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ENERGY
Objectives: After completing this
module, you should be able to:
 Define
kinetic energy and potential
energy, along with the appropriate
units in each system.
 Describe the relationship between
work and kinetic energy, and apply
the WORK-ENERGY THEOREM.
Energy
What is energy?
You can see its effects,
but it is a difficult
concept to define.
Mechanical Energy
Energy = ability of an object
or a system which enables it
to do work
Energy is measured in
JOULES.
MECHANICAL ENERGY is
the energy due to the position
or the motion of something
Mechanical energy may be
either kinetic or potential.
Potential Energy
(PE)
Potential energy is
energy stored and
held in readiness
due to position.
For example:
A boulder sitting
atop a hill – has
“gravitational
potential energy”
(GPE) due to its
position (height)
The higher the rock is
sitting, the more
GPE it has.
To calculate gravitational
potential energy:
PE = (mass X g) X (height)
or
PE = m·g·h
Units:
mass in kg
“g” in m/s2
h in meters
Example Problem: What is the potential
energy of a 50-kg person in a skyscraper
if he is 480 m above the street below?
Gravitational Potential Energy
What is the P.E. of a 50-kg person at a height
of 480 m?
PE = mgh = (50 kg)(9.8 m/s2)(480 m)
PE = 235200 J
Kinetic Energy
Kinetic energy is the
energy of motion
To calculate KE:
KE = ½
2
mv
Where KE = kinetic energy
m = mass (kg)
v = velocity (m/s)
Examples of Kinetic Energy
What is the kinetic energy of a 5-g bullet traveling at 200
m/s?
K  mv  (0.005 kg)(200 m/s)
5g
2
1
2
1
2
KE = 100 J
200 m/s
What is the kinetic energy of a 1000-kg car traveling at
14.1 m/s?
K  mv  (1000 kg)(14.1 m/s)
1
2
2
1
2
KE = 99405 J
2
2
Law of Conservation of
Energy
Energy cannot be created
nor destroyed; it can only
be transformed.
Total energy remains
constant.
PE transformed to KE
At the top of the hill, the
cart has only PE.
Towards the middle of the
hill, the cart has equal
amounts of PE and KE.
At the bottom of the hill, all
of the PE has been
transformed into KE.
On a pendulum:
Can you think of a similar device used in
construction or on a playground?
On a roller coaster:
Conservation of Energy

TME Initial = TME Final
 Neglecting energy loss to friction/heat
initial (PE +KE) = final (PE + KE)
mghi + ½ mvi2 = mghf + ½mvf2
Conservation of Energy
Sample Problem 1

A child with a mass of 18 kg zooms down
from the top of a 2.5 m tall slide. What is
her speed at the bottom of the slide?
m=
hi =
hf =
vi =
vf =
Conservation of Energy
Sample Problem 2
Ivan throws a ball straight upward with an initial
velocity of 22 m/s. How high above the release point
will the ball rise? g = 10 m/s2
0
0
2
2
mgh1 + ½ mv1 = mgh2 + ½ mv2
Conservation of Mechanical Energy SP3
A skater has a kinetic energy of 57 J at position 1, the
bottom of the ramp. At position, 3, he comes to a stop for
just a moment so that he has 57 J of gravitational potential
energy.
E = 57 J
What is his kinetic energy at position 2, if his gravitational
potential energy at position 2 is 25.7 J?
PE = 25.7 J
KE = ??
Mechanical energy = K + GPE
E = 57 J
Work-Energy Theoremstates that whenever work is
done, energy changes.
Examples
Pushing a wagon- the force applied
becomes kinetic energy
Stretching a spring – your force puts
potential energy into the spring
Lifting an object – the work you put
into raising the object becomes GPE
The Work-Kinetic Energy Theorem
NET Work done by all forces = D Kinetic Energy
Wnet = ½ mv2final – ½ mv2initial
NET Work = D Kinetic Energy
How much more distance is required to stop if a car is
going twice as fast (all other things remaining the same)?
The work done by the forces stopping the car = the change in the kinetic energy
Fd = D½ mv2
With TWICE the speed, the car has
FOUR times the kinetic energy.
Therefore it takes FOUR times the stopping distance.
(What FORCE is doing the work??)
A car going 25 km/h will skid to a stop over a
distance of 7 meters.
If the same car was moving at 50 km/h, how
many meters would be required for it to come to
a stop?
The velocity DOUBLED, therefore the stopping
distance is FOUR times the original distance:
7 meters x 4 = 28 meters
Jacob pushes a Honda with mass
3135 kg from rest to a speed v,
doing 5450 J of work. The Honda
moves 15 m. Neglecting friction,
what is the final speed of the Honda.
Find the force with which
Jacob pushed the Honda.
A 12 g projectile is fired from a
cylinder 48.3 cm long to a speed
of 736 m/s. Use the work-energy
theorem to find average force on
the projectile in the cylinder.
An ice skater starting from rest
is pushed by another skater
with a constant force of 48 N.
How far must the force be
applied in order for her final
kinetic energy to be 351 J?
A truck with mass 2.29 X 10 3
kg takes 5.2 kJ of work to
move from rest to some final
speed in 20.7 m. Find the
final speed, neglecting friction.
Find the net horizontal force to
push the truck.
Energy Key Terms
 Mechanical
 Energy
 Kinetic
 Law
energy
of
Conservation of
Energy
energy
 Potential energy
 Work-energy
Theorem