 Aim:
Algebra, Motion Graphs, and
Kinetic and Potential Energy
 Algebra,
Motion Graphs, and
Kinetic and Potential Energy
Practice calculations
 Homework: read p. 155-160
 Next class
Sometimes the variable you are looking for is
mixed in with the other variables…
Example:
A = BC
D
A = 15
C=6
D=2
Solve for B
… so you must Rearrange the Formula so that
variable is alone on one side of the equals sign
B=
Example:
A = BC
D
A = 15
C=6
D=2
Solve for B
Two ways to do this type of rearrangement question:
Method 1:
- Rearrange the formula and then replace the
symbols with their number values
Method 2:
- Replace the symbols with their number values, then
rearrange
Method 1 is a lot less messy!
Multiply
Divide
Add
Subtract
Squared
Square Root
Multiply
Divide
Add
Subtract
Squared
Square Root
Solve for B in the Following Formulas:
A=B+C
A=B-C
A = BC
A= B
C
A = B - CD
A = B2
A = BC
D
A = 15
C=6
D=2
A=C+
B2
A = 15
C=6
WORK INDIVIDUALLY FIND THE
ACCELERATION?
Velocity (m/s[N])
Time (s)
Graphs can be used to show different
types of motion.
3 types of graphs that can show
the same type of motion:
 Distance vs. Time
 Velocity vs. Time
 Acceleration vs. Time
Distance vs. Time
Velocity vs. Time
Acceleration vs.
Time
Distance vs. Time
Velocity vs. Time
Acceleration vs.
Time
Distance vs. Time
Velocity vs. Time
Acceleration vs.
Time
Distance vs. Time
Velocity vs. Time
Acceleration vs.
Time
 Determine
the Acceleration
Velocity (m/s[N])
Time (s)
is the energy of motion.
 The amount of kinetic energy depends
on the speed and mass
of the object.

Ek = ½
2
=
mv
Ek = kinetic energy (J)
m = mass of object (kg)
v = speed of object (m/s)
=
2
mv
2
Units:
Ek = ½ mv2
(J) = ½
(kg)(m/s)2
1) A car with a mass of 1500 kg is
moving at a speed of 14 m/s. What is
the kinetic energy of the car?
2) A hockey puck has a mass of 0.21kg.
If the hockey puck has 73J of kinetic
energy, what is its speed?

The transfer of mechanical energy
from one object to another
W = Fd
 can either add or remove kinetic
energy from an object.
Positive Work (adding KE ):
A pitcher does work on a ball
 transfers kinetic energy to the ball.

is done if you remove kinetic energy from an
object (if a force is applied opposite to the
object’s motion, or the object slows down).
Example:
catching the ball removes kinetic energy
causing it to slow down

is stored energy.
Elastic
 Chemical
 Nuclear
 Gravitational

An object is elastic if it always returns
to its original form after its been
distorted
 Work done on an elastic object to
distort it gives it elastic potential
energy


E.g. bungee cords

chemicals that lose little energy when
bonds are formed have the potential of
releasing even more energy by
undergoing chemical reactions
This chemical reaction
releases thermal energy
(heat)
Glucose is the principal form of chemical
energy for plants and animals… the
reaction that breaks down glucose and
supplies the energy is called the CELLULAR
RESPIRATION reaction
C6H12C6 + 6O2  6CO2 + 6H2O + Energy

very large nuclei (uranium and
plutonium) have the potential to split
into two smaller nuclei and release
large amounts of energy


very large nuclei (uranium and
plutonium) have the potential to split
into two smaller nuclei and release large
amounts of energy
Einstein said during a nuclear reaction,
some of the mass of the reactants was
converted into energy (mass of products
does not = mass of the reactants in
nuclear reactions)
E  mc
2

the potential energy an object has due to
its location above the Earth’s surface (a
mass at a height)




is a property of all objects with mass.
any two masses attract each other with a
gravitational force
this force is not noticeable unless one of
the masses is very large (moon, planet,
star)
if there is no force opposing the force of
gravity on an object, its motion will
change

if there were no air friction, all objects
near Earth’s surface would fall with the
same acceleration, called the
acceleration due to gravity (g = 9.81
m/s2)
http://www.youtube.com/watch?v=5C5_dOE
yAfk

is the force of gravity acting on an
object
Weight ≠ Mass

is the force of gravity acting on an object
Weight ≠ Mass
Mass = Quantity of Matter in an Object
 is the force of gravity
acting on an object
Fg  mg
Force of gravity (weight) (N )
 m = mass (kg)
 g = acceleration due to gravity
(9.81m/s2)


When all of the work done on an object
gives it gravitational potential energy,
the work done is equal to the
gravitational potential energy gained.
W  E p
W  Fd
W  Fh
since
W  mgh
since
Fg  mg
W  E p
E p  mgh




Ep = gravitational potential energy (J or )
m= mass (kg)
g = acceleration due to gravity (9.81m/s2)
h = Change in height (m)


E.g. The shelf in your locker is 1.8 m
above the floor. If your science book has
a mass of 1.2 kg, what is its gravitational
potential energy relative to the floor if it
is sitting on the shelf?
E.g. If you did 565 J of work on a 12 kg
box by carrying it up a flight of stairs,
how high is the flight of stairs?
The second law of thermodynamics says:
No process can be 100% efficient.
Some energy will always remain in
the form of thermal energy.
During any process, some energy is always
transformed into a form that is not useful. This
energy is often said to be wasted.
USEFUL ENERGY: Energy that performs a task
WASTE ENERGY: Energy converted during
process into a form that is not useful, such as
heat
Example: Light Bulb
 useful energy = light
 wasted energy = heat
is a ratio of the useful
energy output to the total energy input. In other
words, the percentage of the energy we put in
to a system that is converted into the type of
energy we want.
useful output energy
efficiency 
100%
total input energy
To use the equation, you must be able to identify
the useful energy output and the total energy
input
.
Example:
You climb up the steps of a slide at the waterpark. The top of the
slide is 100 m above the pool below. Your mass is 55.0 kg and
you are traveling at a speed of 4.30 m/s at the bottom of the slide.
Calculate the efficiency of the transformation of gravitational
potential energy into kinetic energy.
1) Energy Input → Gravitational potential energy
E p  mgh
2
 55.0kg  9.81m / s 100m
= 53 955 J
2) Energy Output → Kinetic Energy
1 2
E k  mv
2
1
2
  55.0kg 4.30m / s 
2
= 508.475J
3) Calculate Efficiency
efficiency 
useful
total
output energy
 100%
input energy
508.475 J

 100%
53955 J
= 0.942%

A simple pendulum is a simple example of
energy transformations
Input Energy Converter Useful Output +Waste
Energy
Chemical
Potential of
Gasoline
E
X
A
M
P
L
E
S
Ignition
(reaction) of
 Internal
Combustion
Engine
Mechanical
Energy of Motor
 and Movement
of Wheels
+
Gravitational
Physical
 Propulsion
Potential
Energy of
Child on Slide
Kinetic Energy of
 Sliding Down
Chemical
Potential of
Food
(Ex. Glucose)
 Breakdown
of Glucose
(Chemical
Reaction)
 Muscle
Movement,
Digestions,
Respiration, etc
+
Mechanical
Energy From
a Turbine
A
 Generators
Magnetic
Field and
Spinning
Motion
Current =
 Electrical Energy
+
+
Heat and Noise
Heat (from
friction) and
some Noise
Heat
Heat and Noise

You use the chemical energy obtained from your
food to pedal your bicycle up a steep hill, thus
gaining gravitational potential energy. You then
coasted down the hill, transforming the
gravitational potential energy into kinetic energy.
Suppose the you pedalled up a hill and gained a
vertical distance of 25 m. You turned around and
coasted down the hill. At the bottom of the hill,
you were coasting at a speed of 13 m/s. If the
combined mass of yourself and your bicycle is 68
kg, what was the efficiency of the transformation
of your gravitational potential energy into kinetic
energy?
Do practice problems page 227 # 1-9 (odd)

Formula:
What do we care about efficiency?
One way to reduce pollution caused by
machines is to stop using them.
Problems with this idea:
1. We rely on machines to improve our
standard of living
2. Food shortage across the globe would
occur
3. Production of goods could not meet
demand (economic impact)
On average, cars are only about 20% efficient.
Where does the other 80% of the energy go?
Where does the other 80% of the energy
go?

36% - lost to the coolant

38% - Heat in the exhaust gases

6% - Frictions between the moving parts

What percentage of energy in an
incandescent light bulb is converted into
light energy?

What percentage of energy in an
incandescent light bulb is converted into
light energy?
5%
The remaining 95% is converted into
heat
Compact Fluorescent bulbs are 20%
efficient.
Almost half of all the electrical energy
generated in North America is used to
drive electric motors.

Plant cells use solar energy to help
facilitate a chemical reaction called
photosynthesis, in which glucose is
formed.

Glucose = a molecule that can then be
broken down to release useable energy to the
plant for growth, reproduction, etc.
In general, plants have relatively low
efficiency….approximately 1%!
However, nearly all of the energy used by
society originally came for the sun and
was stored in plants.
When calculating the efficiency of
photosynthesis, what factors increase
the uncertainty of these measurements?
When calculating the efficiency of
photosynthesis, what factors increase the
uncertainty of these measurements?
1. Amount of light reaching the leaf
2. Amount of light absorbed by leaf
3. The rate at photosynthesis can occur
Joffre Power Plant
Red Deere
Using the ‘waste’ thermal energy from a
electric power plant to heat buildings,
greenhouses etc. This can increase the
energy efficiency of a power plant from
40-80%!
Three benefits of saving energy:
 Saves money
 Reduces environmental pollutants
 Conserves natural resources
(especially non-renewables)