class notes; 4.26.11.
Work and Horsepower
NO Quiz TODAY
Personal Horsepower Lab
Lab Due Wednesday
Thursday More information coming tomorrow!!
A couple more tickets available.-------------------Twins Physics Day
Early bus stuff
Dress for the weather
Leave at 8:30
http://www.ftexploring.com/energy/energy-1.htm
Lab is due tomorrow
Today during work time
Find out answers to questions
• Reading Notes (1 page )
– Gravitational Potential Energy
• Homework:
– Physics: Work (no angles)
– Check your understanding of Potential
Energy
Mechanical Work Equals ZERO
no change in speed no work
no change in height  no work
Force is ┴ to motion no Work
W=F*d
1 N m = 1 Joule
F
90°
• W = 0! Carrying a weight
corresponds to W = 0.
• F is perpendicular to d, θ = 90°:
• W = 0. IF you are pushing against an
immovable object, d =0 so W = 0!!
d
d =0
Gravitational Potential Energy
Both blocks acquire the
same gravitational
potential energy, mgh.
The same work is done
on each block. What
matters is the final
elevation, not the
path followed
Work = F * d
Using the force and the distance along the ramp
• The amount of work done by a force on any object is given
by the equation
Work = F d cosΘ
• F is the Applied force,
• d is the displacement
• θ is the angle between the F & d
Work and Potential Energy
The work done on the ball gives the
ball gravitational potential energy.
Gravitational potential energy =
mgh
Which Path Requires the Most
WORK?
• Suppose that a car
traveled up three
different roadways
(each with varying
incline angle or slope)
from the base of a
mountain
Vertical distance only affects the PE
•
•
•
•
The PE at the top of each is 30 J,
The work to move up each would be 30 J.
How can this be????
For Work use Force || to displacement!!
Fg
UP
d
Fg
UP
d
Fg
UP
d
Calculations:
Watts and Horsepower
• James Watt patented the
steam engine in 1769.
• To sell it, he needed to tell
people how many horses it
would replace.
• He measured how quickly
farm horses could do work.
• There are few horses that
actually produce exactly
one horsepower of
power.
POWER
Work, Power and Energy
• Notebooks 30 pts + 5 EC for vertical loops
• More Equations and Notes today
• Tomorrow is the last day to bring in Valleyfair
$$$41.50 and permission slip.
Work: The Transfer of Mechanical
Energy
• The baseball pitcher does work on the ball.
The ball gains kinetic energy.
• To do the greatest possible amount of work,
the greatest possible force
the greatest possible distance
Kinetic energy
• The amount of translational kinetic energy (from
here on, the phrase kinetic energy will refer to
translational kinetic energy) which an object has
depends upon two variables: the mass (m) of the
object and the speed (v) of the object. The
following equation is used to represent the kinetic
energy (KE) of an object.
•
• where m = mass of object
• v = speed of object
Units of work and energy
• Like work and potential energy, the
standard metric units of measurement for
kinetic energy is the Joule. As might be
implied by the above equation, 1 Joule is
equivalent to 1 kg*(m/s)^2.
Analyze the animation and use the principles of
work and energy to answer the given questions.
• Use energy conservation principles to determine the speed of
a 0.050-kg Hot Wheels car that descends from a height of
0.60-meters to a height of 0.00 meters. Assume negligible air
resistance.
•
• Use energy conservation principles to determine the speed of
a 0.050-kg Hot Wheels car that descends halfway down a
0.60-meter high hill (i.e., to a height of 0.30 meters). Assume
negligible air resistance.
•
• If the mass of the Hot Wheels car was twice as great (0.100
kg), then what would be the speed at the bottom of the 0.60meter high hill?
•
• If the 0.050-kg Hot Wheels car is brought to a rest over a
distance of 0.40 meters, then what is the magnitude of the
frictional force acting upon the car?
Which Path Requires the Most
Energy?
• Suppose that a
car traveled up
three different
roadways (each
with varying
incline angle or
slope) from the
base of a
mountain
Analyze the animation and use the principles of
work and energy to answer the given questions.
• Use energy conservation principles to determine the speed of
a 0.050-kg Hot Wheels car that descends from a height of
0.60-meters to a height of 0.00 meters. Assume negligible air
resistance.
•
• Use energy conservation principles to determine the speed of
a 0.050-kg Hot Wheels car that descends halfway down a
0.60-meter high hill (i.e., to a height of 0.30 meters). Assume
negligible air resistance.
•
• If the mass of the Hot Wheels car was twice as great (0.100
kg), then what would be the speed at the bottom of the 0.60meter high hill?
•
• If the 0.050-kg Hot Wheels car is brought to a rest over a
distance of 0.40 meters, then what is the magnitude of the
frictional force acting upon the car?
Work
Work = Force x Distance
F = 500 pounds (2000 N)
D = 8 feet (2.5 meters)
-----------------------------------
W = 2000 N x 2.5 m
= 5000 N-m
----------------------------------Alternative unit: Joule
1 N-m = 1 joule (J)
Work
Work = Force x Distance
If the wall doesn't move,
the prisoner does no work.
Energy
Work is done on the bow.
The work done is stored
in the bow and string as
elastic potential energy.
After release, the arrow is
said to have kinetic
energy, 1/2 mv2.
Energy is measured in the
same units (joules) as
work.
Energy Transformation
The work done in lifting the mass
gave the mass gravitational
potential energy.
Potential energy then
becomes
kinetic energy.
Kinetic energy then does work
to push stake into ground.
Energy Transformation
• Power = Work/ Time
1 joule / second = 1 watt
Power
Total mechanical energy
• As discussed earlier, there are two forms
of PE discussed in our course gravitational potential energy and elastic
potential energy. Given this fact, the above
equation can be rewritten:
• TME = PEgrav + PEspring + KE
Total
Mechanical
energy
stays the
same
until it hits
the water.
Work and Energy
How High Will It Go?
The motion of the sled in the animation below is similar to the
motion of a roller coaster car on roller coaster track.
• As on a roller coaster, energy is transformed from potential
energy to kinetic energy and vice versa. Provided that external
forces (such as friction forces and applied forces) do not do
work, the total amount of mechanical energy will be held
constant.
Energy Conservation on an Incline
• If air resistance is neglected, then it would be
expected that the total mechanical energy of
the cart would be conserved. The animation
below depicts this phenomenon (in the absence
of air resistance).
•
Total mechanical energy is constant
conservative force 
gravity transfers PE-KE
• The diagram below depicts the motion of Li
Ping Phar (esteemed Chinese ski jumper) as
she glides down the hill and makes one of her
record-setting jumps.
Measurement of Horsepower
• The maximum horsepower
developed by a human being over
a few seconds time can be
measured by timing a volunteer
running up the stairs in the lecture
hall.
• If a person of weight W runs up
height h in time t, then h.p. = Wh/t
X 1/550 ft-lbs/sec.
• A person in good shape can
develop one to two horsepower. It
will be entertaining to the students
if the professor tries it too.
• Should the person be allowed a
running start?
http://www.physics.ucla.edu/demoweb/demomanual/mechanics/energy/faith_in_physics_pendulum.html
http://www.physics.ucla.edu/demoweb/demomanual/mechanics/uniform_circular_motion/index.html
Height at A = 60m
The car's mass is 500kg.
• A roller coaster with two loops and a small
hill, see diagram below
• In the diagram A is the highest point of the coaster, B
is 3/4 height of A, C is 1/2 of A, D is 1/4 of A, E is the
ground level, and F is 1/8 of A.
Point
(A-F)
Height
(m)
PE
(J)
KE
(J)
TME
(J)
Speed
(m/s)
PE = mgh
HA = 60m
2
Speed
use
KE
=
½
m
v
m =500kg
KE = TME (previous) – PE
A
to
F
A
h
(m)
60
B 45
C 30
D 15
E 0
F 7.5
PE
(J)
KE
(J)
(500(9.8)(60) =
294,000-294,000=
294,000 J
0 Joules
TME
(J)
Speed
(m/s)
294,000J
0 m/s
PE = mgh
KE = ½ m
2
v
HA = 60m
m =500kg
A
to
F
A
PE
(J)
h
(m)
60
B 45
PE = mgh
Speed use KE = ½ m v2
KE = TME (previous) – PE
KE
(J)
TME
(J)
Speed
(m/s)
0 m/s
(500(9.8)(60) =
294,000-294,000=
294,000 J
0 Joules
294,000J
(500(9.8)(45) =
294,000-220,500 =
294,000J
220,500 J
73,500J
17.1 m/s
Equation:
KE = ½ m v2
Substitute:
73,500J = ½ 500kg v2
X 2 …/ by 500…take √ ..
v= 17.1 m/s
Mechanical Energy Equations
Page 7 section #3
W1Force of Gravity pulls down
W1
Mechanical Work  PE  KE
TME does not change
W4
W2
W4
The transfers
W1 of energy
during the
1st Bounce
W4
W2
W3
W2Force of Gravity pulls down
W1
Mechanical Work  PE  KE
TME does not change
W4
W2
W3
W3ball compressed
W1 Mechanical Energy lost to HEAT
TME does change
W2
W4
W3
W1
W4Force of Gravity pulls down
Mechanical Work  KE  PE
TME does not change
W4
W2
W3
Notice the speed change
Missing mechanical energy??
Energyinitial – Energyfinal = Energylost
Frictional Work
• According to the Cedar Point
website the maximum speed
of the Magnum XL-200 is 72
mph not 76 mph as we
calculated above.
• The difference is due to
frictional forces acting on the
roller coaster cars.
• Assuming that the mass of a
loaded roller coaster car is 600
kg what is the frictional (nonconservative) work done on
the car by the track?
Analyze the
transfers of
energy
during the 1st
Bounce
Work on
incline
• Answer the following about the above picture:
• Draw the three forces acting on the object.
• If the object slides down the incline, what work
was done with gravity?
• What work is done against the motion?
• What is the net work done?
• Predict the final velocity of the object.
Mechanical Energy
Follow the bouncing ball
Bouncing balls
•
• When a ball is dropped, it transfers its GPE to
kinetic energy. As the ball hits the floor, its
kinetic energy is turned into elastic potential
energy (and some heat, and noise). High speed
photography can show how the ball gets
deformed.
• The elastic potential energy is transferred to
kinetic energy as the ball bounces. Some
energy is lost as heat as the ball bounces, so it
does not achieve the height from which it was
dropped.
Bouncing balls
• different types of balls at room
temperature and when they are frozen.
• When a ball is dropped on a surface,
molecules in the ball can deform or absorb
the kinetic energy of the fall. If they return
to their original shape they push the ball
away from the surface. If the energy is
absorbed, the ball does not bounce.
Bouncing balls
Bouncing balls
Conservative and non-conservative
work
•
Forces can be categorized as internal forces or external forces. There are
many sophisticated and worthy ways of explaining and distinguishing
between internal and external forces. Many of these ways are commonly
discussed at great length in physics textbooks. For our purposes, we will
simply say that external forces include the applied force, normal force,
tension force, friction force, and air resistance force. And for our purposes,
the internal forces include the gravity forces, magnetic force, electrical
force, and spring force.
Internal Forces External Forces
Fgrav
Fspring
Fapp
Ffrict
Fair
Ftens
Fnorm
In the following descriptions, the only forces doing work upon the objects are internal
forces - gravitational and spring forces. Thus, energy is transformed from KE to PE (or vice
versa) while the total amount of mechanical energy is conserved. Read each description an
indicate whether energy is transformed from KE to PE or from PE to KE.
•
Description of Motion
KE to PE or PE to KE?
Explain.
• 1. A ball falls from a height of 2 meters in the absence of air
resistance.
•
• 2.A skier glides from location A to location B across a friction free
ice.
•
• 3.A baseball is traveling upward towards a man in the bleachers.
•
• 4.A bungee cord begins to exert an upward force upon a falling
bungee jumper.
•
• 5.The spring of a dart gun exerts a force on a dart as it is launched
from an initial rest position.
resistance and tension forces) doing work upon an object. Read the description
and indicate whether the object gained energy (positive work) or lost energy
(negative work). (NOTE: If this is part is difficult, review the section on work.)
Then, indicate whether the gain or loss of energy resulted in a change in the
object's kinetic energy, potential energy, or both. Click the buttons to view
answers.
Description
+ or - Work?
Change PE or
KE or Both?
• Megan drops the ball and hits an awesome forehand. The racket is
moving horizontally as the strings apply a horizontal force while in
contact with the ball.
• A tee ball player hits a long ball off the tee. During the contact time
between ball and bat, the bat is moving at a 10 degree angle to the
horizontal.
•
• Rusty Nales pounds a nail into a block of wood. The hammer head
is moving horizontally when it applies force to the nail.
• The frictional force between highway and tires pushes backwards on
the tires of a skidding car.
• A diver experiences a horizontal reaction force exerted by the blocks
upon her feet at start of the race.
Work out due to friction
6th section
Mechanical Energy Equations
A boulder resting at the top of a hill has
potential energy.
Potential energy changes to kinetic
energy due to work done by gravity
PE
Roller coaster W/P/E
• The Work pulling the coaster to the top of the
1st hill is the Potential Energy at the top of the
hill and the Energy available for the entire ride.
• The total mechanical energy at any point of the
roller coaster is the PE + KE if there were no
frictional forces
KEinitial + PEinitial + Wexternal = KEfinal + PEfinal
Energy Transformation on a
Roller Coaster
A GIF Animation
A roller coaster ride also
illustrates the work-energy
theorem.
• The theorem is often stated in the form of the
following mathematical equation.
• KEinitial + PEinitial + Wexternal = KEfinal + PEfinal
• The left side of the equation includes the total
mechanical energy (KEinitial + PEinitial) for the initial
state of the object plus the work done on the
object by external forces (Wexternal) while the right
side of the equation includes the total mechanical
energy (KEfinal + PEfinal) for the final state of the
object.
A roller coaster ride also
illustrates the work-energy
theorem.
• KEinitial + PEinitial + Wexternal = KEfinal + PEfinal
Frictional Work
• Frictional Work
• According to the Cedar Point
website the maximum speed of
the Magnum XL-200 is 72 mph
not 76 mph as we calculated
above. The difference is due to
frictional forces acting on the
roller coaster cars. Assuming
that the mass of a loaded roller
coaster car is 600 kg what is
the frictional (nonconservative) work done on
the car by the track?
Test Form A
Mass = 800 kg
Test Form B
• 1. Find the Total Mechanical Energy at the
end of the first horizontal platform.
• 2. Find the Acceleration on platform
• vf
2=
vi
2+
2ad
• Then Find g’s
• 6.
radius = 30 meters
Height at A = 60m
• a roller coaster with two loops and a small hill, see
diagram below
• In the diagram A is the highest point of the
coaster, B is 3/4 height of A, C is 1/2 of A, D is 1/4
of A, E is the ground level, and F is 1/8 of A. The
car's mass is 500kg.
Point
Height(m) PE(J)
KE(J)
TME(J)
Speed
(m/s)
coaster
Roller coaster W/P/E
• The Work pulling the coaster to the top of the
1st hill is the Potential Energy at the top of the
hill and the Energy available for the entire ride.
KEinitial + PEinitial + Wexternal = KEfinal +PEfinal
• The Total Mechanical Energy at any point of the
roller coaster is the PE + KE if there were no
frictional forces
Energy Transformation on a
Roller Coaster
A GIF Animation
Height at A = 60m
The car's mass is 500kg.
• A roller coaster with two loops and a small
hill, see diagram below
• In the diagram A is the highest point of the coaster, B
is 3/4 height of A, C is 1/2 of A, D is 1/4 of A, E is the
ground level, and F is 1/8 of A.
Point
(A-F)
Height
(m)
PE
(J)
KE
(J)
TME
(J)
Speed
(m/s)
PE = mgh
HA = 60m
2
Speed
use
KE
=
½
m
v
m =500kg
KE = TME (previous) – PE
A
to
F
A
h
(m)
60
B 45
C 30
D 15
E 0
F 7.5
PE
(J)
KE
(J)
(500(9.8)(60) =
294,000-294,000=
294,000 J
0 Joules
TME
(J)
Speed
(m/s)
294,000J
0 m/s
PE = mgh
KE = ½ m
2
v
HA = 60m
m =500kg
A
to
F
A
PE
(J)
h
(m)
60
B 45
PE = mgh
Speed use KE = ½ m v2
KE = TME (previous) – PE
KE
(J)
TME
(J)
Speed
(m/s)
0 m/s
(500(9.8)(60) =
294,000-294,000=
294,000 J
0 Joules
294,000J
(500(9.8)(45) =
294,000-220,500 =
294,000J
220,500 J
73,500J
17.1 m/s
Equation:
KE = ½ m v2
Substitute:
73,500J = ½ 500kg v2
X 2 …/ by 500…take √ ..
v= 17.1 m/s
TME = KE + PE
800 kg
h
(m)
PE
(J)
Speed
m/s
KE
(J)
TME
(J)
Top of 1st hill (Need to first find the TME available)
80 m
10 m/s
800(9.8)(80)=
627,200 J
PE = mgh
½ (800)(10)2=
40,000 J
667,200 J
KE = ½ m v2
TME = KE + PE
800 kg
h
(m)
Stays same if no
friction
PE
(J)
Speed
m/s
KE
(J)
TME
(J)
Speed at the bottom of the 1st hill
0 m
??
0 J
PE = mgh
667,200 J
667,200 J
KE = ½ m v2
TME = KE + PE
800 kg
h
(m)
Speed
m/s
PE
(J)
KE
(J)
TME
(J)
Speed at the bottom of the 1st hill
0 m
40.8
0 J
667,200 J
667,200 J
Equation:
KE = ½ m v2
Substitute:
667,200 J= ½ 800kg v2
X 2 …/ by 800…take √ ..
v= 40.8 m/s
Coaster g’s
Back side: Save for tomorrow
Weight Equation
A boulder resting at the top of a hill has
potential energy.
Potential energy changes to kinetic
energy due to work done by gravity
PE
Use:
To convert from Newtons to kg
And from kg to Newtons
The Total Mechanical Energy
• As already mentioned, the mechanical energy
of an object can be the result of its motion (i.e.,
kinetic energy) and/or the result of its stored
energy of position (i.e., potential energy). The
total amount of mechanical energy is merely the
sum of the potential energy and the kinetic
energy. This sum is simply referred to as the
total mechanical energy (abbreviated TME).
• TME = PE + KE
• As discussed earlier, there are two forms of
potential energy discussed in our course gravitational potential energy and elastic
Mechanical Energy as the Ability
to Do Work
Sample PE calculation
A boulder resting at the top of a
hill has
potential energy.
Gravitational
Potential
Energy is the
energy
stored due to
height.
Work can
change the
height of the
Boulder
Work can
change the
potential
energy of the
Boulder
Potential energy changes to kinetic
energy due to work done by gravity
PE
4.17.09.notes
WPE Introduction
& Equation sheet
Hand in Valley Fair $$
and slip
Lab Question:
Who had the highest
Horsepower??
You may turn Lab in
today or Monday….
1st 0.73 Mike
3rd 0.95 Joey
4th 0.88 Parker
5th 1.01 Chris
6th 0.91
Seth
WPE Introduction
TODAY:
4-17-09
Notes and Equation Sheet
Valleyfair:
Friday, May15th --Passing by Friday 5pm
Cash By 7:30 am Friday May 15th
Book notes Pg. 224-231
½ page
New sheet
Mechanical Work Equations
in any direction
Page 7 section #1
To Do Work, Forces Must Cause
Displacements
•
•
To Do Work, Forces Must Cause Displacements
Let's consider Scenario C above in more detail. Scenario C involves a situation similar to the waiter who
carried a tray full of meals above his head by one arm straight across the room at constant speed. It was
mentioned earlier that the waiter does not do work upon the tray as he carries it across the room. The
force supplied by the waiter on the tray is an upward force and the displacement of the tray is a horizontal
displacement. As such, the angle between the force and the displacement is 90 degrees.
5th section
Mechanical Work Equations
Page 7 section #2
Who or What is applying the Force??
Mechanical work
and Energy
work is done upon an
object whenever
a force acts upon it
and
changes the height
or
changes the speed
The amount of work done is dependent height
A boulder resting at the top of a
hill has
potential energy.
• Gravitational
Potential
Energy is the
energy stored
due to height.
• Work can
change the
height of the
Boulder
• Work can
change the
potential
energy of the
Boulder
Mechanical Energy Equations
Page 7 section #3
Horizontal displacement does not
affect the gravitational PE
• Knowing that the potential energy at the top of
the tall pillar is 30 J, what is the potential energy
at the other positions shown on the hill and the
stairs.
Assignment
4.17.09
Lab report
due MONDAY
NOTEBOOK:
Book notes Pg. 224-231 (½ page)
Work and Energy Problems
Work and energy are Scalar, so we do
not use +/- on numbers for direction
Potential
energy
(height)
Work
Kinetic energy
(speed)
Work and Energy Problems
Work and energy are Scalar, so we do
not use +/- on numbers for direction
PE = mgh
W=F*d
KE = 1/2 mv2
• A ball starts from rest on top
of a tall pillar and falls to the
ground below. Assume the
effect of air resistance is
negligible.
• PEi = KEf
• (Since initially at rest, KEi = 0
and cancels. Since the final
height is 0, PEf = 0 and
cancels.)
Example from
6. A 50-kg platform diver hits the water below
with a kinetic energy of 5000 Joules. The height
(relative to the water) from which the diver dove
was approximately ____ meters.
*the potential energy change
*the work done.
5000 J
5000 J
Work and Energy Problems
Work and energy are Scalar, so we do
not use +/- on numbers for direction
PE = mgh
PE = 5000J
• W=F*d
• KE = 1/2 mv2
• KE = 5000 J
5000J=50(9.8)h
h=5000 /490
h= 10.2 m
• W = 5000 J
transferring
PE to KE
Example from
7. Using 1000 J of work, a small object is
lifted from the ground floor to the third floor
of a tall building in 20 seconds. What
power was required in this task?
•
the potential energy change
•
the work done
•
the power delivered
Work and Energy Problems
Work and energy are Scalar, so we do
not use +/- on numbers for direction
• PE = mgh
• PE = 1000J
• W=F*d
• KE = 1/2 mv2
• W = 1000 J
transferred
to PE
P=W/t
P=1000J / 20sec=50 Watts
4.20.09 notes
Work, Potential Energy & Problems
NOW. . . . .
Hand in Personal Horsepower Lab by 2:15
Hand in Valleyfair $$ and Slips together by 2:15
hOMEWORK Worksheet
Work time
A boulder resting at the top of a
hill has
potential energy.
• Gravitational
Potential
Energy is the
energy stored
due to height.
• Work can
change the
height of the
Boulder
• Work can
change the
potential
energy of the
Boulder
Potential energy changes to kinetic
energy due to work done by gravity
PE
Work to PE
or PE to work
• a force acts upon it
and
changes the height
Measurement of Horsepower
• The maximum horsepower
developed by a human being over
a few seconds time can be
measured by timing a volunteer
running up the stairs in the lecture
hall.
• If a person of weight W runs up
height h in time t, then h.p. = Wh/t
X 1/550 ft-lbs/sec.
• A person in good shape can
develop one to two horsepower. It
will be entertaining to the students
if the professor tries it too.
• Should the person be allowed a
running start?
http://www.physics.ucla.edu/demoweb/demomanual/mechanics/energy/faith_in_physics_pendulum.html
A bouncing basketball captured with a stroboscopic flash at 25
images per second. Ignoring air resistance, the square root of the
ratio of the height of one bounce to that of the preceding bounce
gives the coefficient of restitution for the ball/surface impact.
Bouncing of ball
• If a soccer ball is dropped on
a hard surface, it will bounce
back to a height lower than
its initial position. Such kind
of motion is called the
bouncing of the soccer ball,
which plays an important role
in the motion of the ball. Let
us study the mechanism of
the bouncing of the ball in
• The relative
details.
bounciness of different
types of balls
• The coefficient of restitution is how you
quantify bounciness or give bounciness a
number, and you do that by dividing the
bounce height by the drop height, then
finding the square root of that. When...
Read more:
http://wiki.answers.com/Q/What_is_the_C
oefficient_of_Restitution_of_bouncing_a_b
asketball#ixzz1JW73FiKE
• As a result, a ball with smaller coefficient
of restitution rebounds to lower height in
successive bounces and a shorter time is
required for the ball to stop.
• For example, grass reduces the coefficient
of restitution of a soccer ball since the
bending of blades causes further loss of its
kinetic energy.
• Therefore, it would take a shorter time for
the soccer ball to stop if it is kicked on
grass instead of hard floor.
changing its temperature.
• We can also change the bounciness of a ball by changing its
temperature. Take two baseballs that bounce to about the same
height. Put one in the freezer for an hour and leave the other at
room temperature. Then compare their bounciness again. You
should notice that the room temperature ball bounces a little bit
higher. The cold ball would bounce about 80 percent as high as the
room temperature ball. Although the difference of bounciness is not
dramatic, it's enough to see that temperature can be a factor: it
could make the difference between a home run and a pop fly.
• However, the change in bounciness due to the change in
temperature is taken for granted for some sport. For example,
squash player rely on the pre-game warm up to warm up the ball as
well as the players.
Surface bounced on
• Example…grass reduces the coefficient of
restitution of a soccer ball since the
bending of blades causes further loss of its
kinetic energy. Therefore, it would take a
shorter time for the soccer ball to stop if it
is kicked on grass instead of hard floor.
COR
• Coefficient of restitution of a tennis ball is
0.712. Thanks ...
•
1910 soccer ball [ii]
1950 soccer ball [ii]
2004 Euro Cup ball [ii]
•
In the late 1980s, the leather casing ball was replaced by totally synthetic ball in soccer
competitions. The covering material of the totally synthetic ball is synthetic leather made from
polymer. For high quality ball, the casing is made of the synthetic leather panels stitched together
through pre-punched holes by waxed threads. The bladder of a totally synthetic ball is usually
1910
ball [ii]The ball is then
1950
soccer
ball [ii]
2004through
EuroaCup
ball [ii]
latexsoccer
or butyl bladder.
inflated
by pumping
air into its bladder
tiny hole
on the casing. The totally synthetic ball could resist water absorption and reliably maintain its
shape.
•
The Internal structure of a totally synthetic soccer ball [ii]
•
Nowadays, the official soccer rules called the "Laws of the game", which are maintained by the
International Football Association Board (IFAB), specify the qualities of the ball used in soccer
matches. According to the laws, the soccer ball should satisfy the following descriptions:
•
it is spherical in shape,
•
its casing is made of either leather or other suitable material,
•
its circumference is not more than 70 cm and not less than 68 cm,
•
its weight is not more than 450 g and not less than 410 g at the start of the match.
•
its pressure inside equal to 0.6 - 1.1 atmosphere at sea level.
Figure explaining the extra
pressure inside the soccer ball.
The relative bounciness of
different types of balls [iii]
• Energy change in the falling ball after release
until hitting on the ground.
(Note that here "G.P.E." and "K.E." stand for the
gravitational potential energy and kinetic energy
respectively.)
Work must be done in order to
distort an elastic object
•
. Therefore, if you pull a spring outward so that it become longer, some
energy must have been transferred from yourself to the spring. The energy
stored in an distorted object due to its deformation is called the elastic
potential energy. So, when talking about the elasticity of the ball, we are
indeed talking about the spring-like behavior of the ball. In other words, we
are considering the tendency of the ball to return to its original spherical
shape when it is being squeezed. Where does the elasticity of the ball come
from? The elasticity of a solid ball arises from the elasticity of the
constituting material which is due to the interatomic or intermolecular force
inside. In contrast, for air-filled ball like soccer ball, its elasticity is resulted
from the extra air pressure inside the ball. What happens to a ball after you
dropped it above a hard floor? The gravity pulls the ball toward the ground
and thus the ball falls leading to the lost of its gravitational potential energy.
By the law of conservation of energy, the ball must gain kinetic energy and
so it falls towards the ground with an increasing speed. Subsequently, the
ball hits the hard floor with a high speed. (Note that the ball always moves
with the downward acceleration of g = 9.8 m/s2 as it falls.)
The elasticity of an object
means
• the tendency of the object to return to its equilibrium shape, the
natural shape of the object with no net force applied on it, when it is
being deformed. And the force for the object to restore to its
equilibrium shape is called the restoring force, which is always
directed in opposite to the deformation of the object. Almost all real
rigid body are elastic, i. e. having certain extent of elasticity. A trivial
example of an elastic object is the spring. You probably have the
experience that a spring would tend to restore to its original size
when you stretch it to be longer. Scientist found that, providing the
deformation is not too large, the relationship between the distortion
and the restoring force is given by the Hooke's law:
"The restoring force exerted by an elastic object is proportional to
how far it has been distorted from its equilibrium shape."
The restoring force Fs on a spring in case of different extension.
Law of conservation of energy
•
In the law of conservation of energy, it was stated that:
"Energy can neither be created or destroyed but can only be changed from one form
to another."
Therefore, the amount of total energy in an isolated system must be constant. For
example, let us consider a piece of charcoal placed in an isolated room. If we burn
the charcoal, the chemical energy inside the charcoal is changed into the thermal
energy of the room. Then the temperature inside the room would be increased.
When the ball hits the ground, the ball exerts force on it. By the Newton's 3rd law of
motion, the ground exerts a force on the ball as well. The motion of the ball would be
stopped by the (stationary) hard floor resulting in the compression of the ball. So the
work done on the ball leads to the increase of the elastic potential energy of the ball.
That means some of the kinetic energy of the ball (which is converted from the
gravitational potential energy of the ball) is converted into the elastic potential energy
when the ball hits the ground. On the other hand, some of the kinetic energy is lost as
thermal energy during the impact due to either the internal friction of the ball or the
heating of the surface.
•
Energy change in the falling ball during the impact
After losing all the kinetic energy,
the ball becomes momentarily at
rest.
• The squashed ball would simply act like a compressed spring. The
ball pushes the ground with a restoring force proportional to its
displacement from the equilibrium position (Hooke's law). In
consequence, the ground pushes back the ball with a force of equal
magnitude but opposite in direction. Thus the ball bounces back in
upward direction. During the rebound, the stored elastic potential
energy is released as the kinetic energy of the ball which is then
converted to gravitational potential energy as the ball moves up.
Moreover, some of the elastic potential energy is lost again due to
friction or heat which results in slight heating of the ball. The ball
keeps on going upward until it comes to rest after losing all its kinetic
energy again. Due to the lost of some of the initial gravitational
potential energy into thermal energy, the ball cannot bounce back to
the original height.
What is the
Coefficient of Restitution?
(also called: Elastic Coefficient)
What is the slope of each of the graphs?
• Use the slope of the graphs to find the
Coefficient of Restitution, just like we did for
the Spring Constant.
• The Coefficient of Restitution tells us how
“springy” the ball is.
• The slope of the graph represents this
constant. The constant will be the same for a
given ball.
PE Bouncing Ball Lab
Work and Potential Energy and Problems
Patterns in graphs
Increasing/decreasing/ no change
Linear or curved line of best fit.
Bouncing ball lab
measure height at the first bounce up
and the second bounce
Work to PE
or PE to work
• a force acts upon it
and
changes the height
Measurement of Horsepower
• The maximum horsepower
developed by a human being over
a few seconds time can be
measured by timing a volunteer
running up the stairs in the lecture
hall.
• If a person of weight W runs up
height h in time t, then h.p. = Wh/t
X 1/550 ft-lbs/sec.
• A person in good shape can
develop one to two horsepower. It
will be entertaining to the students
if the professor tries it too.
• Should the person be allowed a
running start?
http://www.physics.ucla.edu/demoweb/demomanual/mechanics/energy/faith_in_physics_pendulum.html
Bouncing Ball
Bouncing a Ball
•
•
•
•
What you need:
a tennis ball
a basketball
a room without breakables
• Instructions:
Drop the tennis ball from waist height and see how high it bounces.
Drop the basketball from the same height and see how high it bounces.
Put the tennis ball on top of the basketball and drop them both at arms
length from waist height.
• Results & Explanation:
The tennis ball should bounce a lot higher than before. When the balls hit
the ground, momentum from the basketball was transferred to the tennis
ball making it go much higher than before.
Mechanical Work Equals ZERO
no change in motion  no work
Force is ┴ to motion no Work
W=F*d
F
90°
d
1 N m = 1 Joule
• W = 0! Carrying a weight
corresponds to W = 0.
• F is perpendicular to d, θ = 90°:
• W = 0. IF you are pushing against an
immovable object, d =0 so W = 0!!
d =0
Which Path Requires the Most
Energy?
• Suppose that a car
traveled up three
different roadways
(each with varying
incline angle or slope)
from the base of a
mountain
Vertical distance only affects the PE
•
•
•
•
The PE at the top of each is 30 J,
The work to move up each would be 30 J.
How can this be????
For Work use Force || to displacement!!
Fg
UP
d
Fg
UP
d
Fg
UP
d
Work = F * d
Using the force and the distance along the ramp
• The amount of work done by a force on any object is given
by the equation
Work = F d cosΘ
• F is the Applied force,
• d is the displacement
• θ is the angle between the F & d
Force not in same direction as
displacement:
we use the component in the
direction of the motion
• Let
be an unbalanced
force applied to an object,
and let d be a resulting
displacement.
Concepts
Involving
Work
F || = F * cos Θ
If F|| is the component of F along d, then the
WORK done by F, is given by W = F|| x d
Work = F * cos Θ * d
Work = F * d * cos Θ
Work is of the nature of a force times a distance !
Work = F║ d
But if Force not Parallel to motion:
Work done by a force parallel to the displacement
is
Work = F d cos Θ
Add Page 7 section #1
Mechanical Work Equations
Work on
incline
• Answer the following about the above picture:
• Draw the three forces acting on the object.
• If the object slides down the incline, what work
was done with gravity?
• What work is done against the motion?
• What is the net work done?
• Predict the final velocity of the object.
Units of Work
• Whenever a new quantity is introduced in physics, the standard
metric units associated with that quantity are discussed. In the case
of work (and also energy), the standard metric unit is the Joule
(abbreviated J). One Joule is equivalent to one Newton of force
causing a displacement of one meter. In other words,
• The Joule is the unit of work.
• 1 Joule = 1 Newton * 1 meter
• 1J=1N*m
• In fact, any unit of force times any unit of displacement is equivalent
to a unit of work. Some nonstandard units for work are shown below.
Notice that when analyzed, each set of units is equivalent to a force
unit times a displacement unit.
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
A trolley of mass 10 kg is pulled along the floor. The pulling force is 36 N, at an angle of 30� above the
horizontal. Ignore friction.
What other forces are acting on the trolley?
Gravity and normal reaction force.
What is the total vertical force acting on the trolley? Why can we say this?
Zero.
No vertical motion � zero vertical acceleration � Fy = 0.
What is the magnitude of the normal force?
The vertical forces are gravity, the normal force, and the vertical component of the pulling force.
Let's find the horizontal and vertical components of the pulling force:
Px = P cosq = 36 cos30 = 31 N
Py = P sinq = 36 sin30 = 18 N
The gravitational force (ie the weight of the trolley) is:
w = mg = 10 ×9.8 = 98 N
Now we either say that the total vertical force is zero:
Fy = w + N + Py 0 = -98 + N + 18 80 N = N or we can say that the forces up equal the forces down (but
be careful with sign and direction!)
up = down N + Py = w N + 18 = 98 N = 80 N
What is the total force acting on the trolley?
The vertical forces add to zero, the total force must be the horizontal pulling force, equal to 31 N
horizontally.
What is the acceleration of the trolley?
F = ma 31 = 10 a 3.1 m/s2 = a
The acceleration is 3.1 m/s2 horizontally, in the direction the trolley is being pulled.
diagram showing the forces
acting on a block that is
resting on an inclined plane
Measuring the coefficient of
friction on a flat surface
Measuring the coefficient of
friction on an inclined surface.
://en.wikibooks.org/wiki/How_To_Build_a_Pinewood_Derby_Car/Physics
FRICTION VS. PULLING ANGLE
• PURPOSE: To demonstrate how pulling angle affects the frictional
force, and to show that the minimum force required to pull an object
occurs when pulling at the angle of repose a, where the coefficient
of friction u=tana.
• DESCRIPTION: A wooden board of weight w, lying on a sandpaper
surface, is pulled at an angle a by a string connected to a spring
scale. The force F required to move the board is given by: F = w / [
(1/u)cosa + sina]. Differentiating F with respect to a, the minimum
force is seen to occur at the angle of repose, u=tana. Pulling
horizontally is definitely not the most efficient angle!
• SUGGESTIONS: Pull horizontally to determine u, then check the
angle of repose by tilting the sandpaper surface. Then pull at a
variety of angles to demonstrate that pulling at the angle of repose
requires the least force.
Moving objects can do work (bowling ball
displaces pins; hammer pushes in nail; car
creams cow) energy of motion = kinetic
energy.
Energy is the ability to do work
• Suppose a "bullet" of mass m moving at vo mushes into
a block of soft clay and experiences a constant force F
(decelerating at a constant rate, a).
•
• The force required to slow down the bullet is F = ma,
where a is the deceleration. The work done through the
distance s, W = Fs = mas.
• During the deceleration, v2 = vo2 + 2as; or as = 1/2(v2 vo2)
• or Work done ON OBJECT = . (would get same result
for non-constant F and a).
Potential energy changes to kinetic
energy due to work done by gravity
PE
A boulder resting at the top of a
hill has
potential energy.
• Gravitational
Potential
Energy is the
energy stored
due to height.
• Work can
change the
height of the
Boulder
• Work can
change the
potential
energy of the
Boulder
Example: PEKE
• You are standing on the edge of a cliff and
decide to push a rock that has a mass of
2kg off the edge with your foot. Using
conservation of mechanical energy,
determine how fast the rock is going just
before it impacts the ground 75m below.
Assume that there is no air resistance. If
you dropped a 20kg rock from the same
spot would the velocity be the same?
Driver’s Training and braking
• Speed of a car increased by
50%. By what factor will
minimum braking distance be
increased (ignore reaction
time)?
• Braking force same.
Therefore:
• Distance = 2.25times original
Mechanical Energy: traditional
definition = the ability to do work.
Work done in stopping a car:
The mechanical work done on the object = the
change in kinetic energy;
If W is positive, KE increases; IF W is negative,
KE decreases.
-- often called Work-Energy Theorem (Net work
done = change in kinetic energy
Work done by gravity
• Suppose a car of mass 1200 kg falls vertically a distance
of 24 m (starting from rest; i.e., voy = 0).
• (a) What is the work done by gravity on the car?
• Fgrav = mg; Dy = 24 m; Force and displacement in same
direction (down).
• Fgrav = Fnet
• because gravity is only force acting on car.
Using Work-Energy Theorem
• (b) Find final velocity of car.
• Using constant acceleration (g):
• Using Work-Energy Theorem:
•
•
• Plug in: v = 22 m/s.
A mass m is moving in a straight line at velocity vo. It comes into contact
with a spring with force constant k. How far will the spring compress in
bringing the mass to rest?
A spring exerts F proportional to x in both compression and extension
(for reasonable x).
Driver’s Training and braking
• Speed of a car increased by
50%. By what factor will
minimum braking distance
be increased (ignore
reaction time)?
• Braking force same.
Therefore: Distance = 2.25
times original
Both cases body uses chemical energy for muscles
to exert these forces (you get tired, need more
Twinkies to keep going)--in terms of mechanical
work performed: ZIP!
Work done holding the box up
Work, PE, KE
• In the diagram at left no work is done moving
an object along a horizontal direction when
there is no friction (recall Galileo's principle of
inertia. No force is required to keep an object
moving. A small amount of work is necessary to
start it moving and an equal amount is "given
back" when it is stopped.)
• Whether the motion is circular (as with the
pendulum), up a series of steps, or in one
horizontal movement followed by lifting the
height h, the work done is the same to raise the
object to a height h.
This is what we mean by "Path Independence".
Work, PE, KE
The spring has more mechanical
(elastic) potential energy when
compressed.
Pendulum
graph with low friction
• Energy slowly "leaks away" from
mechanical system
Pendulum --graph with high
friction
KE -- PE
• Assume the track is frictionless and the car
starts from rest.
• 1. At what position is kinetic energy the
greatest?
• 2. When placed in order of least amount of
kinetic energy to greatest, positions of the roller
coaster are; 3. At what position does ET = EP
only?
Work, KE,PE
• 4. A 50.0 kg crate is pushed 4.00 m across a
level frictionless surface with a force of 58.0 N.
The kinetic energy of the moving crate is?
• 5. An object is dropped from rest a certain height
above the floor. Its speed at the moment before
it hits the floor is independent of:
•
6. When work done on a frictionless horizontal
surface, all the work is transformed into:
Work, KE,PE
• 7. A sled slides down a snowy hill. As the sled
descends the hill the total mechanical energy;
• 8. A boy rides up a hill on his bike. As he
ascends the hill his kinetic energy;
• 9.Friction makes molecules vibrate with;
• 10. As potential energy of a closed or isolated
system increases, __________ decreases
Work, KE,PE
• 11. This type of energy is called "energy of
position"?
12. This type of energy is called the energy of
motion?
• 13. Which of the following is a unit for work?
• 14. A figure skater exerts an upward force of
25.0 N on his skating partner while he glides
35.0 m on the ice. How much work is done on
the lifted skater?
Work, KE,PE
• 15. Work is done when a rubber band is
stretched. Energy is then stored in the
band until it snaps back. The stored
energy is best known as ___________
energy
• 16. A crane raises a 20.0 N object above
the ground in 2.50 seconds. The work
done by the crane is 500 N. What is the
power output of the crane?
Work, KE,PE
• 17. For a free falling object, the ratio of the force of
gravity to the acceleration is:
• 18. Which two quantities are measured in the same
units? 19. A moving body must undergo a change of:
20. Two objects of equal mass are a fixed distance apart.
If the mass of each object would be tripled, the
gravitational force between the objects would?
•
Gravitational Potential Energy
Elastic Potential Energy
The Potential Energy in figures a, b,
and c are:
The Kinetic Energy is the energy an
object has by virtue of its motion. The
kinetic energy of an object of mass m
moving at a velocity v is , for pure
transitional motion.
II. Total Mechanical Energy
The Total Mechanical Energy of an object is
the sum of its kinetic and potential energies, .
total mechanical energy of the
system is conserved
• Law of Conservation of Energy: When the
work done on a system by non-conservative
forces is zero, then the total mechanical energy
of the system is conserved (i.e., constant).
Energy Transformation for a Pendulum
KE PE
No friction!!
• The conservation of mechanical energy is demonstrated in the
animation below. Observe the KE and PE bars of the bar chart;
their sum is a constant value.
•
Read each description and indicate
whether energy is transformed
from KE  PE or from PE  KE
• A ball falls from a height of
2 meters in the absence of
air resistance.
Read each description and indicate
whether energy is transformed from
KE  PE or from PE  KE
• A skier glides from location A to location B
across the friction free ice.
Read each description and indicate
whether energy is transformed from
KE  PE or from PE  KE
• A baseball is traveling upward
towards a man in the bleachers.
Read each description and indicate
whether energy is transformed from
KE  PE or from PE  KE
• A bungee chord begins to exert an upward
force upon a falling bungee jumper.
Read each description and indicate
whether energy is transformed from
KE  PE or from PE  KE
• The spring of a dart gun exerts a force on
a dart as it is launched from an initial rest
position.
The following descriptions involve external
forces indicate whether the gain or loss of
energy resulted in a change in the object's
kinetic energy, potential energy, or both
• Megan drops the
ball and hits an
awesome forehand.
The racket is
moving horizontally
as the strings apply
a horizontal force
while in contact with
the ball.
Read each description and indicate
whether energy is transformed from
KE to PE or from PE to KE
• A baseball player hits the ball into the
outfield bleachers. During the contact time
between ball and bat, the bat is moving at
a 10 degree angle to the horizontal.
Read each description and indicate
whether energy is transformed from
KE to PE or from PE to KE
• Rusty Nales pounds a nail into a block of
wood. The hammer head is moving
horizontally when it applies force to the
nail.
Read each description and indicate
whether energy is transformed from KE
to PE or from PE to KE
• The frictional force between highway and
tires pushes backwards on the tires of a
skidding car.
Read each description and indicate
whether energy is transformed from
KE to PE or from PE to KE
• A diver experiences a horizontal reaction
force exerted by the blocks upon her feet
at start of the race.
Read each description and indicate
whether energy is transformed from
KE to PE or from PE to KE
• A weightlifter applies a force to lift a barbell
above his head at constant speed.
law of conservation of the total
mechanical energy
• (i.e. if Wnc=0 then ET= constant).
• And then,
Work - Energy Theorem
• Let be the total mechanical energy of an
object at position one (1).
• Let be its total mechanical energy at
position two (2). The change in the total
mechanical energy, from position one to
position two, is .
non-conservative forces.
• Work - Energy Theorem: The change in
the total mechanical energy of a system
(or object), from position one to position
two, is equal to the work done on the
system (or object) by the non-conservative
forces.
How Far Will It Skid?
• This
mathematical
relationship
between
initial speed
and stopping
distance is
depicted in
the animation
Work and Energy--Energy Transformation for a Dart
• The animation shows that the energy of the dart/gun system is
initially present in the form of the elastic potential energy (PEs)
and gravitational potential energy (PEg). The springs of the dart
gun are compressed which accounts for the elastic potential
energy. Furthermore, the dart is initially elevated at a height of
1-meter above the ground which accounts for the gravitational
potential energy. The presence of these two initial forms of
energy are shown by the PEg and PEs bars of the bar chart.
External-internal forces
We categorize a force as internal or external because:
• internal forces conserve mechanical energy (keep same)
• external forces either add or remove mechanical energy
Internal Forces
External Forces
Fg
Fsp
FA
Ffr
Fair
FT
F┴
The Work-Energy Theorem
Internal vs. External Forces
Forces can be categorized as internal
forces or external forces.
External-internal forces
• The significance of categorizing
a force as internal or external is
related to the ability of that type
of force to change an object's
total mechanical energy when it
does work upon an object.
• When work is done upon an
object by an external force, the
total mechanical energy
changes of that object is
changed
conservation of mechanical energy-practice
• Example 1
• You are standing on the edge of a cliff and
decide to push a rock that has a mass of 2kg off
the edge with your foot. Using conservation of
mechanical energy, determine how fast the rock
is going just before it impacts the ground 75m
below. Assume that there is no air resistance. If
you dropped a 20kg rock from the same spot
would the velocity be the same?
conservation of mechanical energy-practice
• Example 2
• A 4kg block slides across a frictionless
table with a velocity of 5m/s into a spring
with a stiffness of 2500N/m. How far does
the spring compress?
Net force—
net work
• In the picture above, answer the following: The picture
represents a 2 kg object which starts from rest. The force
represents the net force.
– Describe the motion of the object for its first 10 m.
– Describe the motion of the object for the distance interval of 10 m to 15
m.
– Determine the acceleration of the object for the first 10 m.
– How long will it take the object to go the 10 m?
– What is the net work done over the 10 m interval?
– What is the object's speed at the end of the 10 m interval?
– What is the net work done from 10 m to 15 m?
– What is the object's speed at the end of the 15 m?
PE and KE and
work
• In the picture above, the object is rolling along the horizontal surface.
Answer the following:
• Describe the motion of the object when it leaves the edge of the surface.
• How long does it take the object to reach the ground?
• What is the speed of the object the instant before it hits?
• What is the initial gravitational U of the object?
• What is the initial EK of the object?
• What is the initial mechanical energy of the object?
• Draw a graph representing the change in EK of the object.
• On your graph, when will gravitational U equal EK.
• Draw a graph representing the mechanical energy of the object.
Elastic PE
and KE
• Two blocks, one with mass M and the other with mass m, are connected by
a light frictionless spring. You hold mass m and compress mass M. When
mass M is released, it rebounds with speed v. Mass M is compressed a
distance d. Using only the given variables and constants, answer the
following:
• What is the spring constant?
• What work is done to compress mass M?
• Draw a graph of the change in elastic U as the spring is compressed and
then released.
• What is the maximum speed of the object?
• What is its speed when it is compressed 1/3 d?
Work on
incline
• Answer the following about the above picture:
• Draw the three forces acting on the object.
• If the object slides down the incline, what work
was done with gravity?
• What work is done against the motion?
• What is the net work done?
• Predict the final velocity of the object.
Variables for power
The standard metric unit of power is
the Watt.
• Power is the rate at which work is done. It is the
work/time ratio. Mathematically, it is computed
using the following equation.
Variables for power
Energy Transformation for Downhill Skiing
• Along the inclined section of the run, the total
mechanical energy of the skier is conserved provided
that:
• there is a negligible amount of dissipative forces (such
as air resistance and surface friction), and
• the skier does not utilize her poles to do work and thus
contribute to her total amount of mechanical energy
Stopping Distance of a Hot Wheels Car When the Hot
Wheels car collides with the box and skids to a stop,
external forces do a significant amount of work upon the
car. The force of friction acts in the direction opposite the
car's motion and thus does negative work upon the car.
This negative works contributes to a loss in mechanical
energy of the car.
Summary of Energy Forms
Mechanical
Energy Type
Formula
Kinetic
Gravitational
Elastic
PEg = mgh
KE.PE and pendulum
http://www.hcc.hawaii.edu/distance/sci122/Programs/p19/p19.html
more there
Energy Tranformation
E = mgh3
E = mgh2 + 1/2 mv22
E=1/2mv12
E = mgh3
Energy Conservation
• TME is the sum of both
types of energy.
• TME is the same at all
points if there is NO
friction.
Elastic force
• the amount of force is directly proportional
to the amount of stretch or compression
(x); the constant of proportionality is
known as the spring constant (k).
Elastic potential energy
• There is a special equation for springs
which relates the amount of elastic
potential energy to the amount of stretch
(or compression) and the spring constant.
The equation is
Use 9.8 m/s/s to determine the
gravitational PE.
gravitational potential
energy
• These relationships are expressed by the
following equation:
• PEgrav = mass * g * height
PEgrav = m * g * h
• In the above equation, m represents the mass
of the object, h represents the height of the
object and g represents the acceleration of
gravity (approximately 10 m/s/s on Earth).
PE to KE in freefall
Forces on a spring
PE- gravitational and elastic
Kinetic energy
•
•
•
•
•
The amount of kinetic energy which an object has
depends upon two variables:
the mass (m) of the object
and the speed (v) of the object.
The following equation is used to represent the
kinetic energy (KE) of an object.
•
• where m = mass of object
•
v = speed of object
Units of work and energy
• Like work and potential energy, the
standard metric units of measurement for
kinetic energy is the Joule. As might be
implied by the above equation, 1 Joule is
equivalent to N-m
N = kg m/s/s
For elastic force, F= kx, Area
under curve from 0 to xf =
PE and
KE for
pendulum
PE and
KE for
horizontal
spring
Elastic potential
energy
The second form of potential energy which we will
discuss in this course is elastic potential energy.
Elastic potential energy is the energy stored in elastic
materials as the result of their stretching or
compressing. Elastic potential energy can be stored
in rubber bands, bungee chords, trampolines,
springs, an arrow drawn into a bow, etc.
The amount of elastic potential energy stored in such
a device is related to the amount of stretch of the
device - the more stretch, the more stored energy.
(a) Show that the system is nonconservative
(b) How much work is done by the
non-conservative force?
• Skier with Friction
• A skier of mass 80
kg starts from rest
down a slope
where h = 110 m.
The speed of the
skier at the bottom
of the slope is 20
m/s.
Potential
energy
problem
• 1. A cart is loaded with a brick and pulled at
constant speed along an inclined plane to the
height of a seat-top. If the mass of the loaded
cart is 3.0 kg and the height of the seat top is
0.45 meters, then what is the potential energy
of the loaded cart at the height of the seat-top?
Work problem
• . If a force of 15.0 N is used to drag the loaded
cart (from previous question) along the incline
for a distance of 0.90 meters, then how much
work is done on the loaded cart?
Kinetic energy problem
• 1. Determine the kinetic energy of a 1000kg roller coaster car that is moving with a
speed of 20.0 m/s
• If the roller coaster car in the above
problem were moving with twice the
speed, then what would be its new kinetic
energy?
Kinetic energy problem
• Missy Diwater, the former platform diver
for the Ringling Brother's Circus had a
kinetic energy of 15 000 J just prior to
hitting the bucket of water. If Missy's mass
is 50 kg, then what is her speed?
Kinetic energy problem
• 4. A 750-kg compact car moving at 100
km/hr has approximately 290 000 Joules
of kinetic energy. What is the kinetic
energy of the same car if it is moving at 50
km/hr?
Ben's power rating.
• Suppose that Ben Pumpiniron elevates his 80-kg body up the
2.0 meter stairwell in 1.8 seconds. If this were the case, then
we could calculate Ben's power rating. It can be assumed that
Ben must apply a 800-Newton downward force upon the stairs
to elevate his body. By so doing, the stairs would push upward
on Ben's body with just enough force to lift his body up the
stairs. It can also be assumed that the angle between the
force of the stairs on Ben and Ben's displacement is 0
degrees. With these two approximations, Ben's power rating
could be determined as shown below.
•
the expression for power can be
rewritten once more as
force*velocity. This is shown below.
• This new expression for power reveals that a
powerful machine is both strong (big force) and
fast (big velocity).
Work and power
practice
• 1. Two physics students, Will N. Andable and
Ben Pumpiniron, are in the weightlifting room.
Will lifts the 100-pound barbell over his head
10 times in one minute; Ben lifts the 100pound barbell over his head 10 times in 10
seconds. Which student does the most work?
Which student delivers the most power?
Explain your answers.
Work and power practice
• During the Personal Power lab, Jack and
Jill ran up the hill. Jack is twice as massive
as Jill; yet Jill ascended the same distance
in half the time. Who did the most work?
Who delivered the most power? Explain
your answers.
Work
and
power
practice
• 3. A tired squirrel (mass of 1 kg) does
push-ups by applying a force to elevate
its center-of-mass by 5 cm. Determine
the number of push-ups which a tired
squirrel must do in order to do a mere
1.0 Joule of work. If the tired squirrel
does all this work in 4 seconds, then
determine its power.
Work and
power
practice
• 3. A tired squirrel (mass of 1 kg) does pushups by applying a force to elevate its center-ofmass by 5 cm. Determine the number of pushups which a tired squirrel must do in order to
do a mere 1.0 Joule of work. If the tired
squirrel does all this work in 4 seconds, then
determine its power.
Work and power practice
• 4. If little Nellie Newton lifts her 40-kg
body a distance of 0.25 meters in 2
seconds, then what is the power delivered
by little Nellie's biceps?
Work and power practice
• Your monthly electric bill is expressed in
kilowatt-hours, a unit of energy delivered
by the flow of l kilowatt of electricity for one
hour. Use conversion factors to show how
many joules of energy you get when you
buy 1 kilowatt-hour of electricity.
Work and power practice
• An escalator is used to move 20
passengers every minute from the first
floor of a department store to the second.
The second floor is located 5-meters
above the first floor. The average
passenger's mass is 60 kg. Determine the
power requirement of the escalator in
order to move this number of passengers
in this amount of time.
• 9. Calculate the potential, kinetic, and
mechanical energies, velocity, work, and
power of the ball at the various locations.
Important equations used throughout this lab packet are listed below for reference.
PE  m gh
Eo  E f
•
W


KE
Important equations used throughout this
lab packet are listed below for reference.
• % KELOST =  100g = -9.8 m/s2
1
KE  mv 2
2
1 2
y  v o t  gt
2
KE  KE f  KEo
1 2
x  v o t  at
2
KE
% KELOST =
KE o
Key Terms
•
•
•
•
•
•
•
•
•
•
•
•
•
energy
chemical energy
sound energy
light energy
nuclear energy
potential energy
heat energy
mechanical energy
gravitational potential energy
point of reference
kinetic energy
Work-Energy Theorem
Law of Conservation of Energy
An Eskimo pulling a sled with a rope at
an angle θ to the horizontal.
•
Problem An Eskimo returning from a successful fishing trip pulls a sled
loaded with salmon. The total mass of the sled and salmon is 50.0 kg, and
the Eskimo exerts a force on the sled by pulling on the rope. The coefficient
of kinetic friction between the sled and the ground is 0.200.
(a) The Eskimo pulls the sled 5.40 m, exerting a force of 1.10 102 N at an
angle of θ = 0°. Find the work done on the sled by friction, and the net work.
(b) Repeat the calculation if the applied force is exerted at an angle of θ =
30.0° with the horizontal.
Figure 5.6 An Eskimo pulling a sled with a rope at an angle θ to the
horizontal. Strategy See Figure 5.6. The frictional work depends on the
magnitude of the kinetic friction coefficient, the normal force, and the
displacement. Use the y-component of Newton's second law to find the
normal force , calculate the work done by friction using the definitions, and
sum with the work done by the applied force without friction to obtain the net
work on the sled. Part (b) is solved similarly, but the normal force is smaller
because it has the help of the applied force app in supporting the load.