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Energy
What is it?
It is how nature keeps score.
Like a “currency” of the
universe.
To cause a change requires energy
Dr. Joseph W. Howard
©Spring 2008
First Steps
How do we “measure” effort?
How do you get paid ($$$) in the world?
Job!
($$$)
Work!
Dr. Joseph W. Howard
©Spring 2008
Work & Energy
Technical Definition of Work
net
WORK = FORCE  DISTANCE = mad
ENERGY IS THE CAPACITY TO DO WORK.
It takes some work (energy) to cause a change.
Dr. Joseph W. Howard
©Spring 2008
Work Example
A donkey pulls a 10 kg box a distance of
5 m by applying a 90 N net force. How
much work has the donkey done?
Work = Net Force × distance
Work = (90 N) × (5 meters)
Work = 450 Ngm = 450 Joules
90N
10kg
5m
Dr. Joseph W. Howard
©Spring 2008
Conceptual Pitfall
Hoyt carries a very heavy boulder 10m across
the garden at a constant speed of 3 m/s. What
is the overall work done on the boulder?
Work = ZERO!!
3m/s
10m
Dr. Joseph W. Howard
©Spring 2008
Types of Energy
Kinetic & Potential Energies
KE is often thought of as
energy of motion
PE is often thought of as
energy of position
Dr. Joseph W. Howard
©Spring 2008
Gravitational PE
A 10 kg ball rests at the top of a set of
stairs. The stairs reach a height of 3 m
above the ground. What is the potential
energy of the ball?
P .E .  mgh
m

P .E .  (10kg )  9.8 2  (3m)
 s 
P .E .  294 N gm  294 Joules
Dr. Joseph W. Howard
©Spring 2008
Kinetic Energy
An oxygen atom has a mass of 2.66 10-23 g. If an
oxygen atom were moving at 200 m/s, what would
the kinetic energy of that atom be?
1
K .E .  mv 2
2
1
m

26
K .E .  2.66  10 kg  200 
2
s



K .E .  5.32  1022 Joules
Dr. Joseph W. Howard
©Spring 2008
2
Kinetic Energy
A 3-kg ball is rolling at a constant speed. If you had
to transfer 30 J of energy to the ball to cause this
motion, what must the velocity of the ball be?
1
K .E .  mv 2
m
2
2(30 kg 2  m)
2
s
v

1
2
3.0kg
30 J   3.0kg v 
2
m2
2
v  20 2
2(30 J )
2
v 
s
3.0kg
m
m2
2
v  4. 5
v  20 2
2(30 N  m)
2
s
s
v 
3.0kg
Dr. Joseph W. Howard
©Spring 2008
Law of Conservation of
Energy
Total energy in any process is
constant.
The energy may be transferred or
transformed, but not created nor
destroyed.
Dr. Joseph W. Howard
©Spring 2008
Law of Conservation of
Energy
Total Energy at
Total Energy at
the beginning of = the end of an
an event
event
Form of energies my change
Dr. Joseph W. Howard
©Spring 2008
Conservation of Energy
Consider a 20-kg ball rolling down a hill that is 5 m
high. How fast will the ball be moving when it
reaches the bottom of the hill?
KE  PE  KE
 PE
top
What energy here?
top
bottom
bottom
m

PEtop  (20kg )  9.8 2  (5m)  980 Joules
 s 
980 Joules  KEbottom
5m
The PE energy at the top
becomes the
KE energy at the bottom
1
980 Joules  (20kg )v 2
2
m
v  9. 9
s
What energy here?
Dr. Joseph W. Howard
©Spring 2008
Conceptual Pitfall
A young boy skates down each of the frictionless playground
ramps illustrated below. Which ramp will give the
skateboarding boy the fastest speed at the bottom of the
ramp?
h
A
D
C
B
Ramp A
Ramp B
Ramp C
Ramp D
Any Ramp, all ramps will produce the same speed
at the bottom.
Dr. Joseph W. Howard
©Spring 2008
Law of Conservation of
Energy
Total Energy at
Total Energy at
the beginning of = the end of an
an event
event
Form of energies my change
Dr. Joseph W. Howard
©Spring 2008
Conservation of Energy
A 5 kg bowling ball falls from rest a distance of 78.4 m.
How fast is the ball falling at that point?
What energy here?
KEtop  PEtop  KE bottom  KE bottom
1
mgh  mv 2
2
m
1
(5kg )(9.8 2 )(178.4m)  (5kg ) v 2
s
2
78.4m
3841.6 J  (2.5kg ) v 2
What energy here?
m2
v  1536.6 2
s
2
v  39.2
Dr. Joseph W. Howard
©Spring 2008
m
s
Conservation of Energy
Consider dropping a ball from a height of 15 m in a
vacuum. What is the velocity of the ball the instant it
strikes the ground?
What energy here?
15m
The PE energy at the top
becomes the
KE energy at the bottom
What energy here?
KEtop  PEtop  KE bottom  PE bottom
1
mgh  mv 2
2
m
1
m (9.8 2 )(15m)  m v 2
s
2
1 2
m
v  (9.8 2 )(15m)
2
s
v 2  2  (9.8
v  17.1
Dr. Joseph W. Howard
©Spring 2008
m
)(15m)
2
s
m
s
Conservation of Energy
A 5kg ball is rolling along a sidewalk with a
constant velocity of 3 m/s. Suddenly, the ball
encounters a 0.5 m dip in the sidewalk and then
continues rolling along a flat section of the
sidewalk. What will the velocity be for the ball
after it encounters the dip?
What energy here?
What energy here?
Dr. Joseph W. Howard
©Spring 2008
Conceptual Pitfall
Tracks A and B are of equal length and have hills of
the same curvature except A curves up and B curves
down.
If two identical balls are rolled
simultaneously with the same initial velocity,
which will reach the end of its track first?
A
B
a. A
b. B
c. same
Dr. Joseph W. Howard
©Spring 2008
Energy & Motion
A 10kg dog runs from a speed of 4 m/s up to a
speed of 10 m/s in 3 seconds. What is the dog’s
acceleration? How far does he run in those 3
seconds?
How much did the dog’s kinetic energy change?
How much work did the dog accomplish?
Dr. Joseph W. Howard
©Spring 2008
Two pumpkins of equal size and mass are dropped
off the roof of the Henson Science Hall. One lands
on the sidewalk and the other lands on the grass.
Which one of the following statements is true of
the force and impulse on the pumpkins as their fall
was stopped?
•
Both of the pumpkins experienced the same force and the same
impulse.
•
Both of the pumpkins experienced the same impulse, but the
pumpkin that hit the sidewalk experienced a greater force.
•
Both of the pumpkins experienced the same force, but the
pumpkin that hit the grass experienced a smaller impulse.
•
The pumpkin that hit the sidewalk experienced a greater force and
a greater impulse than the pumpkin that hit the grass.
•
The relationship between the impulses and forces on the pumpkins
can not be determined without knowing the height of the building.
Dr. Joseph W. Howard
©Spring 2008
Two water slides sit side by side at the water amusement park and these
both sit near a high dive tower, as shown below. Your annoying little
brother wants to do the ride that promises the fastest attainable speed
at the bottom. What recommendation can you make to your brother
about which ride should he should choose? Assume that there is no
friction on the slides and that air resistance is negligible.
Water slide A
High dive
Water slide B
Water slide B
Water slide B or the High Dive
High Dive
Water slide A
Any of the rides