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SPH3U Physics Review Package
Physics (Sir Wilfrid Laurier Secondary School)
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SPH3U Physics Review Package
SPH3U
Welcome to Accidentville, where the average life expectancy is 31 years old.
The citizens of this municipality are quite clumsy, to say the least.
You and your team of physicists will spend the day in Accidentville’s most
popular landmark— Beaver Hospital and Children’s hospital. You will use your
understanding of the four physics units you have learned thus far to analyze the
physical science behind the various problems and accidents you come across.
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Unit Summaries
Before you get analyzing, let’s refresh on our four units of physics:
Kinematics
This unit of physics studies the motion of objects over a period of time by using observed values
of position, direction, distance, velocity and acceleration.
Values:
d= displacement measured in meters (m) *
t= time measured in seconds (s)
v₁= initial velocity measured in meters per second (m/s) *
v₂= final velocity measured in meters per second (m/s) *
a= acceleration measured in meters per second per second (m/s²)*
* : has direction (north, south, east, west, up, down, left, right, forward, backwards)
Common Formulas:
Vₐᵥ = d/t → to find average velocity when given displacement (m) and time (s)
Vₐᵥ = d/t → to find average speed when given distance (m) and time (s).
aₐᵥ = v/t → to find average acceleration when given average velocity (m/s) & time (s).
a= (v₂ - v₁)/t → to find acceleration when given initial & final velocity (m/s) and time (s).
The big five equations:
Used when you are given certain values, and need to find a
specific value. They can be rearranged for any situation.
d= ((v₁ + v₂)/2)t → when given initial & final velocity (m/s)
and time (s). m= ((((m/s)+(m/s))/2)s
d= v₁t + ½ at² → when given initial velocity, acceleration
(m/s2) and time (s). m= (m/s)s + ½(m/s²)s²
d= v₂t - ½ at² → when given final velocity, acceleration
(m/s2) and time (s). m= (m/s)s - ½(m/s²)s²
v₂= v₁ + at → when given initial velocity, acceleration (m/s2) and time (s). (m/s)= m/s + (m/s²)s
v₂² = v₁² + 2ad → when given initial velocity (m/s), acceleration (m/s2), and displacement (m).
(m/s)²= (m/s)² + 2(m/s²)m
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Common Misconceptions/Possible Errors in Kinematics:
Subscript and superscript → When
calculating problems, your formulas
will most likely involve values such as
Distance and displacement → These
v₁ & v₂. What the numerical
are two different terms. Distance
subscripts refer to is 1= initial value,
refers to the path between two or
and 2= final value. However, do not
more points whereas displacement
make the mistake of misreading
refers to a position relative to a
subscripts and superscripts. Common
specific point. Therefore,
formulas such as v₂² = v₁² + 2ad
displacement has direction, and
involve use of both.
distance does not.
2D Displacement direction → These
types of problems involve the use of
two directions in the format of [Xθ°Y].
You might find yourself confused
When something is decelerating, it is
only “slowing down” → This is not
necessarily true. While an object
may be losing velocity in one
direction, it is simultaneously
gaining velocity in the opposite
which direction comes first:
The direction of the first
displacement comes first!!!
Example:
direction.
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Word Problem:
Your first examination of the day is under the wing of trauma surgeon, Dr.
Eve.
Dr. Eve informs you the following:
“The patient was transported from a concert after
being struck on the head with a glass bottle that was
thrown from an elevated seat behind them. The bottle
was thrown horizontally with a velocity of 12 m/s from
a seat 8 m above the ground. The patient has a height
of 178 cm.”
Determine:
(i) the time it takes the bottle to hit the person’s head
(ii) the impact velocity of the bottle
Multiple Choice:
1. The suspect who threw the bottle leaves the concert and heads 80m [N], and turns
60m [E]. What is the suspect’s final displacement?
a) 100m [N37°E]
b) 140m [N37°E]
c) 100m [NE]
d) 10,000m [N37°E]
2. Rearrange the following equation to solve for acceleration: v₂² = v₁² + 2ad
a) 2(v₂² - v₁²)/d= a
b) (v₂² - v₁²)/2d= a
c) (v₂² + v₁²)/2d= a
d) v₂² - v₁²/2d= a
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KINEMATIC SOLUTIONS:
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Multiple Choice Solutions for Kinematics:
1. The suspect who threw the bottle leaves the concert and heads 80m [N], and turns
60m [E]. What is the suspect’s final displacement?
e) 100m [N37°E] → correct: 80m2 + 60m2= c2 → c2= 10000 → square root → 100m → tanθ=
60/80 and hit the second function tan on calculator = 36.9° → Therefore, 100m [N37°E].
f) 140m [N37°E] → wrong: did not use pythagorean theorem
g) 100m [NE] → wrong: there has to be an angle
h) 10,000m [N37°E] → wrong: forgot to find the square root of c²
2. Rearrange the following equation to solve for acceleration: v₂² = v₁² + 2ad
e) 2(v₂² - v₁²)/d= a → wrong: order of operations incorrect
f) (v₂² - v₁²)/2d= a
g) (v₂² + v₁²)/2d= a → wrong: v₁² should be subtracted from v₂²
h) v₂² - v₁²/2d= a → wrong: without brackets, equation messes up
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Forces
This unit of physics applies Newton's Laws of Motion and free-body diagrams to study the
change in motion that occurs in an interaction between two masses.
Values:
F→ force measured in Newtons (N)
m→ mass measured in kilograms (kg)
a→ acceleration measured in meters per second squared (m/s2)
μS→ coefficient of static friction, unitless
μk→ coefficient of kinetic friction, unitless
k→ spring constant measured in Newtons per meter (N/m)
x→ distance spring is stretched/compressed measured in meters (m)
G→ gravitational constant which is 6.67 × 10-11Nm2/kg2
d→ displacement measured in meters (m)
*All formulas can be rearranged to solve different variables
Formula:
Purpose:
FNet = ma
Fg = mg
Find total force by multiplying mass by acceleration of an
object. N= kg(m/s2)
Find force of gravity by multiplying mass of an object by
gravity of its environment. N= kg(m/s2)
μS =
𝐹𝑆
𝐹𝑁
Find coefficient of static friction by dividing the force of
static friction by the normal force of an object/system.
unitless= N/N
μK =
𝐹𝐾
𝐹𝑁
Find coefficient of kinetic friction by dividing the force of
kinetic friction by the normal force of an object/system.
unitless= N/N
FG =
𝐺𝑚1𝑚2
2
𝑑
Find the force of gravity between two objects by
multiplying the gravitational constant by both masses and
divide by their distance-squared.
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Formula:
Purpose:
FNet = ma
Fg = mg
Find total force by multiplying mass by acceleration of an
object. N= kg(m/s2)
Find force of gravity by multiplying mass of an object by
gravity of its environment. N= kg(m/s2)
μS =
𝐹𝑆
𝐹𝑁
Find coefficient of static friction by dividing the force of
static friction by the normal force of an object/system.
unitless= N/N
μK =
𝐹𝐾
𝐹𝑁
Find coefficient of kinetic friction by dividing the force of
kinetic friction by the normal force of an object/system.
unitless= N/N
N= (Nm2/kg2)(kg)m2
Fs = kx
Find spring force by multiplying the spring constant (not the
same for all springs) by the distance the spring is stretched
or compressed. N= (N/m)(m)
Common Misconceptions/Possible Errors in Forces:
“If an object is at rest, no forces are acting upon it” → This is incorrect because for an object to
be stationary, it needs balanced forces to be keeping it in place. If there were no gravity or air
resistance, an object would be in a constant free fall, meaning hardly any forces are acting
upon it to keep it in place, or apply force to it.
“Greater force is exerted in the direction of motion than the opposite” → This is incorrect
because in situations where objects lose force/velocity, that means that force in the opposite
direction is greater.
For example, a ball being thrown up into the air will have a higher applied force than gravity,
but as it makes its way back to the ground, gravity, which is the force in the opposite direction to
the applied force, will be greater.
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Word Problem:
Your second examination of the day is under the wing of pediatric
emergency physician, Dr. Ally.
Dr. Ally informs you the following:
“Two young patients, weighing 25kg and 30kg,
are suffering concussions as a result of a sled
crash that had an applied force of 220 N, at an
acceleration at 3.25 m/s2. The sled weighs 15kg.”
Determine:
(i) the force of friction
(ii) the coefficient of friction
Multiple Choice:
1. What is the spring constant of an inhaler with a spring force of 30 N that stretches 3cm
from its equilibrium?
a) 100 N
b) 1000 N
c) 1000 N/m
d) 0.09 Nm
2. The four general forces labeled in a full body diagram are:
a) Fg, Fn, Fa, Fs
b) Fg, Fn, Fa, Ff
c) Fg, Fa1, Fa2, Ff
d) Fg, Fa, Fn, mg
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FORCES SOLUTIONS:
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Multiple Choice Solutions for Forces:
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1. What is the spring constant of an inhaler with a spring force of 30 N that stretches 3cm
from its equilibrium?
e) 100 N → wrong: 3cm was not properly converted. X 0.3m ✓ 0.03m, incorrect units
f) 1000 N → wrong: incorrect units
g) 1000 N/m → correct: 30N / 0.03m = 1000 Newtons per meter
h) 0.09 Nm→ wrong: multiplied 30 by 0.003 instead of dividing
2. The four general forces labeled in a full body diagram are:
e) Fg, Fn, Fa, Fs → wrong, yes spring force can be used but it is not general
f) Fg, Fn, Fa, Ff → correct: Force of gravity, normal force, applied force, frictional force
g) Fg, Fa1, Fa2, Ff → wrong: yes there can be multiple applied forces, but it is not general
h) Fg, Fa, Fn, mg → wrong: mg is the formula of the force of gravity
Energy
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This unit of physics focuses on the ability of work, which is the measurement of an object that
moves over a distance due to an external force, and this can exist in energy forms such as
potential, kinetic, thermal, electrical, and nuclear.
Values:
W→work measured in Joules (J)
t→ time measured in any unit of time that
F→ force measured in Newtons (N)
matches half life
m→ mass measured in kilograms (kg)
h→ half life measured in any unit of time
g→ 9.8 m/s
2
that matches time
P→ power measured in Watts (W)
c→ speed of light, 3.0 x 108 m/s
Q→ heat absorbed/released measured in
c→ heat capacity measured in Joules per
Joules (J)
kilogram-celsius (J/(kg°C)
Lf and Lv→ latent heat of fusion/vaporization
v→ velocity measured in meters per second
measured in Joules per kilogram (J/kg)
(m/s)
A→ final mass of substance measured in
d → displacement measured in meters (m)
any unit of mass that matches initial mass
h→ height measured in meters (m)
Ao→ initial mass of substance measured in
*All formulas can be rearranged for different
any unit of mass that matches final mass
variables
Formula:
Purpose:
W = FΔd
Find the amount of work done using force and
displacement. J= N x m
EK = ½ mv2
Find the energy of a moving object using mass
and velocity. J= ½ kg(m/s)2
Eg = mgh
Find the potential gravitational energy using
mass, gravity, and height. J= kg (m/s2)(m)
W = ΔEK
Total amount of work done is equal to the sum
of all kinetic energy. J Δ= J + J + J…
Em = Eg + EK
Mechanical energy is equal to the sum of
kinetic energy and gravitational energy in the
same instance of the same object. J = J + J
Efficiency = Ein/Ein x 100%
Efficiency of a powered device is equal to the
input energy divided by the output energy,
multiplied by a 100%. Nothing is ever 100%
efficient, however no energy is destroyed, only
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transformed. %= J/J x %
P = ΔEΔt
Power is the total energy/work done multiplied
by the time done by an object. W= J/s
Q = mcΔT
Heat absorbed/released is equal to the mass
multiplied by its heat capacity, multiplied by
the final temperature minus the initial
temperature. J= kg(J/(kg°C)(°C2-°C1)
Qreleased + Qabsorbed = 0
The energy released and absorbed equals
zero. This can be used when trying to find a
variable from either the kinetic or gravitational
potential energy formulas. J + J = 0
Qf = mLf
The amount of energy absorbed/released from
a solid to liquid, or liquid to solid state-change.
Using mass and latent heat of fusion which can
be looked up on a chart of latent heat. J=
kg(Jkg)
Qv = mLv
The amount of energy absorbed/released from
a liquid to gas, or gas to liquid state-change.
Using mass and latent heat of vaporization
which can be looked up on a chart of latent
heat. J= kg(Jkg)
A = Ao(½)t/h
In half life questions, solve for the final mass by
taking the initial mass and multiplying it by a
half to the power of the time that passes over
the half life of the substance. mass = mass(½)
to the power of time/time
E = mc2
Find the amount of energy using mass and the
speed of light. This equation proves mass and
energy are essentially interchangeable.
J= kg(3.0 x 108 m/s). c is a constant.
Common Misconceptions/Possible Errors in Energy:
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“Efficiency is never 100% because energy is lost” → Even when electricity is used to power a
heater, some energy is "wasted" in the form of light and sound. Many believe that because
things "use up" energy, however, the “loss” of energy in one form means that energy has
transformed. Also, efficiency does not refer to the amount of energy used in an event, rather it
refers to the amount of a specific kind of energy, like light, sound or heat.
For example, a ball being dropped from a height will not bounce back up to the height it was
dropped from. Rather it will reach a lower height, but energy has not been lost; only transformed
into other forms such as heat, sound, etc.
“Only movement is correlated with energy” → Objects that are not moving can have stored
energy, known as potential energy.
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Word Problem:
Your final examination of the day is under the wing of dermatologist, Dr.
Ashley.
Dr. Ashley informs you the following:
“A patient has been referred from the ER after
accidentally placing their hand in a pot of scalding hot
water. They were wearing a 50g metal ring which was
at room temperature (20°C) before the patient placed
their hand in a 500mL pot of water at 100°C. The ring
and water reached a final temperature of 98.28°C.”
Determine:
(i) the material of the ring
(ii) use the heat capacity of the discovered metal to
prove the final temperature
Multiple Choice:
1. Which of the following is correct?
i)
1 J = 1 kg of water
j)
1 L = 1 kg
k) 1 L = 1 J/s
l)
1 L = 1 kg of water
2. If a hospital bathroom requires 35 light bulbs to be powered, each at 70 Watts, what
is the cost in dollars of electricity per week if it costs 5¢/kWh?
i)
$20.58/week
j)
$20,5800/week
k) $588/ week
l)
$2058/week.
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ENERGY SOLUTIONS:
mcΔt + mcΔt = 0
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Multiple Choice Solutions for Energy:
1. Which of the following is correct?
m) 1 J = 1 kg of water→ wrong: 1 J= 1 N x 1 m
n) 1 L = 1 kg = → wrong: this is only true for water
o) 1 L = 1 J/s→ wrong: 1 J/s = 1 W
p) 1 L = 1 kg of water → correct: metric system correlates 1 liter of water to 1 kg of water.
2. If a hospital bathroom requires 35 light bulbs to be powered, each at 70 Watts, what
is the cost in dollars of electricity per week if it costs 5¢/kWh?
m) $20.58/week → correct: 35 bulbs x 70 W = 2.45 kW, E= 2.45 kW x 168 hours = 411.6 kWh,
411.6 kWh x 0.05 = $20.58
n) $20,5800/week → wrong: did not convert into kilowatt hour instead of watt-hour in E= Pt
formula.
o) $588/ week → wrong: did not multiply 70 W by 35 light bulbs. This only accounts for a
single bulb
p) $2058/week → wrong: did not convert cents to $ by dividing by 100, or converting cents
to dollars before multiplying kWh.
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