The slides Ms. Gilbert says are
SUPER IMPORTANT
!! IMPORTANT !!
MATH REVIEW
Some Useful Unit Conversions
1000 g = 1 kg
60 min = 1 h
3600 s = 1 h
1000 m = 1 km
1 m/s = 3.6 km/h
All graphs need:
●
●
●
●
Axis labels, with units
Descriptive title (“Y” vs “X” for _________ )
Consistent scale that fits entire data set
If drawing a line of best fit, use a ruler and
extend the line past your data points
○ If you can’t draw a line through all points,
try to make sure there are an equal number
of data points on either side of the line of
best fit
Find Slope of the Best Fit Line
What does scientific notation look like?
A positive exponent
means the number is
greater than 1
3
Number is between
1 and 10
-2
A negative exponent
means the number is
less than 1
Converting numbers from standard form TO scientific
notation
1. Position the decimal so there is one non-zero digit to the
left of the decimal
2. Count how many places you moved the decimal to the
right or left. This will be the exponent of the 10.
3. If the original number was less than 1, the exponent will
be negative. If the original number was greater than 1,
the exponent will be positive.
Convert numbers FROM scientific notation to standard
form
1. Look at the value of the exponent on the 10. This is how
many places you will move the decimal point.
2. If the exponent on the 10 is positive, the original number
was greater than 1. Move the decimal point to the right
that many places.
3. If the exponent on the 10 is negative, the original number
was less than 1. Move the decimal point to the left that
many places.
The difference between precision and accuracy
Right Angle Triangles:
Pythagorean Theorem & SOH CAH TOA
If you know the lengths of two sides, you can find
the third using the Pythagorean Theorem:
a2 + b2 = c2
The sides and angles of a right angle triangle are
related through the trigonometric ratios.
Remember: SOH CAH TOA
Non-90o Triangles
Kinematics
Kinematics: The Study of Motion
The study of motion involves kinematics and dynamics.
Kinematics → deals with describing the motion of objects
→ how and where things move
Dynamics → deals with explaining the motion of objects
→ why objects move; the relationship of motion
to the forces that cause it
Scalars vs. Vectors
To describe motion, we can use two types of quantities:
Scalar → a measurement that has a magnitude (size) only
→ no direction given
E.g. time, distance, speed
Vector → a measurement that gives both magnitude and
direction
→ often indicated by an arrow above the symbol
E.g. displacement, velocity, acceleration
Quantities That Describe Motion
Position → distance and direction of an object relative to some reference point
→ symbol: d
Displacement → the change in position of an object, including the direction
→ Δd = df - di
(the triangle is called “delta” and represents a change)
Distance → the total length of the path taken to get from one point to another
→ symbol: d
Quantities That Describe Motion
Speed = total distance
v=d
total time
t
Velocity = total displacement v = Δd
total time
direction
→ measured in m/s
→ measured in m/s,
Δt
includes
Because we are using the total distance and total displacement, these
equations represent average speed and average velocity over the length
of the entire trip.
The speed or velocity at a particular instant is called the instantaneous
speed or instantaneous velocity.
Equal
distances in
equal times
Position/Time
graph is Straightline
Constant Speed
Walk this
way lab
Motion Diagram:
evenly space dots
Summary of Distance vs. Time Graphs
Summary of Speed vs. Time Graphs
Summary of acceleration vs. time graphs
Acceleration
(m/s2)
Increasing velocity
Constant velocity
Decreasing velocity
Time (s)
Unequal
distances in
equal times
Graph doesn’t follow
straight line
Changing Velocity
First
differences are
unequal
Dot diagram:
uneven spacing
Summary
State of Motion
Time Interval
Interpretation of
∆d/∆t
Label
Constant velocity
large
Object moves ∆d for
every ∆t interval
Velocity, v
Changing velocity
large
The object moves ∆d
during ∆t
Average velocity,
vave
One moment
in time
The object would travel
∆d for every ∆t if
velocity stopped
changing.
Instantaneous
velocity, v1, v2, etc.
Most physics work involves changing velocity. So, we get lazy
and say “velocity” instead of “instantaneous velocity”.
The quantity calculated from the slope of the velocitytime graph is called acceleration. The general form of
this equation is:
#
Equation
Variables included
Variable NOT
included
1
a, vf, vi, t
d
2
d, vf, vi, t
a
3
d, a, t, vi
vf
4
d, a, t, vf
vi
5
vf, vi, a, d
t
Vectors
Vector quantities are represented by arrows
called vectors.
The length of the arrow indicates the magnitude
of the vector
The arrow also indicates the direction of the
10 km [E]
10 km [W]
vector.
5 km [E]
Forces
Units of Force:
• Measured/calculated in Newtons
• 1 N represents the amount of force required
to accelerate a mass of 1 kg at a rate of 1
m/s2.
1 N = 1 kg m
s2
Some Common Forces:
Type of Force
Definition
Gravity
Symbol
Fg
Normal
FN
Perpendicular to surface that object is in contact with
Friction
Ff
Keeps surfaces in contact;
Parallel to surface that object is in contact with
Kinetic Friction
FK
Opposes motion of moving object
Static Friction
FS
Prevents objects at rest from starting to move
Air Resistance (“drag”)
Fair
Friction on object moving through the air
Tension
FT
Pull on object by string, rope, fibre, or cable
Applied
FA
Any contact force, in general
Gravitational pull towards Earth;
Force of attraction between any objects that have mass
FBDs
Free-body diagram (FBD): shows all forces acting on the object
being analyzed
How to draw FBDs:
• Object can be represented by a square/rectangle/circle
• Forces are represented by vectors (arrows)
• Vectors start on object
• Lengths of vectors are proportional to magnitudes of forces
• Indicate which direction is positive
Newton’s 1st Law
An object at rest stays at rest and an object in motion stays
in motion with the same speed and in the same direction
unless acted upon by an unbalanced force.
Newton’s Second Law of Motion
In equation form:
Fnet = ma
acceleration (m/s2)
Fnet → net force (N)
m → mass (kg)
a→
Mass vs. Weight
Mass: the amount of matter in an object (in kg)
Weight: the force of gravity on an object
For objects in free fall, the2net force acting on them is Fg, and their
acceleration is g = 9.8 m/s [down].
Using Newton’s 2nd Law,
Fg = mg
weight
mass
acceleration
due to gravity
Newton’s 3rd law in action
For every action
force, there is a
reaction force that
is equal in
magnitude but
opposite in
direction.
Fnet = 0 → constant velocity!
Terminal Velocity
The maximum constant velocity reached by a
falling object is called the terminal velocity.
Law of Universal Gravitation
Where FG = magnitude of gravitational attraction
m1 = mass of one object
m2 = mass of second object
r = distance between centres of objects
G = Universal Gravitational Constant
= 6.67 x 10-11 Nm2/kg2
The first person who successfully measured G was
the English physicist, Henry Cavendish, who
measured the very tiny force between two lead
masses by using a very sensitive torsion balance.
Approximate Coefficients of Friction
μK
μS
Oak on oak, dry
0.30
0.40
Waxed hickory on dry snow
0.18
0.22
Steel on steel, dry
0.41
0.50
Steel on steel, greasy
0.12
Steel on ice
0.010
Rubber on asphalt, dry
1.07
Rubber on asphalt, wet
0.95
Rubber on concrete, dry
1.02
Rubber on concrete, wet
0.97
Rubber on ice
0.005
Leather on oak, dry
0.50
Materials in Contact
Energy
Work
The energy transferred to an object by a force
applied over a measured distance.
In general,
W = FΔdcosθ
θ = angle between
direction of motion and
force applied
When the applied force and the displacement are in
the same direction (θ = 0o):
W = FΔd
This is a scalar.
Gravitational Potential Energy
Recall that
W = FΔdcosθ
To raise an object to a height, h, you give it energy, based on the above
equation.
In this case, F = mg, Δd = h, and θ = 0o so
W = Eg = mgh
Units: Nm = J (Joules)
Kinetic Energy
• Energy of an object due to its motion
• Depends on object’s mass and speed
EK = mv2
2
Units: J (Joules)
Mechanical Energy
• The sum of the gravitational potential energy and kinetic
energy.
• Objects may have JUST potential energy, JUST kinetic
energy, or have BOTH.
Emechanical = Eg + EK = Etotal= ET
Energy
Types
THE LAW OF CONSERVATION OF
ENERGY
Energy cannot be created or destroyed, only
transformed from one form to another
without any loss.
ENERGY BEFORE = ENERGY AFTER
According to the Law of Conservation of Energy,
the total mechanical energy that we begin with
must equal the total energy that we end with.
ET,before = ET,after
ET1 = ET2
Eg1 + EK1 = Eg2 + EK2
Power
▶ The rate at which work is done, or the rate at
which energy is transferred from one form to
another
▶ Mathematically,
P=W
∆t
or
P = ∆E
∆t
W = Work (J), ∆t = time (s), ∆E = Energy (J)
Energy Sources of interest in this course:
Fossil fuels
Nuclear fission
Nuclear fusion
Passive solar heating
Photovoltaic cells
Hydroelectricity
Wind
Tidal
Biomass
Geothermal
For more information, see this part
of the textbook.
Nuclear Energy - Quickest Lesson
EVER
■
Thermal energy: kinetic energy of the particles of
a substance due to their constant, random motion.
■
Heat: transfer of thermal energy
fast-moving particles colliding with
slower-moving ones
■ Three Methods of Heat Transfer:
1. Conduction
2. Convection
3. Radiation
Specific Heat Capacity
■
Specific heat capacity, c, is
the amount of heat energy
that is needed to increase
the temperature of 1 kg of
a particular substance by
Pg 281
1°C.
■
Units (J/kg°C)
Heat Transfer
■
Dependence on:
- Temperature difference (∆T = Tf - Ti)
- Mass of substance (m)
- Type of substance (related to c)
■
The quantity of heat (Q) absorbed/lost when a mass m
changes in temperature by ΔT is:
Q = m∆Tc
Waves & Sound
Vibration Vs. Wave
● Vibration: the cyclical motion of an object about an equilibrium
point
● Mechanical wave: the transfer of energy through a material
(medium) due to vibration
Transverse Waves
A transverse wave describes a
wave in which the particles
vibrate perpendicular to the
direction of the flow of energy.
Examples: a guitar string or water waves
Longitudinal Waves
A longitudinal wave describes
a wave in which the particles
vibrate in the same direction
as the energy flow.
Examples: sound waves & seismic Pwaves
Parts of a Wave
57
The Universal Wave Equation
All waves obey the same equation that relates wavelength (m), frequency (Hz),
and speed (m/s):
v = λf
Transmission
Refraction: When a wave passes from one
medium to another.
● wavelength changes and the wave
seems to “bend” at the boundary
(n1sinθ1 = n2sinθ2)
Transmission
Diffraction: When a wave passes through
an opening smaller than its wavelength
● The wave spreads out.
Reflection
When a wave encounters a fixed end, the
wave is reflected back inverted.
When a wave encounters a free end (v1 <
v2), the wave is reflected back upright.
Interference
Principle of Superposition
At any point the amplitude of two interfering waves is
the sum of the amplitudes of the individual waves.
Step 1: draw the two waveforms, exactly as
shown, but with their horizontal midpoints
aligned.
Step 2: For each segment of the graph paper,
label the amplitudes of the top and the
bottom waveforms.
2 2 2 2 2
-2
0
-1.5 -1 -0.5
Step 3: Add the amplitudes for each segment
and draw the resulting waveform.
Step 4: Draw the waveforms moving away
from each other, with the same
characteristics they started with
Damping
We can observe absorption of wave energy by a
medium as a reduction in the amplitude of the
wave.
Resonance
The condition in which the frequency of a wave equals the resonant frequency of
the wave’s medium.
● Energy input = energy lost
● Amplitude remains constant
Standing Waves
Formed when two identical waves travelling in opposite
directions interfere.
● A node is a point that does not vibrate
● An antinode is a “supercrete/trough”
The distance between nodes, dn, is:
n denotes number of nodes (n = 1,2,3,....)
The length of the
medium, Ln, is given
by:
The Speed of Sound
The speed of sound, vs (m/s), increases by 0.606 m/s for every 1oC increase in
temperature:
vs = 331.4 + 0.606T
Mach #
Ernst Mach (1838–1916), an Austrian physicist, researched sound
waves and devised a way to describe air speeds of objects, vo, in
multiples of the speed of sound, vs.
Thinking about it...
The Doppler Effect
Calculating the Doppler Effect
If either the detector or the source is moving (or both are moving), the
frequency we observe, fobs, and the frequency of the source, f0, are
related by the following formula:
NOTE: If the source is approaching
the detector, the speed is negative.
If the source is receding from the
detector, the speed is positive.
Music Vs. Noise
Music: sound that originates from a
combination of musical notes that originate
from a source that vibrates in a uniform manner
with one or more constant frequencies
Noise: sound that originates from a source that
vibrates in a random manner
Frequency & Length of String
If tension is constant, then speed is constant...which means fL is constant. So, we can write:
f1L1 = f2L2
→ if we reduce the length, the frequency will increase.
Two Free Ends
L
λ
n=2
● Length of the medium is equal to the number of the harmonic, n,
times half the standing wave’s wavelength,
Free/Fixed Air Columns
● Shortest possible length to produce a standing wave would be λ/4
● Next would be λ/2, then 3λ/4, and so on…
● The general equation for determining the length of the medium
with an antinode at one end and a node at the other end is
Electricity &
Magnetism
Electric Current
●
In physics, the word “electricity” refers to electrical energy and the movement
of charge.
● This movement of charge is known as electric current
● Current = the flow rate of electrons passing through a wire
● the amount of charge (amount of electrons - measured in Coloumbs) that
passes through a wire per unit of time (second)
● unit =Current
Ampere (A)
(I) = charge passing a point (Q) / time (s)
● symbol = I
The direction of electric current
It might help to realize that a positive charge flowing west along a wire is
electrically equivalent, in every way, to a negative charge flowing east
Electric Current
Electric current comes in two forms: direct current and
alternating current.
Electric Potential Difference
As current passes through the stove element, it experiences opposition to the
flow, resulting in a loss of electric potential energy
● Results in an electric potential difference (V) between two points in the
circuit.
● Also called voltage
● Measured in volts (V).
Resistance
► degree to which a substance
resists the flow of electric
current through it
► is measured in ohms. The
symbol is (omega)
Ω
Ohm’s Law
Ohm’s Law states as long as the temperature stays
constant,
V = IR
where V is the potential difference (V)
I is the current (A)
R is the resistance (Ω)
V = IR
I = V/R
R = V/I