDt2

• A = (vf – vi)/Dt

• Many motion questions can be handled through the conservation of energy idea– If you are asked for the final velocity of an object

use the conservation of energy idea• Don’t forget the vector sign convention– Down is negative

• An object is dropped from the top of a 20 m cliff. Time? Velocity?

• An object is thrown down at 10 m/s from a 20 m cliff. Time? Velocity?

• An object is thrown up at 10m/s from a 20 m cliff … what is it’s maximum height?

Forces/Dynamics

• Key Understandings– What is a force– Force of gravity – surface– Force of gravity – planetary– Force of friction– Newton’s second law

Forces

• A push or pull that can– Move an object– Create pressure

• Measured in newtons• A vector quantity so direction is important• Fundamental forces

Fundamental Force• Gravity

– Attraction of masses caused by graviton– Weakest force, infinite distance

• EM– Attraction of charges caused by electron spin state– Second strongest force, infinite distance

• Nuclear Strong– Attraction of sub nuclear particles caused by strong force (colour force)– Strongest force, only acts diameter of nucleus

• Nuclear Weak– Dictates radioactivity – neutron decay– Smallest distance of action, second weakest force

Force of gravity – on surface

• AKA the weight of the object• Often equals the normal force on the object• Fg=mg

Force of Gravity - planetary

• NUG – Newtonian Universal Gravity• Inverse square law– F 1/d2

– If the distance between objects is doubled the force experienced is ¼, if the distance is tripled then the force experienced is 1/9.

• Be prepared to use the fact that mass attracts mass in an application setting (tides, grand conjunctions, LaGrange points, etc.)

Force of friction

• For this course friction opposes motion– Static = prevents initial motion– Kinetic = tries to bring an object to rest

• The amount of friction depends on the types of surfaces in contact and the normal force

• Ff = mFN

Newton’s Laws

• Law of Inertia – Object at rest will remain at rest, object in motion will remain moving UNLESS acted on by an unbalanced force

• Law of Acceleration – an unbalanced force accelerates an object in the direction of the acceleration– FNET =ma

• Action-Reaction – Every action force has an equal /opposite reaction force.

Dynamics Problems

• Draw a diagram of the situation• Draw a FBD• Use Newton’s second law in the vertical• Use Newton’s second law in the horizontal• Use the components to answer the question

Motion and Force Problems

• The acceleration of an object can be used to tie the concepts of motion to the concept of Newton’s second law

• A 100 kg crate is pushed with a force of 100 N across a floor of coefficient 0.1. What is the acceleration of the crate?

• A 50 kg crate is pushed with an unknown force across a floor of coefficient 0.1. The crate accelerates at a rate of 2 m/s/s. What was the force?

• Batman is travelling at a speed of 100 km/h towards a stop sign. He slams on the brake and comes to a complete stop in 10 m. What is the coefficient of friction between the tires and the road?

Energy

• The energy is divided into three sections:– Conservation of energy– Thermal Energy– Nuclear Energy

Energy, Work, Power

• Energy: ability to do work• Work: a force moving an object through a

displacemnt – W = FDd

• Power: the rate at which work is done– P = W/t

Conservation of Energy

• If the object is moving it has kinetic energy– Ek = ½ mv2

• If the object can drop to a lower position it has stored energy– Ep =mgh

• Energy is always conserved:– Total energy at any location EQUALS total energy

at all other locations

• A crate of Tofu is dropped from a 100 m high cliff. How fast is it travelling when it has reached the halfway in it’s journey?

Thermal Energy

• Heat is the total energy of the particles of a substance

• Temperature is the average kinetic energy of the particles

• Heat can transfer from a hotter object to a colder object– Three methods of heat transfer

Heat Transfer

• Conduction– Vibration of particles cause molecular collisions

which transfer the energy. Requires a medium and direct contact

• Convention– Particles of the substance move because of lower

density. Requires a medium which can flow.• Radiation– Energy transfers as a wave

Heat

• All objects can carry/hold/transfer different amounts of heat

• Q=mcDT– SHC is a measurement of the amount of energy

required to change the temperature of 1 kg of a substance by 1°C

– Q is positive if temperature is gained

Theory of Mixtures

• When objects are placed in contact– Heat will transfer until all objects in contact are at

the same final temperature– +Qcold = -Qhot

• This can be used to identify unknown substances

• 200 grams of copper (c=390 J/kg°C) is heated to 200°C and dropped into a container containing 200 mL of water at 20°C. The water is sitting inside of a 10 gram styrofoam cup (c = 1300 J/kg°C). What is the final temperature of the metal?

Three types of radiation

• Alpha– Helium nucleus, heaviest, high energy, easy to

stop. Used in smoke detectors.• Beta– Ejected electron (neutron decay), can be stopped

by a few sheets of paper. Used to measure thicknesses

• Gamma– High energy/pure energy. Used to irradiate foods

Nuclear Fission

• Uranium can be caused to fission by the addition of a slow moving neutron– Two daughter particles, 3 fast moving neutrons

and energy will be created– This process can be explained by the change in the

strong force required to hold the nucleus together

Reactor Requirements

• A moderator is slow fast neutrons• A control system to absorb excess neutrons• A method to quickly shut down the reactor