Download Introduction To Sports Physics

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0. Introduction to Coaster Physics
Coaster Engineers & Energy
0.1 Mission Impossible ?
Riders sat in a giant ice cube and slid down an
iced over wooden ramp. The first US coaster
appeared in 1884 at Coney Island. The coaster
had a top speed of 10 mph. Before the Great
Americas and six flags, there existed thousands
of small local parks across the country. Most
went bankrupt during the Great Depression. Ask
an older Chicagoan (parents?) if they rode the
Comet or the Bob at the famous Riverview Park
before it closed in 1967. A man named Walt
Disney helped create a new surge in theme parks.
Advances in computer modeling and steel
technology promoted the rapid rise of steel
structure coasters. These new thrill machines
travel through twisted loops at speeds
approaching 100 mph and at g-forces usually
only experienced by astronauts. Great America
opened in 1976 with the Demon and Whizzer
rides. The park added the Tidal Wave (no longer
exists!) in 1978, then American Eagle in 1981,
followed by Shockwave (1988), Iron Wolf
(1990), Batman (1992), and the Raging Bull
(1999). Where else can you free fall over 100
feet all day for only a few bucks? If you want to
find the latest scoop on the best parks, check out
these certifiably awesome web sites:
Your team’s mission is to create the "ultimate"
roller coaster. Your thrill machine will include
loops, bumps, turns, and maybe even advanced
features like banked turns, camel backs, or
pretzel double loops. Instead of designing a
coaster, you might have the choice of building
your own kind of thrill ride. The final product
should conform to all project rules, be physics
accurate, and should have a death-defying
thrilling, yet safe appeal. So let's start coasting!
Is RAGING BULL the ultimate coaster?
Probably not. Each
year amusement parks
try to make the ultimate
ride, only to be foiled
the next year by a
competing park. What
would it take to make
the most thrilling
coaster? Certainly you
can’t do it by yourself.
It takes teams in the real world to make great
things happen. Certainly if you knew the
physics behind it all, you could probably invent
some cool new rides that might even be safe.
Web sites to wet your
Yes, I want to build the ultimate coaster park!
This text will help you and your teammates to
master everything you need to know. In
addition, it will hopefully offer interesting
insights and cool “did you know” sorts of
information about the world of coasters. Of
course you also have to do all the labs and
homework to build your knowledge. (You knew
there was a catch). Remember to consult your
book and your teacher whenever you hit a
roadblock. Don’t forget to teach your teammates
along the way and share your own experiences:)
appetite:
www.rcdb.com - over 600 coaster previewed
www.ultimaterollercoaster.com – news & rides
www.discovery.com/exp/rollercoasters/ - build it
http://www.sixflags.com/greatamerica/rides/
www.learner.org/exhibits/parkphysics/coaster.html
http://www.district86.k12.il.us/central/faculty/jvetrone/coasterphysics.html - our class web site!
www.coasterquest.com – how they work
www.thrillride.com – who builds them
www.fmcg.com/jmiller – famous coaster builder
www.ridezone.com – other rides, old & virtual
0.2 Theme Parks:
Amusement parks have thrilled the young and
old for many years. One of the first coasters was
built in St.Petersburg during the 15th century.
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0.3 Coaster ENGINEERS (you!)
To achieve the delicate balance between “death
defying excitement” and “absolute safety”, an
engineer must fully understand the laws of
physics and know which materials to use in
building a new ride. He must also consider cost,
safety, rider appeal, and environmental issues.
Of all these, safety cannot be compromised.
Theme parks are designed to prevent accidents,
but unfortunately no park is 100% safe.
How much power will it take to lift the
riders up the first hill?
5.
How do I make the track exactly the right
length so the ride slows to a stop without
using brakes? (a tough calculation?)
6.
What material should I make the ride out of
so it’s strong, not too heavy, and will last?
7. How do I ensure the riders won’t get hurt?
(you can’t make money if the rider gets maimed
or too sick so he never returns to your park)
On April 18, 1998, 15
people were stuck upside
down for 3 hours on the
Demon ride at Great
America. No one got hurt,
but many complained of
reoccurring nightmares and
headaches. Recently they
were awarded together a
sum of about $450,000 as compensation. The
accident was blamed on a wheel pin, which
vibrated loose and jammed the coaster.
8.
How do banks, rolls, & turns add thrill?
Add some of your own Now!
9.
10.
11.
Top 5 qualities you’ll need as a ride engineer
5.
4.
3.
2.
1.
4.
Know when and how to listen to others
Stay focused on your goals
Support and encourage team members
Speak up when you know you’re right
Know what you’re talking about
12.
13.
14.
You should try to polish these skills whenever
working with your team members, and especially
whenever the class does team-building events.
15.
0.4 Brainstorming Questions
16.
Here are some questions an engineer must try to
answer in designing the ultimate coaster.
Continue to reflect and talk to your teammates.
Write comments in the margin as you go along.
There are no wrong questions. Just remember to
stay focused on your mission and not get lost in
all the details of cool rides.
1.
What determines a ride’s maximum speed?
2.
How much will friction slow down the cars?
3.
Does friction cause any electrical problems?
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Project hint:
" your team should ask and
answer questions like these
as you design your ride! "
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0.5 Outline of Roller coaster Course
You could explain most of how a roller coaster works using only two principles: gravity and the law of conservation of
energy. But to actually know the velocity, acceleration, and forces on a coaster at any point, a coaster engineer must
know many more physics concepts. Here's an outline of what we will learn!
Coaster Questions
Physics Concepts
Math Equations
What is the coaster project?
Coaster Background Info
How can I determine the speed?
Energy (KE,PE)
What does it take to start & stop?
Work (forces, power, friction)
Why I feel pushed into my chair?
Horizontal G-Forces
(gravity,Newton's laws)
F = ma
Turns
(centripetal force, inertia, loops & turns)
a = v2/r
Why don't I fall out on turns?
Why do I feel sick on loops & bumps?
Vertical G-Forces
(projectiles, free body diagrams)
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KE = 1/2 mv2 PE = mgh,
PE + KE = PE + KE
Work= F*d
Power = Work/time
Weight = m*(g)
g’s (top) = a/-9.8 - 1
g’s (bottom) = a/9.8 + 1
CoasterFZYX
0.6 Review Questions
Roller Coaster History:
1.
In what country is St.Petersburg, site of the
first recorded coaster in the 1400’s?
2.
The first US coaster was when & where?
3.
This Chicago coaster park closed in 1967
4.
16. Which coaster at G.A. is known for its
continuous spiral of banked turns?
17. How many stories do you fall on Giant
Drop?
Which ride at Great America is older, Shock
Wave or the Demon?
18. How many times have you already asked
when are we going to Great America?
Mission Possible
5.
Besides making awesome rides, what other
considerations are there in designing a ride?
6.
How much cash did each person receive for
hanging upside down for 3 hours on the
Demon ride?(assume same amount for each)
7.
What safety devices exist on roller coasters?
8.
Suggest 4 categories for the types of rides
typically found at an amusement park
9.
Which qualities of a good engineer do you
feel match your work habits?
(answer – too many! - mid May )
10. Which qualities will you personally try to
work on to develop this quarter ?
Coaster Trivia
11. In what town is Great America located?
12. This ride at G.A. is often called spin & barf!
13. How many vertical & corkscrew loops are in
the Demon roller coaster?
14. Which roller coaster has 7 loops and the first
ever banked curve on the first drop?
15. Which coaster(s) at G.A. are made mostly of
wood?
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1. Running Roller Coasters
Energy
1.1 What makes the fastest coaster?
energy (screeches) and light energy (sparks).
During a collision, the car may bounce so it has
spring or elastic energy. If the car were jolted
off the ground, it would have potential energy.
Any time you lift an object, you increase its
potential energy. There also exists nuclear
energy inside the atoms making up the car, as
well as chemical energy between those same
atoms. Finally, if the car receives any permanent
damage (a dent or scratch), the car has
deformation energy.  Finally, if you add all
the types of energy an object has at any
particular moment, the sum is called the total
energy
Thrill parks attract visitors in part by having a
variety of rides. Some roller coasters use
wooden tracks with lots of hills and turns but no
loops. Steel coasters often flip the riders in
multiple loops and banked turns. Much of the
thrill of any coaster is going fast. Compare the
speeds of these coasters at Great America.
Fastest rides at Great America
Coaster
Raging Bull
Eagle
Shockwave
Iron Wolf
Vipor
Whizzer
Top Speed (mph)
72
66
65
55
50
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1.3 Conservation of Energy
The exciting part of energy is changing from one
type to another. As the bumper car moves
electrical energy (electricity) is converted to
kinetic energy (motion). As a coaster goes down
a hill it gives up potential energy (height), and
gains kinetic energy (speed). Unfortunately,
energy can not be entirely converted to another.
What is the key to designing a coaster to make it
run very fast? The answer lies ahead!
Efficiency is the percent of energy retained (i.e.
still available) after an energy conversion. Did
you know a typical car is 30% efficient? Only
30% of the chemical energy in gasoline is
converted to kinetic energy that moves the car.
Where did the rest go? Heat! Whenever energy
is changed into another type, heat is also
produced. Most of the time heat is undesirable,
and it can never be fully converted back to more
useful energies. Even so, if you include heat
with all other energies present, you will find the
total energy of any completely described
situation is constant. That’s a powerful law
called conservation of energy.
1.2 Energy - #1 physics concept?
Energy is a term often used to describe people or
objects. It's also a powerful physics concept.
Energy can be defined as the ability to do work.
The more energy present in you or any object,
the more likely something can be made to
happen or change. Amusement park rides
possess many kinds of energy. Imagine a
bumper car. It is energized by electricity so it
has electrical energy. All objects in motion
have kinetic energy. When the bumper car goes
forward or backward, it has kinetic energy. A
car that is stopped has no kinetic energy. After a
while the car wheels warm up due to friction
with the ground. Energy associated with heat is
called thermal energy. The electrical rod
touching the ceiling creates examples of sound
Energies are not lost or created; they are just
converted from one type to another. Think of an
object's energy as a shirt having many pockets
for different types of energy. An object, for
example a marble, can lose or gain certain types
of energy by switching pockets, but the total
energy stays the same. There is an old saying -
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"what you get out of something is what you put
into it". Does what you just read support this
statement?
Weight = m*g
So also
1.4 PE stands for Potential Energy
PE = Weight * height
Gravity is a force that must be overcome to lift
an object. Since energy is put into an object to
raise it, that object gains height energy called
gravitational potential energy ("PE").
How about Great America on the moon?
Potential energy depends on three factors:
mass, height, and gravity.
On the moon, the acceleration of gravity is only
1.6 m/s2. All objects have the same mass, but
weight about six times less! . A moon ride would
take much less work to lift up to the first hill, but
it would also have much less potential energy. In
summary, potential energy depends only on
weight and vertical height.
The higher an object, the more work it took to
get there, and hence the more PE possessed by
the object. A coaster has the most PE at the top
of the heighest hill. It should also makes
common sense that more massive objects will
have more potential energy than lighter ones.
The PE of a coaster is higher if more people are
on board since it takes more work to lift a
heavier coaster. Finally, PE depends on gravity
since gravity determines the weight of a coaster.
Gravity or more accurately, the acceleration of
gravity is given the symbol “g”, and has a value
of about 9.8 m/s2 on earth.
Hints:
1.
2.
3.
Don’t confuse mass (in kilograms) with
weight (measured in newtons)
Mass is in kilograms (1000 grams = kg)
Energy is in Joules (sounds like jewels)
En garde, I have a sharp equation for you!
Calculating
Potential
Energies
1. How much more PE does a 1.0 kg banana have
after raising it higher by 3.0 meters?
(BTW, that’s a 2 1/4 pound fruit!)
PE = m*g*h
Answer
PE = mgh = 1kg * 9.8 * 3 m = 29 Joules (J)
PE = potential energy in joules (J)
m = object’s mass in kilograms (kg)
h = height of object in meters (m)
g = gravity (about 9.8 m/s2 on Earth)
2. What is the PE of a cheeseburger in your mouth?
(assume burger weights 1N, mouth is 1.5 m high)
Answer
PE = Weight * height = 1N * 1.5m = 1.5 Joules (J)
The above equation can be used to find the
potential energy anywhere along a roller coaster
along as the coaster’s mass and vertical height
are known. The weight of an object is simply its
mass multiplied by the acceleration of gravity.
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1.5
Who is Rube Goldberg?
Can perpetual motion machines exist?
Theoretically it is possible to have perpetual
motion. The total energy must stay the same so
the conservation of energy law is not
violated. However, technically it has been
impossible to make or even design on paper such
a device. Ultimately some additional energy
from outside the machine is needed or the device
requires heat to travel from cold to hot, which it
can’t. For more info, check out
http://prisoner.soe.bcit.bc.ca/rjw/pmm
Reuben Lucius Goldberg was a cartoonist who
poked fun at and designed silly gadgets such as
an automatic back scratcher, a self-operating
napkin, and a 20-step method to turn off the
room lights. His cartoons live on and have
inspired many people to invent very complicated
gadgets to do very simple things. Some have
appeared in movies such as Flubber, Goonies,
Back to the Future, and the Nutty Professor.
Rube Goldberg- like gadgets are the essence of
the Mousetrap board game. There also exist
annual contests to create the most excessive
gadget to do the simplest task. A competition is
held each year for high school students in
Chicago. More information can be found out at:
http://www.anl.gov/OPA/rube/
1.7
Kinetic energy is the energy of motion. It takes
energy to make things move, so moving object
have kinetic energy. . Students walking to class
have KE, while those simply standing in the
hallway have no KE. A roller coaster has its
greatest KE which it has its greatest speed.
Likewise it takes more energy to move more
massive objects. If two students fall at the same
speed on the Giant Drop ride, the heavier student
will have more kinetic energy.
Years ago, engineering fraternities at Purdue
University sought to win the contest by setting
another fraternity’s house on fire. The college
quickly smothered that competition!
Why should we care about Rube Goldberg?
You may be assigned to create a poster or
working model of your own Rube Goldberg
design. You will be expected to describe all the
changes in energy that would occur in your
Goldberg machine. Who knows? Your machine
might win in a real contest or even be sold on
those late night TV ads. Someone invented the
first electric toothbrush; it could have been you!
1.6
Kinetic Energy (KE)
So, kinetic energy depends only on two
variables, mass and speed:
I’m back!!!
2
KE = ½ m * v
KE = kinetic energy in joules (J)
m = mass in kilograms (kg)
v = velocity in meters/ second (m/s)
Perpetual Motion Machines
The United States Patent Office still has an open
application for a perpetual motion machinesome gadget that does something forever. Such
a gadget would convert between energy types
forever without changing any energy into heat.
If heat were created, it would have to be
converted back 100% into a practical form of
energy. If such a device existed its owners would
be very rich. Imagine a car that never needs
refueling! Somehow gas fumes and heat would
have to be collected and reused over and over.
Note velocity is speed in a certain direction. For
energy calculations, direction is not needed.
Calculating kinetic
Energies
a. What is the KE of a 2 kg bowling ball at rest?
b. What is KE if the same ball is rolling at 6 m/s?
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Hence, one can solve for one of the velocities if
the other velocity and two heights are known.
This method can be used anywhere on the track,
not just at the top and bottom of hills.
Answer
a. KE = 0 since at rest!
b. KE = ½ * 2kg * 62 = 36 Joules (J)
Coaster
Problems
So which property explains why one
roller coaster is faster than another?
1.
The fastest coaster will have the most kinetic
energy. Where did that energy come from? KE
was converted from the potential energy of the
first hill. So the fastest coaster has the biggest
drop. You knew that already, but now you the
physic reasons for it. (we ignored air resistance
and friction for now). But what about mass? A
more massive coaster will have more potential
energy at the same height. Be prepared to explain
why the coaster's speed doesn't depend on its
mass!
1.8
Answer
Find energy at top:
PE = mgh = 2000*9.8*20 = 392,000 J
KE = 1/2mv2 = 1/2*2000*42 = 16,000 J
Total Energy = PE + KE = 408,000 J
Find energy at bottom:
PE = mgh = 2000 *9.8 * 0 = 0 (at bottom!)
KE = don't know yet
Total Energy = 408,000 J (same as above)
Coaster Problems
There is a simple way to find the speed of a
coaster at any height along the ride as long as
one knows another speed at a different height.
Consider two points “A” and “B” on a roller
coaster. We can calculate the total energy at
each point by assuming the coaster has only
potential and kinetic energy. Minor errors due to
effects of friction will be ignored for now.
So, KE at bottom = Total energy at top
1/2*2000*v2 = 408,000 J
v = 20.2 m/sec
(about 44 mph)
2.
B
At point A:
PE = mg hA
KE = ½ mvA2
Your are traveling at 2.0m/sec at the top of a
20. m high hill. What is your coaster's speed
when you are at the top of the next hill (10.
m high)? Mass of coaster is 2000 kg
Answer
A
hA
A 2000. kg coaster is moving at 4.00 m/sec
at the top of a hill having a 20.0 m drop.
What is the coaster's speed at the bottom of
the drop?
Find energy at 1st hill:
hB
PE = mgh = 2000*9.8*20 = 392,000 J
KE = 1/2mv2 = 1/2*2000*22 = 4,000 J
Total Energy = PE + KE = 396,000 J
At point B:
PE = mg hB
KE = 1/2mvB2
Find energy at 2nd hill:
PE = mgh = 2000 *9.8 *10 = 196,000 J
KE = don't know yet
Total Energy = 396,000 J (same as above)
We can now invoke the conservation of energy.
The total energy at either point is the same.
So, 196,000 + KE = Total energy on 1 st hill
196,000 + 1/2mv2 = 396,000 J
1/2*2000*v2 = 200,000 J
v = 14 m/s
KE + PE (height A) = KE + PE ( height B)
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1.9
Summary
Simple Roller Coaster Equation
Assumes only force is gravity
So no friction or external work done
Conservation of total energy
(super important!)
You can’t make or destroy energy,
only change it to another type of
energy!
KE + PE (height A) = KE + PE ( height B)
Efficiency (% not lost to heat)
Eff =(Energy out/ Energy in )*100
Unit Conversions
Potential energy
1 m/sec = 2.24 mph.
(height energy)
1 kg =
PE = m*g*h
1 mile = 1610 m
-doubles if double mass
-doubles if double height
Also note:
2.22 lbs
1 ft = 0.305 m
1 hr =
Weight = m*g
Kinetic Energy (motion energy)
KE = ½ m * v2
-doubles if double mass
-quadruples if double speed
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1.10
Review Questions
Energy
1.
Name 3 differences between the older
coaster ride Eagle, and the new Raging Bull
2.
What in your opinion is the most important
question to answer when creating a new
ride?
3.
Define energy in your own words
4.
Give an example of kinetic energy
5.
You may have heard the phrase: you have a
lot of potential! Explain using physics
6.
What type of energy is associated with the
bonding between atoms to form molecules?
7.
Why would you want sport shoes to have
stored elastic energy?
8.
The fission or breaking apart of atoms is an
example of __________ energy being used.
9.
A toaster or hair dryer needs ________
energy to provide __________ energy.
Potential energy
17. What does the symbol g stand for?
18. How could a bowling ball and tennis ball
have the same potential energy?
19. When is your PE higher, when in social
studies on the second floor or math on the
first floor?
20. What is the weight of a 70 kg student?
21. What is the potential energy of a 1/2 pound
hamburger in your mouth (assume your
standing so your mouth is 1.5m high above
the ground)?
22. How much energy must you expend to raise
yourself another 2.0 m while on a ladder?
Assume your mass is 55kg
23. You stand at the top of a staircase which is 4
meters tall (about 12 feet). All of a sudden
you trip and fall all the way down, plowing
into an unwary freshman at the bottom. If
you have 80 kg of mass, how much energy
do you give the unlucky freshman?
10. If a brittle object is dropped on the floor, it
may suffer _____________ energy.
24. Tricky one! How much energy would a 60
kg person have if he hiked up a 20 meter
crater on the moon, where gravity is only
1/6 as strong as it is on the Earth?
11. Which energy types are often maximized at
rock concerts?
12. Which energy allows you to read this page,
pick up radio signals, or microwave food?:
25. What is the hidden source of energy in those
perpetual motion balancing toys that seem to
rock back and forth forever?
13. List the types of energy in the order you
used them to get to school today:
Kinetic Energy
Conservation of Energy
26. Calculate the kinetic energy of a100 kg
student walking at 0.8 m/sec to class
14. Which energy (PE,KE, or total) is constant?
27. What happens to an object’s kinetic energy
if its velocity is doubled? Tripled?
15. How is energy conservation like recycling?
16. Why is heat energy often called the
graveyard for energy conversions?
28. What happens to an object’s kinetic energy
if its mass is doubled? Tripled?
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29. What happens to an object’s kinetic energy
if both its mass and velocity are doubled ?
30. What is the velocity of a Viper car if it has a
mass of 1000 kg and its KE is 310,000 J ?
Coaster Problems
31. What is the total energy of a 65 kg student
on the Giant drop at the moment she is
screaming 20 m above the ground and
moving at 9 m/sec?
32. Where on a roller coaster is your kinetic
energy at its maximum?
33. Where on a roller coaster is your potential
energy at its maximum value?
34. Mark on the swing ride below where the
maximum KE and maximum PE are experienced
people on ride
35. If a 10 kg object drops from rest from height
of 5m, how much PE does it have to start?
36. For the same object, how much KE will it
have just as it hits the ground? (ignore all
forms of friction including air resistance)
37. What is the speed of a 200 kg water sled at
the bottom of a 20 m hill, if it is moving
forward at 3 m/sec at the top of the hill just
before falling?
38. American Eagle ride has a 147 foot drop. If
you are traveling at 2 m/sec at the top of the
drop, what is your speed at the bottom of the
drop? (you don’t need mass!).
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2. Starting & Stopping Roller Coasters
Work, Power, Machines
2.1 The thrill of starting & stopping
What is the scariest part of a coaster ride? Some riders say "the start!" Imagine after getting into the Eagle ride at Great
America, you car gets pulled up a steep incline for 330 feet at 9 ft per second That’s over 36 seconds to think and worry
about the impending first drop! What is the least scariest part of the ride? Most thrill seekers would say the end since
the ride is over and the coaster is coming to a slow stop. Now imagine you are a roller coaster engineer. You already
know that energy is what keeps the coaster coasting. But how do you get the coaster up the first hill and how do you
stop it at the end of the ride? If you had to design your own coaster, you may think of a coaster ride as having six main
parts:
coast
push-off
brake
UNLOAD
LOAD
First, the passengers must be loaded safely on a car which is either stationary or moving very slowly. Then the coaster is
pushed out of the loading area and down the track to the bottom of the climbing hill. A mechanical mechnism then
catches and pulls the coaster up the first hill. From the top of the hill the coaster has all the energy needed to coast up
and down without any outside assistance. At the end of the ride brakes of some sort are applied to slow down the
coaster to no or very little speed. Finally, the passengers unload from the car and new passengers load to repeat the
cycle.
If the coaster has all the energy to coast, where did that energy come
from and where does that energy go at the end of the ride?
By the end of this unit, you shuld be able to answer the following questions:
1) What determines how much work it takes to start and stop a coaster?
2) How does the time it takes to start and stop affect the power needed to do the work?
3) How do machines make it easier to do the work of starting and stop a coaster?
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2.2 Work, Power & Machines
is needed. Unfortunately this technology is too
expensive and impractical at this time to be used
at amusement parks. However, owners of
amusement parks still pay gigantic electric bills
for the operation of power devices including
pulleys and brakes.
You already know the potential energy of the
first hill is what keeps the coaster coasting. But
something has to be done to the coaster to get it
to the top - work has to be done! Work gives
energy to the car. Energy is the ability to work,
and work is the means to convert energy from
one type to another. The faster the work is done,
the greater the power. The work to lift a coaster
up the first hill is done by machines since
machines can do the same work as humans
without getting tired. A very powerful machine
can do a lot of work in a very short time.
Likewise some sort of machine is necessary to
push-off the coaster after passengers are loaded.
Hence, some work is done on the coaster to get it
moving and then even more work is done pull
the coaster up the first inclinebefore additional
work is The work doneaway from the loading
platform. they can be designed to produce a
larger forces and sustain those forces over a
longer Humans are not strong enough or In the
case of a roller coaster, a pulley type machine
converts electrical energy into both potential and
kinetic energy since the coaster is not only
gaining height but is also moving as it climbs up
the first hill. Hence, the total energy of a coaster
can be slightly more than the potential energy of
the first hill. As the coaster goes down hills,
potential energy is converted to kinetic energy
and the coaster gains speed. So if the total
energy is conserved, as it must, why must the
second hill be not quite as high as the first? Did
the coaster lose energy? Of course it can’s lose
or gain energy. But it
does convert some of its kinetic energy into other
forms of energy, which can not be converted
back. The main change in energy is due to heat
created by friction between the coaster and the
rails it rides on. If you have ever ridden on a
coaster, you may have seen, heard, or smelled
other forms of energies. What happens to all the
energy at the end of the ride? Once the coaster is
stopped and at ground level, it has neither kinetic
energy nor potential. Work must be done again
by another machine to convert the car’s initial
and kinetic energy into other forms, mainly heat.
This is usually done by using brakes near the end
of the ride. Some rides use a combination of
brakes plus a small reloading hill. You may
wonder why not convert the car’s energy back
into electrical energy? Indeed this is a new area
of technology based on devices called
capacitors, which store electrical energy until it
Project Clue:
The ultimate roller
coaster ride will be both
money and time
efficient in getting
riders to the top of the
first hill. Friction will
be minimized so rides
can get the most kinetic energy out of the first
hill’s potential energy. Creative and safe
methods will be used to slow riders to a stop
without creating excessive heat due to braking.
2.3 Physics definition of work:
You may think of work is something to do and
get paid for it. The physics definition is similar,
but a bit more precise. Work is when you do
something to an object’s motion, which increases
or decreases the object’s energy. Getting paid is
not a requirement! How do I know I did physics
work was done on an object if I don’t know if
the object’s energy changed? First ask yourself if
a force must be overcome to make the object
move. Second, did the object actually move?
Here’s some more clues to “physics” work.
You know you did work if you
1.
You exert a force (push or pull) on an object
2.
the object moves some distance in the same
or opposite direction of your force
No work is done if
1.
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object’s motion requires no force anyway
CoasterFZYX
2.
object doesn’t move as a result of the force
How do you calculate work?
The equation for work involves only two
variables, force and displacement (distance in a
certain direction).
Questions
Is work
done or
not?
W = F * d
W = work in joules (J)
F = force in Newtons (N)
d = displacement in meters (m)
For example, a quarter pound hamburger weighs
about 1 Newton. If you exert just enough force to
lift the burger about 1 meter, you have done
about 1 Joule of work on the burger. Of course
you have only moved your muscles a small
distance, so you have not burned a significant
amount of calories (energy used to do the work).
Do you do work on your backpack when
you…
(a) pick it up? ______ (yes or no)
(b) hold it? _______
(c) drop it? ______
(d) watch it while it’s falling? ______
(e) carry it and walk to class? _____
(f) fly in a plane with it on your lap? ____
(g) accidentally crush it in a garbage
compactor?_
(h) write FZYX rocks! on the outside of it ?
____
(i) float in space while holding it?_____
Problem solving clue:
Work = change in energy
If you are not given force or distance, you can
determine the amount of work done by the
change in energy.
2.3 Sample Work Problems
How can work be positive or negative?
Q. How much work does it take to lift a box that
weighs 3.0 Newtons upstairs that are 4.0 meters
tall?
If you do positive work, you increased an
object’s energy by forcing it to go in the
direction of your force. This is like pushing a
door forward. Negative work is when you use
force to retard motion. This is like when you put
your hand out to stop a swinging door from
hitting you in the face!
A. Since the force needed is just the box’s
weight, 3.0N, and the distance is 4.0m, then
work = F * d = 3.0 N * 4.0 m = 12 Joules.
Q. For the same problem, what if you climb two
stairs at a time to the same height of 4.0 meters?
Is work the same thing as energy?
A. Since the amount of work only depends on
the total distance and not the amount of steps or
time taken, the answer is the same!- 12 Joules
Work can be thought of as a nebulous synonym
for any energy, which involves overcoming a
force to alter an object’s position, shape, or
nature. For example, (gravitational) potential
energy is the work done against gravity. Elastic
energy is the work done against the spring-like
forces of an elastic material such as rubber
bands. When you apply enough force to
permanently alter or deform something, that’s
called energy of deformation. Heat (thermal)
energy is often the work done against friction.
A roller coaster designer must ensure all bumps,
rubs, and braking does not create forces that may
overheat or destroy parts!
Q. How much work does is take to stop a 6200
Newton car traveling at 25 m/s (about 50mph) ?
A. The work to stop the car is just the change in
energy of the car. Since the car’s final energy
will be zero (it’s stopped and not on a hill), the
work is just the initial kinetic energy = ½ mv2.
The mass is weight/10 = 6200/10 = 620 kg.
So Work = ½ * 620 * 252 = 190,000 Joules
(note: sig figs used so rounded answer)
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force of 10,000 N. The incline is 35 meters
long and 25 meters high.
Problems
Working
out work
(12) How fast is a 5000 kg loaded coaster moving
after a catapult uses 25,000 Joules to start the
coaster moving towards the first incline?
Try these puzzlers on your own!
(1) How much force is needed to lift a 2 N book?
(2) If you lift the book twice as high as your
friend, you do _____ as much work.
(3) A child uses 5 Joules of work to drag his 10
Newton toy bag. How far did he drag it?
Attention!
Attention!
Attention!
(4) If all other factors are the same, why are
longer guns more powerful?
Hint: the units of power are Joules / second
Is your coaster almost ready?
Important lab coming up!
(5) How much energy does a garbage can have
after a disgruntled work kicks it 12 meters
using 5.5 Newtons of kicking force?
(6) How much work is done on the floor when
you stand on it? When you jump on it?
2.4 Coaster Project lab I- Friction
This is the first lab in which your group will be
testing out your own coaster. You do not have to
have the entire project finished. But you do need
to have already decided and built several feet of
track and the vehicle that will roll on this track.
You are to bring in the track and vehicle to
school for this lab. You can later make
modifications if needed.
(7) How much more work does it take to brake a
coaster to a stop if it goes twice as fast?
(8) How much work does a male cheerleader do
on a 500 N female cheerleader when he holds
her 2 meters above the ground?
Goal: Determine how much work due to friction
is done by every meter of your track to your car
(9) Why is follow through important in sports?
Method: Using trial & error you will set up your
track so your car will naturally come to a stop.
(10) How much work does a pulley do in lifting a
loaded coaster (15,000 N total weight) up a
hill that is 25 meters high?
Clue: Friction robs you of speed, so work on it!
Lab sheet: see teacher
(11) How much work is done by a pulley that
pulls along (parallel to) the incline with a
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or ask your teacher help ASAP. To answer
question #4, we need to get the scoop on power.
2.5 Coaster Project lab II- Loops
2.7 What is physics power?
IF you understand the first lab, this one is fun.
You have to predict (not just trial & error) the
tallest possible loop possible from a given hill.
Who is more powerful? A mom who lifts her
two kids into the car one at a time, or the macho
dad who puts both kids in the car at the same
time? Of course, …. Dad! Why? Because he
can do the same work as mom but in less time!
Goal: Use lab I values of work done by friction
per meter to predict & build highest loop de loop
P = W/t
Method: Calculate, show teacher answer, try it!
Clue: Don’t forget PE as car rises up loop!
W = work in joules (J)
t = time in seconds (s)
Lab sheet: see teacher
confusing power units:
1 J/s = “watt”
1000 watts = 1 kilowatt (kw)
100 kw = 134 horsepower (hp)
**
1.
2.6 Postlab Blues?
Why did we do these last two labs? Of course it
gave you motivation to start thinking & building.
But recall these questions we had before?
Sample Power Problems **
A quarter pound hamburger has a mass
of about 0.1 kg. If you lift it 0.2 meters to
your mouth in 3 seconds, how powerful of
an eater are you?
Clue:
find work by using W = force * distance, or
using work= change in energy
Brainstorming Questions
1.
What determines a ride’s max speed?
2.
How much will friction slow down the cars?
3.
Does friction cause any electrical problems?
4.
How much power will it take to lift the
riders up the first hill?
5.
How do I make the track exactly the right
length so the ride slows to a stop without
using breads? (a tough calculation!)
Answer:
Power = work/time = work/3 seconds
Work = force & distance
Force = weight = mass * 10 = .1 *10 = 1N
Work = 1N * .2 meters = .2 Joules
So
power = work/time = .2J/3s = .06 Watts
2.
You should now be able to answer all these
questions except #4. If you can’t, then look back
over your notes, check with your physics buds,
16
The Eagle roller coaster uses a pulley to
lift a train (mass of 4000 kg) containing 30
people (60 kg each) up an incline 100
meters long and 42 meters high in a total
time of 37 seconds.
What is the power of the pulley?
CoasterFZYX
Clue: Weight is a vertical force, so you must
use the height as the vertical distance to get
work.
monthly electric bill may cost up to $100. So
how expensive is it to run a coaster?
Answer:
Cost = cost per kilowatt & total kilowatts
Total mass = 4000 + 30*60 = 5800 kg
Total weight = mass *10 = 58,000 Newtons
Work = total weight & height
= 58,000N*42m = 243,600 Joules
Power= work/time = 243,600/37s = 6584 watts
Typically you pay about 4 cents/kw.
So how much does each eagle ride cost?
Is charging $35 per ticket enough?
2.8 Power Lab
Goal: Determine your own power in climbing
stairs and find who is most powerful student
Method: Measure, time, & climb stairs
Project clue: you will also have to determine
the power and cost of your ride and show that
your ticket price covers your power expenses.
Clue: it takes work to climb, but you get what?
Lab sheet: see teacher
2.9 Cost of power
The last problem shows that a typical roller
coaster needs several thousand watts to raise
each train. Additional power is also usually
needed to bring the train to a safe stop. So
The total power needed for each ride is around
10,000 watts or 10 kwatts. Recall that your
average light bulb is only 100 watts, and a
3. Kiddy Land
Fun machines using materials that don’t break
3.1 Alternatives to roller coasters
conditions such as bad backs, pregnancy, or heart
conditions are not advised to ride. Forget
jumping into a coaster if you have a broken leg,
or difficulty moving. Owners of theme parks
can make more money if they can entice all
members of the family to come along and paid
admission. . So how do theme parks
accommodate young kids, kids who don’t like
moving rides, or older adults who can’t enjoy
fast rides? One method is to devote part of the
park grounds to a “kiddy land” – an area having
only non-thrill playground like attractions. Just
look at the success of Disney World, a park
almost exclusively devoted to kids with very few
fast moving rides. In this section we will
discover how to design simple fun attractions
Not every can or wants to ride a roller coaster.
Most of the bigger, scarier rides are marketed to
teens and young adults. Typically, kids under 54
inches are not even
allowed to try. Adults
who have medical
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CoasterFZYX
that are kid friendly and kid tough. Your theme
park must also include a kid attraction, so don’t
forget to jot down and discuss with your partners
any ideas or questions that come to mind 
That means you can use a machine to increase,
decrease, or turn how much you want to push or
pull something. Your force is called the effort
force; the machine produces a resistance force,
since it trying to do something difficult
(resistive). If a machine increases the effort
force you apply, the machine makes it easier for
you to move or lift objects that normally are too
heavy. Such a machine is said to have a positive
mechanical advantage (MA > 1). If a machine
makes it harder for you, it creates a disadvantage
and has a negative mechanical advantage.
3.2 Types of kiddy land attractions
Designing a kiddy land is not so difficult. Just
go to the playground park in your neighborhood,
then make everything the same but bigger and
more complicated. Some playground equipment
is fun because kids can get the feeling of moving
fast, like on slides, merry-go-rounds, and swings.
We will focus on rides that are fun because they
make kids feel stronger, braver, or bigger than
they really are. For example, kids can’t resist the
challenge of climbing to the top of tall structures.
So build a really big gentle ramp so even the
smallest kids and slowest grand parents can
make it to the top. But also include a difficult
short cut to the top – make a steeper ramp, a
climbing net wall, or a knotted swinging rope.
Kids also love to make things “work”. So create
some pretend devices having some sort of gears
or pulleys to lift or pull heavy objects like a huge
bucket of sand. The time tested teeter-totter is
also a kid favorite, maybe since two friends can
play together. How about a “smarter” bigger
teeter totter that helps kids figure out where to sit
so many kids of different sizes can teeter-totter at
the same time. Whatever type of ride you
choose for your own theme park, you will need
something that lets kids do things easier. Such a
device is called a machine. Every complicated
machine is build out of one of 6 simple
machines. We will focus on only three – ramp,
pulley, and lever. Of course you can also use
one of the other three- screw, gears, and wedge.
MA = Fr / Fe
MA = mechanical advantage
Fr = resistance force out of machine
Fe = effort force put into machine
Why would you want a machine with a negative
mechanical advantage? One reason is you
actually want to make it hard for yourself. For
example, weight training and conditioning
machines with a MA < 1 will help you bulk up
by building muscle. Another reason is that by
applying a larger force, you don’t have to exert
yourself over such a long distance to do the same
work. Remember, work = force * distance. So
if you are working in a
Real machines:
cramped space like
under a car hood, you
friction & heat energy produced
might rather use a
machine that requires
Eff < 100%
more force, but over
less distance.
work in > work out
3.4 Ideal Machines
--100 %
efficient!
3.3 Machines – mechanical advantage
Fe*de <
Fr*dr
Only can use forces:
MA = Fr / Fe
Machines are all about
changing force, and
transferring the work.
Ideally you would want a device that would use
all the energy you gave it to do something useful.
Unfortunately such machines exist only in the
fantasy dreams of engineers and high school
teachers! Some energy is always converted to
heat due to the omnipotent presence of friction.
Hence, perpetual motion machines cannot exist.
Did you know a car is only about 30% efficient?
Stairs, power tools, a hinge, a bicycle, curtain
drawstrings, a computer – which of these are
machines? Actually they all are! You may
think of a machine as anything that you plug in
and does something for you. Certainly that’s
true, but more generally what is a machine?
A machine is a device that changes the size or
direction of a force.
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Any machine:
Positive mechanical advantage (MA > 1):
CoasterFZYX
machine force Fr is larger than yours Fe
but your distance de is longer than machine dr
Negative mechanical advantage (MA < 1):
Effort force
machine force Fr is smaller than yours Fe
your distance de is shorter than machine dr
height (h)
Length (l)
3.5 Ramps – how to get to the top!
That’s why cars tend to run very hot. Here is an
easy method to calculate the efficiency of a
simple machine:
Ramps can be either smooth, called inclined
planes, or stepped, called stairs. Ramps are
probably one of the most overlooked simple
machines, but can be found everywhere at a
theme park. Most roller coasters start on a small
boarding hill so the cars can immediately roll
down to the lift hill. That means people have to
walk up the small hill to board, usually using an
inclined plane. You can probably guess at least
two reasons why elevators are not practical. It’s
also the law that you must make public buildings
wheel chair accessible. Again you can find lots
of little curb ramps and bigger corkscrew shape
ramps to wheel up chair bound people as well as
heavy equipment. At kiddy land, you will
usually find tall castles or other fantasy
structures that can be climbed directly vertically
or more easily using some sort of ramp.
Eff = Work out/work in *100%
Most of our calculations will falsely assume we
are using an ideal machine – one that is 100%
efficient so that all of our energy is transferred
with no heat produced. There do exist machines
with very smooth slippery surfaces that are close
to 100% efficient. Maybe you have seen one in a
novelty or hobby store? In any case, ideal
machines are a lot easier to analyze as follows:
Ideal machines:
pretend no friction so
3.6
Eff = 100%
But what is exactly easier about a ramp?
Whether you use it or not, you get to the same
height. So you get to the same energy. So you
used up the same amount of work. But isn’t
easier mean less work? NO! Easier means less
force.
Sample problem:
Easier
means
an ideal ramp is 6 m long, 2 m high:
without the
ramp you
have to use a lot more muscle to get to the top.
Easier does not mean it takes less time.
Someone who can climb the same wall faster is
more powerful since he does the same amount of
work to get the same amount of energy but in
less time. Someone who does the same amount
of work with less force is thinking smart. But
what is the trade off? How can you do the same
work with less force? Go back and look at the
definition of work to see if you can figure it out.
Try!
work in = work out
Fe*de =
Fr*dr
So if rearrange both sides:
MA = Fr / Fe =
Ramp Physics –the juicy part!
d e / dr
Real machines can be analyzed too:
Eff = 100%
In the case of a ramp, you or some device pushes
or pull along the length of the ramp so that an
Object to go up
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object is raised a certain height. The object
could be you walking up a hill or an entire
coaster train being pulled up the lift hill.
Input to ramp:
Fe = force applied along ramp
De = distance object moves up ramp
(equal to entire length if goes to top)
3.7 Ramp This! - a mini-lab!
Goal: apply the equations of an ideal ramp
Output to ramp:
Method: set up a board ramp of your choice!
Fr = force machine overcomes (object’s weight)
Dr = vertical distance object moves
(equal to ramp height if goes to top)
Clue: keep all measurements the same units
3.8 Pulleys - counting strings is easy!
Ramp
question
s&
notes
1.
Why are ramps useful?
2.
What shaped ramps are the most useful?
3.
What is the efficiency of an ideal ramp?
4.
Find 3 ways to find mechanical advantage
using forces, distances, & ramp dimensions:
One of the most popular events in kiddy land
may be wall climbing for kids. Most kids don’t
make it to the top and appear they will fall.
Fortunately they are held up by a safety rope by
someone else is pulling down on. How can that
be that someone can hold up the entire weight of
a climber by pulling down? The answer of
course is the pulley. Pulleys are easy to spot
since they always have a rope or chain somehow
attached. Every coaster uses one on the lift hill.
The calculations for pulleys are easy, but really
seeing how they work is a different matter. We
will consider only non-moving pulleys fixed to a
wall or ceiling. The secret to understanding is
thinking of each rope as having another person
pulling on it, except for the first rope that is tied
to the pulley. If you have two ropes, then only
one rope is holding all the weight. This kind of
pulley switches the direction of force, but
doesn’t reduce it. If you have 3 ropes, that’s
like having 2 ropes holding up the weight – so
you only need to use1/2 of the force. You can
still use the ideal machine equations involving
forces and distances:
MA =
MA =
MA =
5.
What is the above ramp’s MA?
6.
What force would be needed to lift a 60 N
object without the ramp?
Ideal Pulley
Work in = Force you pull * length you pull
7. How much work would it take to lift the
same object a height of 2 m without the ramp?
Work out = object weight * height object moved
8. How much work if you did use this ramp?
MA = total strands of rope/chain - 1
9. What force would be needed to lift the object
to the top using the ramp?
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CoasterFZYX
Sample
Problems
3.
If the boy went up by 4 meters, how many
meters of string do you have to pull?
Practice these tricky
pulley problems
4.
How much work did you do all together
5.
How much PE does the boy have now?
6.
If you lifted him in 40 seconds, what is your
power?
3.9
Levers – it’s all balance
1.
What is the MA of this pulley?
2.
How much force would you need to pull up
a 1000N ten year old boy?
Levers are probably the most common machine.
The simplest kind is the teeter-totter. But there
are actually two more kinds that describe how
everyday objects like hinges, crowbars, and body
joints work. The common feature of all levers is
a pivot point, called a fulcrum. . Like other
machines, levers can be used to change the size
or direction of force. Likewise levers do not
change the energy or work needed to do a job.
Kiddy land will undoubtedly have lots of levers
so kids can turn secret doorways, balance
another, and lift heavy objects. All the equations
for machines are valid for levers. We will
assume the levers are ideal; that is, there is no
friction at the pivot point. We will also assume
that we push or pull vertically on the lever, when
in reality we do so along an arc path. But in this
way we can quickly draw triangles to aid in
measuring distances. It’s only a small error!
Fill in the missing details for the 3 types of levers. The first lever is done for you!
Teeter-totter - Type 1 lever
Fr
Fe
opposite sides of fulcrum
1. Fe = your push/pull
Fr = force applied by lever
4. The sizes of the forces are:
Less, more, or can be equal
dr
de
2. de = distance you push
dr = distance box goes up
5. The direction of forces are:
3. The forces are located :
Opposite of each other
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6. mechanical advantage is:
same side of fulcrum
1, >1, or can be <1
4. The sizes of the forces are:
7. more examples:
scissors, balances
5. The direction of forces are:
1. Fe = force you pull up
Fr = up force on box
2. de =
dr =
Hinge – Type II lever
3. The forces are located :
6. mechanical advantage is:
same side but reversed order
4. The sizes of the forces are:
your force is always bigger
7. more examples:
Joints – Type III lever
1. Fe = force you pull up
Fr = up force on box
5. The direction of forces are:
same
6. mechanical advantage is:
2. de =
dr =
7. more examples:
tennis racket
3. The forces are located:
3.10 Teeter-totter lab
Goal: learn the art & physics of balance
Method: balancing coins of same weight
measure distances moved
Clue:
Fe
dr
de
Fr
f*D= F*d
( little wt times big distance equals
big wt times little distance)
3.11 Drawing lever triangles
Imagination is the key to calculating levers.
Imagine pushing on the lever so that it stays
attached but pivots on the fulcrum. Then draw
the new lever over the old one. Just make sure
you don’t shift the lever or change its size. It
doesn’t matter how much to push on your lever
since the ratios of distances will be kept the same
by the solid location of the pivot. After drawing
in your new lever, draw down or up from where
the forces are on the lever to make triangles. It’s
just really trigonometry with a physics purpose!
You get the distances by measuring on paper
with a ruler. Fr is the weight of the object.
Ideal levers (all types)
Work in = work out
Fe * de = Fr * dr
MA = Fr / Fe = de/dr
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Lever
questions
to ponder
(use physics to back up your answers!)
1.
Why is it easier to pry a nail with a longer
hammer than a shorter one?
2.
Can you hit a ball harder with a longer or
shorter racket and why is that?
3.
Draw a picture of scissors made so “strong”
that can cut through thin sheets of metal:
4.
What force is needed to lift a 100N milk
crate using an ideal lever having an MA= 5?
5.
For the same lever, how far do you have to
push if you want the crate to move by 5 m?
6.
Who did more work, you or the milk crate?
7.
You rescue your favorite soccer ball under
your 5000 N car using a long board. You
lift the board .2 meters, the car moves .04
meters. What force did you exert?
8.
Using a board twice as long, how high could
you lift the car with the same force?
9.
Find the mechanical advantage of the levers:
A.
B.
C.
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