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Lesson 39: Kinetic Energy & Potential Energy
Kinetic Energy
Work-Energy Theorem
Potential Energy
Total Mechanical Energy
We sometimes call the total energy of an object (potential and kinetic) the
total mechanical energy
of
an object.
●
“Mechanical” energy doesn’t mean that it always has to involve machines.
●
An apple falling off a cliff has
gravitational potential
and
kinetic energy
, so it
therefore has
mechanical energy
.
●
We will start off by looking at the individual kinds of energy, and then at how we can start to
join them together into one big idea.
Kinetic Energy
You’ve probably heard of
kinetic energy
in previous courses using the following definition and
formula…
Any object that is moving has kinetic energy.
E
k
= ½
m
v
2
E
k
= kinetic energy (J)
m = mass (kg)
v = velocity (m/s)
We’re going to keep on using that basic formula, but we do need to clear up the definition a little bit.
What is “any object”?
●
“Any object” just refers to anything that we can measure as having a
mass
.
●
This covers everything from small subatomic particles like electrons all the way up to
galaxies.
When they say “moving” we need to ask “Moving relative to what?”
●
Right now you’re sitting motionless at a computer screen, so you have no kinetic energy,
right?
●
This is true relative to the reference frame of the room you’re in. Isn’t the earth
spinning on its axis? Isn’t the whole planet moving around the sun?
●
You need to make sure that you are always sure about what your measurements are
being taken in relation to.
●
Most of the time we measure stuff relative to the surface of the earth, so things
are easier, but be careful.
8/6/2007
© studyphysics.ca
Page 1 of 7 / Section 6.1 & 6.2

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Example 1
: A pop can with a mass of 312g is sitting in the cup holder of my car as I drive down
Yellowhead at 68 km/h.
a)
Determine
how much kinetic energy it has relative to me in the car.
E
k
= ½ mv
2
But relative to me the pop can’s velocity is zero, so…
E
k
= 0 J
b)
Determine
how much kinetic energy it has relative to someone standing on the side of the
road.
E
k
= ½ mv
2
= ½ (0.312 kg) (19 m/s)
2
E
k
= 56 J
Also, be ready to manipulate this formula to solve for other variables…
Example 2
: Determine the velocity of a 150 kg cart if it has 3.60e4J of kinetic energy.
First, see if you can correctly solve the formula for “v”. This is one of the manipulations that
students commonly mix up! You should get…
v
=
2
E
k
m
=
2
3.60e4
150
=
21.9
m
/
s
The concept of kinetic energy can also come in handy if you need to perform calculations of the work
done, as the following example shows…
Example 3
: I am driving my 2500 kg Camaro down the street at 52 km/h. I notice that there is a school
zone ahead, so I hit the brakes to slow down to 24 km/h. If I slowed down over a distance 145 m,
determine
the average force applied by the brakes.
First, you’ll need to change those velocities from km/h into m/s…

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