Transcript Energy in Roller Coasters - San Juan Unified School District

Roller Coasters:
Measures of Effort & Motion;
Conservation Laws
Who likes to ride a roller coaster?!
 Black Hole 2000
 California Screamin’
 Bizzarro
 Nitro
 Medusa
 Space mountain
 Splash mountain
 Big Thunder Railroad
1
Roller Coaster Project: Read handout
In groups of 3-4 make a list for each of
these on a piece of paper
 What do you want to know about the project?
 What physics stuff will you need to learn?
2
P 54
Investigation 1 (pp348-349):
Velocity and acceleration: The Big Thrill
 Sketch a roller coaster with a first hill of 15 m that quickly
descends to 6 m and then turns to the right in a big loop
(radius of 10 m) and then descends back to the ground.
P 55
3
p55
Compare to others:
 Copy the different sketches from 2 other people seated
around you.
 Circle the sketch you like the best
1.Which sketch is the best way to show a hill?
2.Which sketch is the best way to show a loop?
3.What other characteristics make the best sketch?
4
Two views: now create 2 views of the
same coaster.
 Side view (if you were standing on the ground looking at
the coaster
 Top View (if you were above the coaster in a balloon looking
straight down)
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5
A professional design team would like
your help on their roller coaster design
 Start with the side view. (p349). Move your finger along
the track as I read a description to you:
The Terminator Express Roller Coaster car begins from the loading
platform at A and then rises along the lift. It reaches the top of
hilltop #1 at B and then makes its first drop. It then goes into a
vertical loop at C. This clothoid loop (it has a big radius at the
bottom and a small radius at the top) allows the riders to be safely
upside down. The coaster then goes along the track through E, moves
into the backcurve to F, rises over hilltop #2 at G, and then swings
into a horizontal loop at I. The brakes are applied after the loop, and
the roller coaster comes to a stop at J.
 Now move your finger along the top view as I read the
description to you
6
A professional design team would like
your help on their roller coaster design
 Label each part of the track with the kind of
motion: at rest, constant motion, acceleration
(either speeding up, or slowing down, or
changing direction)
1. Which parts of the Terminator Express give the
most thrills?
2. What kind of motion is responsible for the most
thrills?
p56
7
Energy and Work ppt
 Use a computer to find this ppt file on my website.
teacher.sanjuan.edu/webpages/pdifilippo
click on physics
click on Energy in Roller Coasters
Click on file: Energy and Work ppt
 Answer all the questions on the handout.
 Then use the link on the last slide to Build Your Own
Roller Coaster (you must be in slideshow mode for the
link to work)
 Draw your successful coaster (both a top view and a side
view) and Get a stamp from your teacher before you
shut down your computer.
 Now answer PtoGo (p358-359) 1-5, 10 Get
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another stamp when Finished
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Nitro
p58
What happens to you when you
first get on a roller coaster?
From the time you step on until
you get to the top of the first big
hill…What happens first on
every roller coaster? Why?
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Investigation #2 (p360-363)
Which roller coaster track will give
the bigger thrill? Why?
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What effects the speed of the ball at
the bottom of the ramp?
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Mass of the marble
 Hypothesis:
 Data
Type of marble
 Summary:
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Velocity
Height of the ramp (angle of the ramp)
 Hypothesis:
Will 2X the height result in 2x the velocity?
 Data
height
1 brick (6.5 cm)
2 bricks (13.0 cm)
3 bricks (19.5 cm)
 Summary:
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velocity
Length of the ramp
 Hypothesis:
Will 2x the length result in 2X the velocity?
 Data
length
velocity
 Summary:
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Conclusions: What can you do to make
the marble speed up?
1.
2.
3.
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15
Conclusions: What can you do to make
the marble speed up?
1. Increase the length of the ramp
2. Increase the angle of the ramp
3. Increase the height of the ramp
(The velocity is related to the
square of the height of the ramp!)
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Work, defined
 Work carries a specific meaning in physics
 Simple form: work = force  distance
W=F·d
 Work can be done by you, as well as on you
 Are you the pusher or the pushee
 Work is a measure of expended energy
 Work makes you tired
 Machines make work easy (ramps, levers, etc.)
 Apply less force over larger distance for same work
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Work is Exchange of Energy
 Energy is the capacity to do work
 Two main categories of energy
 Kinetic Energy: Energy of motion
 A moving baseball can do work
 A falling anvil can do work
 Potential Energy: Stored (latent) capacity to do work
 Gravitational potential energy (a roller coaster at the top of the first hill)
 Mechanical potential energy (like in compressed spring)
 Chemical potential energy (stored in bonds)
 Nuclear potential energy (in nuclear bonds)
 Energy can be converted between types
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Conversion of Energy
 Falling object converts gravitational potential
energy into kinetic energy
 Friction converts kinetic energy into vibrational (thermal)
energy
 makes things hot (rub your hands together)
 irretrievable energy
 Doing work on something changes that object’s energy by
amount of work done, transferring energy from the agent
doing the work
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Energy is Conserved!
 The total energy (in all forms) in a “closed”
system remains constant
 This is one of nature’s “conservation laws”
 Conservation applies to:
 Energy (includes mass via E = mc2)
 Momentum
 Angular Momentum
 Electric Charge
 Conservation laws are fundamental in physics, and stem from
symmetries in our space and time
 Emmy Noether formulated this deep connection
 cedar.evansville.edu/~ck6/bstud/noether.html
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Energy Conservation Demonstrated
 Roller coaster car lifted to initial height (energy in) takes work
 This work converts gravitational potential energy at the top
 GPE converts to kinetic energy as it drops and picks up speed
 Fastest at bottom of track (no GPE left!)
 Re-converts kinetic energy back into potential as it climbs the
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next hill
Potential energy
 Potential energy (PE or GPE) is stored energy caused by




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gravity pulling an object downward
An object gets to this position because work was done to get
it up there
Work = Force x distance = (mass)(gravity)(distance)
PE = (mass)(gravity)(height)
Example: a 1.5 kg ball raised 1 meter above the table has
PE = (1.5)(10)(1) = 15 Joules of energy
Kinetic Energy
 The kinetic energy for a mass in motion is
K.E. = ½mv2
 Example: 1 kg at 10 m/s has 50 J of kinetic energy
 Ball dropped from rest at a height h (P.E. = mgh) hits the
ground with speed v. Expect ½mv2 = mgh
 h = ½gt2
 v = gt  v2 = g2t2
 mgh = mg(½gt2) = ½mg2t2 = ½mv2 sure enough
 Ball has converted its available gravitational potential energy
into kinetic energy: the energy of motion
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Kinetic Energy, cont.
 Kinetic energy is proportional to v2…
 Watch out for fast things!
 Damage to car in collision is proportional to v2
 Trauma to head from falling anvil is proportional to v2, or to
mgh (how high it started from)
 Hurricane with 120 m.p.h. packs four times the punch of gale
with 60 m.p.h. winds
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Energy Conversion/Conservation
Example
P.E. = 98 J
K.E. = 0 J
8m
P.E. =
K.E. =
6m
P.E. =
K.E. =
4m
2m
0m
25
P.E. =
K.E. =
P.E. =
K.E. =
p59
Energy Conversion/Conservation
Example
10 m
8m
P.E. = 98 J
K.E. = 0 J
 starts out with mgh = (1 kg)(9.8 m/s2)(10 m) = 98
P.E. = 73.5 J
K.E. = 24.5 J
6m
P.E. = 49 J
K.E. = 49 J
4m
2m
0m
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 Drop 1 kg ball from 10 m
J of gravitational potential energy
 halfway down (5 m from floor), has given up half its
potential energy (49 J) to kinetic energy
 ½mv2 = 49 J  v2 = 98 m2/s2  v  10 m/s
 at floor (0 m), all potential energy is given up to kinetic
energy
P.E. = 24.5 J
K.E. = 73.5 J
P.E. = 0 J
K.E. = 98 J
 ½mv2 = 98 J  v2 = 196 m2/s2  v = 14 m/s
Finish for next time:
p59
Read Active Physics p363-367
Answer CU (p367) 1-5
CDP 9-2
Get a stamp when finished
Notebook check and extra credit!
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Phet: Adventures in Energy Skate Park
Use a computer and open the phet sim:
Energy Skate Park
http://phet.colorado.edu/new/simulati
ons/sims.php?sim=Energy_Skate_Park
Complete the document Adventures in
Energy Skate Park
Get a stamp when finished
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p60
Welcome back!
 Let’s review…
 Generate ideas…What words/ phrases
can you use to describe a roller coaster
 Relay…only one person can write at a
time
 No one can take another turn until
everyone has had a turn
 The team with the most recorded wins
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Double your score!
Turn your paper over
Now generate ideas for our Energy
Model
What PHYSICS have we learned
about roller coasters? How do roller
coasters work?
Use full sentences this time!
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Review the Energy model
Driving question: How do roller coasters work?
Energy comes from doing work





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p
Energy model
Driving question: How do roller coasters work? p61
1. Energy comes from doing work
2. Gravitational Potential Energy (GPE) is the same as PE
3. Potential Energy (PE) is stored energy (must be higher than
the ground)
4. Kinetic Energy (KE) is energy in motion
5. Energy can be converted from one form to another
6. The total energy is always the same (Law of conservation of
energy)
7. PE=mgh= (mass)(gravity)(height)
8. KE=1/2 mv2=(1/2)(mass)(velocity)2
9. Twice the velocity means four times as much KE!
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PtoGo (p370)
1. For which track is the speed of the
car the greatest at the bottom? Why?
(assume no friction)
B
A
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PtoGo (p370)
2. State the Law of Conservation of
energy as it applies to roller coasters.
Include in your statement GPE, KE,
mgh, and ½ mv2
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p62
PtoGo (p370)
3.) Enlarged
Mass = 200 kg
g = 10 m/s2
Position/height
GPE = mgh
Top (30m)
Not moving
(200)(10)(30)
= 60,000 J
Bottom (7.5 m)
Moving fast
Top (15 m)
Moving slow
Bottom (5 m)
moving
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on handout
End (0 m)
Stopped/not
moving
KE = 1/2mv2
Total energy =
GPE + KE
PtoGo (p370)
p69
3.)
Mass = 200 kg
36
g = 10 m/s2
Position/height
GPE = mgh
KE = 1/2mv2
GPE + KE
Top (30m)
(200)(10)(30)
= 60,000 J
(½)(200)(0)
=0J
60,000 + 0
= 60,000 J
Bottom (0 m)
(200)(10)(0)
=0J
60,000 – 0
= 60,000 J
60,000 J
Halfway down
(200)(10)(15)
= 30,000 J
60,000-30,000
= 30,000 J
60,000 J
¾ way down
(200)(10)(7.5)
= 45,000 J
60,000 -45,000 60,000 J
=15,000 J
make an energy bar chart on your paper
(PtoGo (p370) #4)
4.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
GPE
KE
GPE + KE
A
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B
C
D
E
Finish PtoGo (p370) #5-10
p62
Next time, come prepared to
answer the following questions
about your project: partner’s
name, materials you will use to
build your coaster, intensity of
ride (mild, medium, or
high), target group of riders,
theme/decorations,
top and side views
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Energy Quiz #1 Thursday
Finish PtoGo (p370) #5-10
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Get your work stamped
p62
How many G’s can you take?
Apparent Weight
 Ride the roller coaster. What changes do you feel as the
coaster moves?
 What is a G-Force?
40
p64
Weight (or not to weight!)
p64
 What is weight? How is it measured?
 What will your weight be if you stand with one foot on each
of two bathroom scales? Explain
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 What is weight? How is it measured?
Weight is a force and force is equal to mass times acceleration
(newton’s second law…)
weight = mass x acceleration
 What will your weight be if you stand with one foot on each
of two bathroom scales? Explain
½ of the force will be on each scale, therefore each scale will
read ½ of that measured on one scale, But
THE TOTAL WEIGHT WILL BE THE SAME
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Calculate the weight:
1.) A football player with mass of 100 kg
2.) a student with mass of 42.5 kg
3.) an adult with mass 60 kg
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p64
What happens to your weight on an
elevator?
 Stays the same
 Goes up
 Goes down
Explain:
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P418 #4
Acceleration
(up, down, zero)
A. Elevator at rest on Zero
top floor
Scale reading
Explanation
(larger, smaller, same)
same
B. Elevator starts
moving down
C. Elevator moves
down at constant
speed
D. Elevator comes to
rest on the bottom
floor
E. Elevator is at rest
on the bottom floor
F. Elevator begins to
move up
up
larger
zero
same
G. Elevator moves
up at constant speed
H. Elevator comes to
rest on the top floor
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I. Elevator at rest on
the top floor
Explain how your weight changes (this
is called apparent weight)
 Objects travelling at constant velocity have no net force acting
upon them (therefore the force of their weight is equal and
opposite to some other force)
 Apparent weight is the net force acting on you in the direction of
earth
 If you are accelerating less than g=10 m/s2 then you “weigh” less
 If you are accelerating more than g=10m/s2 then you “weigh”
more
 If no acceleration (constant speed) then you weigh the same
(F=ma)
 Remember: air resistance is ignored to make the problems easier!
Now finish PtoGo (p418-419) 4-9
CU (p415) 1-5 Get stamps when you are finished!
p65
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Check your Answers:
PtoGo (p418-419) 5-9
5.) Down
6.) Up
7.) Down 10-1.5=8.5
W=(50)(8.5)=42.5N
8.) rest W=(50)(10)=500N
UpW=(50)(10+2)=600N
Constant speed
=(50)(10)=500N
9.) (in your own words)
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CU (p415) 1-5
1.) At constant speed the sum
of the forces is zero.
2.) apparent weight is more
when going up
3.) Going up gives you more
weight because there is more
force acting on you.
4.) in free fall there is zero
force
5.) air resistance slows things
down
Add to our energy model
p61
10. Apparent weight is the net force acting on
you in the direction of earth
11. This g-force (weight) can be compared to
gravity (10 m/s2 = 1g)
12. A safe roller coaster ride can have up to 5 g’s.
Astronauts and fighter pilots experience up to
10 g’s.
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p67
Where does a Popper toy Get it’s energy?
 Turn a popper toy inside out and PLACE it on the table.
Observe what happens.
 Once again compress the popper and DROP it onto the
table. Observe what happens.
 Record in your notebook and answer the following:
1.) What propelled the popper into the air?
2.) Will dropping the popper from greater heights make the
popper jump higher? Explain.
3.) Describe where the popper got the energy to move upward
and downward through the air.
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1.) What propelled the popper into the
air?
 When the popper
50
abruptly returns
to its original
shape, its elastic
potential energy
is transformed
into kinetic
energy and then
gravitational
potential energy
p67
2.) Will dropping the popper from
greater heights make the popper jump
higher? Explain.
 Yes, the popper has
more gravitational
potential energy when
it is dropped from a
greater height. This
results in a greater
energy
transformation.
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p67
3.) Describe where the popper got the
energy to move upward and downward
through the air.
 The popper’s source of energy is the work
done (provided by the elastic potential
energy) to deform it and the work done to
elevate it against earth’s gravity
(gravitational potential energy)
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p67
Active Physics p380-381) 1-13
1.)
Position above
table
EPE (J)
At rest on table
h= 0 m
25
Just after popping
h= 0 m
At peak
h= 0.60 m
½ way up
h= 0.30 m
h= (?)
h=(?)
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KE (J)
GPE (J)=mgh
Mass = 4.16g
Total energy=
EPE + KE + GPE
Active Physics
P to Go (p380-381) 1-13
2.
p67
30
25
20
EPE
KE
GPE
total
15
10
5
0
At rest
54
just after
popping
at peak
1/2 way
up
3/4 way
up
p68
Finish PtoGo (p380-381) 1-11
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Section 7 Investigation (p420-424)
1.) What makes you go in a circle?
 Demo air puck
 Water demo
Active Physics Section 7 Investigation p420
What do you think?
2.) Why don’t you fall out of a roller
coaster when it goes upside down in a
loop?
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Why don’t you fall out of a roller
coaster when it goes upside down in a
loop?
 Do Active Physics
Section 7 Investigation (p420-424)
 Part A: Moving in Curves (10 minutes only!) steps 1-4
 Part B: How much force is required? (10 more minutes!)
 Record answers in your notebook
 Share out
p68
 Answer CU (p429 (1-5)
57
Diagram of centripetal force on a roller coaster
Active Physics Section 7 Investigation (p420-421)
Part A: Moving in Curves
Steps 1-4
p68
1.) Objects want to travel in straight paths
2.) To make a curve you must apply a force towards the direction you
want the object to travel
3.) As soon as you stop applying the force the object will again continue
on a straight path
4.) (your diagram should look
something like the diagram
to the right)
 tutorial
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Active Physics Section 7 Investigation
(p422-424)
Part B: How much force is required?
 You have 10 minutes to follow the
directions and record as many answers
as you can (do at least 1-4)
 keep the string parallel to the floor!
 Get a stamp when finished
 Then we will share out…tomorrow
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p68
Part B (force and speed)
1a.) Centripetal force acts toward the
center of the circle (your fingers have
to exert force to keep the stopper
flying in a circle. If you let go, the
stopper would fly away in a straight
line)
1b. As you twirl the stopper at larger
speeds, your fingers tighten up to
supply a larger force (higher speeds
require more centripetal force).
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Part B (force and mass)
2a. As the mass (number) of the
stoppers on the end of the string
increases, you must supply a
bigger (centripetal) force.
2b. If you change more than 1
variable, you will not know what
causes the change. Therefore, you
must change only one variable,
the mass.
2c. As the mass increases, the
centripetal force required also
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increases.
Part B (Force and radius of circle)
3a. As you twirl the stopper in a
smaller circle, you tighten your
fingers to supply a larger
(centripetal) force.
3b.You must hold the mass and
the speed of the stopper
constant in order to compare
how changes in length affect the
required force.
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Part B (force and vertical circles)
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4b. The force your finger provide
(centripetal force) is less when the
stopper is at the top of the vertical
circle, and larger when it is at the
bottom.
4c. As the speed of the stopper decreases, the string
will eventually go slack, indicating that the string is
no longer exerting a force on the stopper. Then the
stopper will no longer travel on a circular path and
your fingers will not be providing any force to the
string.
Part B
5a. As the speed of a roller coaster increases, a larger
centripetal force is required to keep it moving in a circle at a
constant speed.
5b. As the mass of a roller coaster increases, a larger centripetal
force is required to keep it moving in a circle at a constant
speed.
5c. As the radius of the curve of the roller coaster decreases, a
larger force is required. If the radius increases, the required
force is smaller.
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Part B
6a.A very high speed would require a very large force.
6b. If there were zero speed, there would be no force required.
If you were going very slowly, a very small force would be
required.
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Part B
7a. (diagram)
7b. The velocity vectors should be tangent to the circle at each
position.
7c. The centripetal force vectors should always point toward the
center of the circle.
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Part B
8a. The gravitational force is always downward. At the bottom
of the loop, the normal force due to the track acting on the
car will be upward.
FN
Fg
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Part B
9a. The gravitational force vector should be pointing down.
9b. The force of the track (normal force) should be pointing up,
opposite the gravitational force vector.
9c. The force of the track pointing up (normal force vector)
should be larger than the weight (gravity vector) force acting
down
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Part B
10. The normal force at the bottom must be larger than the
weight to provide a net force upward toward the center of
the circle.
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Part B
11a. The force required to keep the roller coaster moving in a
circle would be very large. At the top of the loop for a roller
coaster going very fast, most of the downward force is
provided by the track. For a person sitting in a roller coaster
car, the downward force would be provided by the seat.
Depending on the speed of the roller coaster, at the top of
the loop, the riders may either feel that they weigh more than
the normal or less. In either case, the seat is pressing down
on the rider to accelerate the rider toward the center of the
circle.
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Part B
11b. The roller coaster goes slower at the top of the loop than at
the bottom, and at the top of the loop the weight contributes
to the force toward the center. This means that the loop does
not have to supply as much force at the top as it would at the
bottom. Therefore, the track would not have to be
constructed to withstand as much force at the top as at the
bottom.
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p69
Summary of forces in a circle
 Draw a large circle. Draw vectors and label the forces of gravity,
normal force, and centripetal force in 4 places (top, bottom, left,
right)
 force diagram for circular motion
top
left
right
FC = Fg + FN
Fg is the same everyplace
FN is the normal force of
the track pushing back on
the cart = the apparent weight
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bottom
Draw a force diagram for a fast-moving roller coaster using
the values in the chart below:
Centripetal force
Weight due to
gravity
Normal force
Top of loop
1000 N
4000 N
Bottom of loop
1000 N
10,000 N
p69
73
What is the apparent weight at the top? The bottom?
Draw a force diagram for a slow-moving roller coaster using
the values in the chart below:
Centripetal
force
Weight due
to gravity
Normal force
Top of loop
1000 N
1100 N
Bottom of loop
1000 N
7100 N
p69
What is the apparent weight at the top? The bottom?
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How do you calculate Fc?
p69
F c = Fg + FN
1.) What is the centripetal force of a roller coaster if the mass is 10 kg
and if the normal force is 25 N?
How do you find the speed in a loop?
Fc =
2
mv /r
r = radius
2.) How fast is a 200 kg roller coaster going if the radius of the loop is
200 m and the centripetal force is 100 N?
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3.) Why don’t you fall out of a roller coaster when it goes
upside down in a loop?
4.) So what keeps the roller coaster car on the track, and
why is a clothoid loop better than a circular loop?
 Clothoid loop: Larger radius at the bottom, smaller radius at the
top. Larger radius means smaller acceleration
 At the top of a small circle the normal force is smaller and as
speed decreases Fc becomes less and less. At the same point FN = 0
leaving a small gap between the car and the track. So Fc must be
greater than Fg to keep the car moving in a circle.
 At the bottom a small radius would contribute to greater
acceleration, beyond what a human body can withstand (4g’s = 40
m/s2). So to slow down the car a larger radius is needed (leading
to the clothoid shape instead of a simple circle).
Finish CU (p429) 1-5 and PtoGo (p433-435) 10-14 only
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p70
Loop-the-Loop: summary
 video
 In the loop-the-loop (like in a roller coaster), the velocity at the
top of the loop must be enough to keep the train on the track:
v2/r > g
 Works out that train must start ½r higher than top of loop to stay
on track, ignoring frictional losses
½r
r
 After watching the video, read over your notes from last time and
record 4 things you learned about loops in roller coasters (write
this at the end of the handout on the lines provided)
 Share out
77
Energy Model update
13. An object moving in a curved path must have a
force pointing toward the center of a circle, or it will
continue in a straight path. This force is called
centripetal force.
14. The normal force is the force that pushes back on an
object and is equal to the apparent weight
15. Centripetal force Fc = mv2/r
16. Centripetal acceleration ac = v2/r
17. For objects travelling in a circular path at a constant
speed, the centripetal acceleration and force are
p61
always perpendicular to the object’s velocity
78
Energy Quiz #2 tomorrow
 Roller Coaster Design due tomorrow
 Finish p70 from yesterday
p71
 Complete this problem
Mass of car = 200 kg
Position of car=
height (m)
g=10 m/s2
GPE=mgh
KE=1/2mv2
GPE+KE= total
energy
Top (30 m)
Bottom (0 m)
Halfway down
7.5 m
79
 Do PtoGo (p380-381) 3-11
How fast is the
car going?
p
Energy “rules”!
List 3 rules that you used to
complete the worksheet last time:



Share out. What other “rules” were shared by your classmates?




80
Friday
1.) QUIZ! You may use your notebooks, but no phones!
2.) Finish p70-72. Get stamps when done!
________________________________________________
3.) Turn in My Roller Coaster Plan (one per team)
5.) NRG SK8TR. Use a computer to complete handout. Get a
stamp when finished. This is page 73.
6.)Extra credit due Monday before school (when we return)
HAVE A GREAT WEEK!
81
Welcome Back!
p
What do you need to do to pass this
class?
The Main Event…
82
What is “the
main event”?
Describe at least 3
things other students
do to distract from the
“main event”
Describe at least 3 things
you do/allow to distract
you from the “main
event”
What are you doing/can
you do in physics to
demonstrate the “main
event”?
Section 8 Work and Power: Getting to
the top (p436-438)
 What do you see?
 What do you think?
 Does it take more energy to pull the RC up a steep
incline than a gentle incline?
 Why is it more difficult to walk up a steep incline
than a gentle incline?
 As a CLASS discuss/record #1
 As a lab group, go to your assigned lab bench
and collect the data, then return to your table
to make the graph (20 minutes total)
P75
83
Section 8 Work and Power: Getting to
the top (p436-438)
 #2-4 Use equipment to fill
in the chart below
Distance
(cm along
ramp)
Force
(in Newtons)
Now make a line graph
of your data (put a graph
stamp in your notebook!)
30 cm
40 cm
50 cm
force
60 cm
70 cm
80 cm
90 cm
100 cm
84
110 cm
p75
Distance (cm)
p75
Sample data
work
force vs distance
1.6
Distance x
Force =
30
1.43
40
1.07
50
0.86
60
0.72
0.8
70
0.61
0.6
80
0.54
0.4
90
0.48
100
0.43
110
0.39
1.4
1.2
1
force vs
distance
0.2
0
0
100
200
Average
work
85
Calculate the amount of work for each data point
and then the average work
As a CLASS discuss/record sample
data/graph
p75
#5: As the ramp gets steeper, the force required to
get the car to the top is __________
#6 As the ramp gets steeper the amount of work
____
#7: What is the average work needed to move the
car up the ramp?
#8: Does it take more energy/work to pull a roller
coaster up a gradual ramp or a steep ramp?
Explain.
 Ppt notes (handout)
 Complete CDP 9-1 and get a stamp
86
Energy Quiz #2 corrections
Working at an advantage
 Often we’re limited by the amount of force we can apply.
 Putting “full weight” into wrench is limited by your mg
 Ramps, levers, pulleys, etc. all allow you to do the same
amount of work, but by applying a smaller force over a
larger distance
Work = Force 
=
Force

Distance
Distance
Mechanical advantage is a ratio of the
force required (or the distance the force is
applied over)
87
p76
Ramps
Exert a smaller force over a larger distance to achieve the same
change in gravitational potential energy (height raised)
Larger Force
Short Distance
M
88
Small Force
Long Distance
p76
Gravitational Potential Energy
 Gravitational Potential Energy near the surface of the Earth:
Work = Force  Distance
DW = mg  Dh
m
Dh
m
p76
89
Work Examples “Worked” Out
 How much work does it take to lift a 30 kg suitcase onto the
table, 1 meter high?
W = (30 kg)  (9.8 m/s2)  (1 m) = 294 J
 Unit of work (energy) is the N·m, or Joule (J)
 One Joule is 0.239 calories, or 0.000239 Calories (food)
 Pushing a crate 10 m across a floor with a force of 250 N
requires 2,500 J (2.5 kJ) of work
 Gravity does 20 J of work on a 1 kg (10 N) book that it has
pulled off a 2 meter shelf
P76
90
How much work?
p76
 To lift 100 kg 1 m?
W = Fd =mgd =
 To push 100 kg up a 10m ramp to a height of 1 m?
W = Fd = mgd =
Why is it easier to push something up a
ramp than lift it to the same height?
91
Ramp Example
 Ramp 10 m long and 1 m high
 Push 100 kg all the way up ramp
 Would require mg = 980 N (220 lb) of force to lift directly
(brute strength)
 Work done is (980 N)(1 m) = 980 N·m in direct lift
1m
 Extend over 10 m, and only 98 N (22 lb) is needed
 Something we can actually provide
 Excludes frictional forces/losses
p76
92
Power
 Power is simply energy exchanged per




unit time, or how fast you get work
done (Watts = Joules/sec)
One horsepower = 745 W
Perform 100 J of work in 1 s, and call it
100 W
Run upstairs, raising your 70 kg (700
N) mass 3 m (2,100 J) in 3 seconds 
700 W output!
Shuttle puts out a few GW (gigawatts,
or 109 W) of power!
93
Energy model:
94
p61
18.) Work = distance x force (and is equal to
the amount of PE at the top) Work is
measured in newton meters =joules
19.) The amount of work is dependent on
how high you must move an object, not the
path that you take to get it there (gradual
slopes require the same work as steep slopes)
20.)Power = work/time. Power is measured
in joules/second = watts
Section 9
Force and Energy: Different insights (p448-450)
 Together: Read /Answer p449 (6-9)
 Individually: Read p 441 and answer CU (p442) 1-5
 Then do PtoGo (p446-447) #2-6 and Energy at the
Amusement Park
 Get a stamp when finished
95
p77
PtoGo (p446-447) #2-6 Answers
2a.) no work (because the displacement is horizontal, not vertical)
b.) 30 J c.) 3000 J d.) 350 J
3. Conserve energy can also mean don’t waste energy
4. The force to lift the cart up the incline would have changed, so the
total work would have changed. The cart’s GPE at the top of the
ramp would be larger. The work in all the trials would be the
same.
5a.) 200000 J b.) 1333 watts
6.) The motor does positive work on the roller coaster to bring it to
its highest point. As the coaster goes down the hill, gravity does
the work to increase the KE (as the GPE decreases)…
p82
96
Section 9
Force and Energy: Different insights (p448-450)
p78
 What do you see? What do you think?
 Draw your concept map in your notebook. Just do #1-5
Roller
Coasters
Energy
Forces and
Interactions
 Go back to your Energy Model and highlight the important
terms.
 Add at least 20 terms from your Energy Model to your
concept map
 Get a stamp when finished
97
Concept map example
98
Section 10
Safety is required, but thrills are desired (p458460)
 What do you see?
p79
 What do you think?
 Does the knowledge that people can get hurt or die on a roller
coaster change the thrill of the ride?
 Would your answer change if you found out that one-half of all
roller coaster rides ended in the death of its passengers?
 As a class, discuss/record #1-6
 Read p464. Answer CU (p464) 1-4
 CU (p453) 1-5/PtoGo (p456-457) #1,2,6,7
 Get stamps when finished
 Notebook check and UNIT TEST NEXT TIME!
 Review/practice test posted on my website
99