Download Physics Activity Guide

Physics Activity Guide
2
TABLE OF CONTENTS
Earthbound Astronauts
3
Mechanics of Motion
4
Angles and Arcs
5
Angles and Arcs II
6
Viking Voyager
7
Bamboozler
8
Zulu
9
Finnish Fling
10
Autobahn
11
Scrambler
12
Mamba
13
RipCord
14
Boomerang
15
Worlds of Fun Railroad
17
Detonator
21
Most of the Physics Day Lesson Guide was originally compiled by the
Informal Science Study of the University of Houston.
3
EARTHBOUND ASTRONAUTS
The following examples will help students understand the concept of weightlessness and G-force.
Before visiting Worlds of Fun:
1. Explain to students that when they are weightless they feel NO forces. If/when they jump off a diving board they
feel no forces (except for air resistance) until the water stops their fall.
2. A roller coaster track is shaped like the path of a diver. Riders will feel weightless as they rush over the peaks and
down the hills. They will feel a sinking feeling as the valleys stop their fall.
3. Space Shuttle astronauts feel this same weightlessness for days. The Shuttle is falling -- but it moves so fast
that it makes an orbit instead of falling to the earth.
4. Astronauts use the word “G-force” to describe the forces that they feel. Explain to students that they feel a 1 Gforce right now. When you feel more than 1G you feel heavier than normal. When you feel less than 1G you feel
lighter than normal.
5. Post the following information for students to see:
PLACE
G-FORCE
Orbiting Shuttle
0G
The Moon
.17 G
Mars
.39 G
Jupiter’s clouds
2.64 G
Shuttle lift off
3.0 G
RIDE
Have students refer to copies of the ride activity sheets. Each sheet gives the G-force for the ride. Now have students
select a ride that gives them the same G-force as these space trip destinations.
Remind students that while they are at Worlds of Fun they are to consider the weightlessness and G-force
information discussed. Tell them there will be additional exercises after the visit.
After visiting Worlds of Fun:
1. Have students recall the moments of roller coaster weightlessness. Ask them to remember how their stomach
seemed to float and their bottom arose out of their seat.
2. Now have them talk with their ride companions and make a list of their reactions to weightlessness.
3. Explain that Space Stations turn so that the astronauts do not feel weightless. Have students think about how they
felt on a circular ride. Ask them to share their thinking about the following situations in a spinning space colony:
a. Where would the floor be?
b. Which way would a helium balloon rise?
c. Which way would a tree grow?
4. Have students imagine they have been chosen to build a space platform floating weightless above earth.
a. If they build a roller coaster on it, just like the ones on earth, what would happen at the first hilltop?
b. Have them name a ride that would work the same in 0 g. as on earth.
c. Have them describe a ride that they could use in space, but not down on earth.
4
MECHANICS OF MOTION
Solve the physics problems on this page.
You will need to use data from the following pages to perform the calculations.
POWER
VECTORS
For a roller coaster find the lift motor horsepower,
Show how the GRAVITY and CENTRIPETAL
the coaster weight, the coaster capacity, and the
FORCE vectors combine at the top and at the
first hill height. Figure out how long it will take for bottom of the loop below.
a full coaster to reach the hilltop with the motor
running at full power (HINT: 1 Watt = 1 Joule/set)
CENTRIPETAL FORCES
PARABOLA PEAKS
Let
v=
Fc =
ac =
r=
velocity
centripetal force
centripetal acceleration
radius of ride
Consider an x:y axis drawn
through a roller coaster.
Write an equation for the
parabolic coaster path assuming a horizontal peak
speed of V and a free fall acceleration of 1G.
Show that Fc =
and that ac =
Calculate the centripetal acceleration for one ride.
Convert your answer to G’s using the fact that 1G = Plot parabolic curves for peak speeds of 2.2
9.8 meters/sec2.
meters/sec and 11.2 meters/sec. Pick a hill from
the following pages that looks like each curve.
ENERGY
By assuming the negligible friction and air
resistance losses, you can consider the sum of
kinetic and potential energies as a constant for a
roller coaster.
BANKED CURVES
A roller coaster curve is properly banked when the
rider is pushed straight down into the seat. Let N =
the force on the rider and q = the banking angle.
Let
v=
velocity
m=
mass
g=
gravity acceleration
h=
height of coaster
Potential energy =
mgh
Kinetic energy =
½ mv2
r=
Gravitational force =
Centripetal force =
If the height of the coaster hill is H and the hill top
velocity is V, what is the equation for the velocity
of the coaster (v) in the valley where h=0? Is the
mass of the coaster a factor in this calculation?
Why or why not?
radius of curve
Ncos q = mg
Nsin q =
Write an equation for q.
On what two factors does q depend?
5
ANGLES AND ARCS
Construct the angle marker to help you solve the problems on Angles and Arcs II.
1. Cut out the angle marker along the
dashed lines.
2. Fold the top section over a pencil.
Roll it to the dotted line to make a
sighting tube.
3. Tape the rolled paper tube and then
let the pencil slide out.
4. Take about 25 cm of string (or
heavy thread) and tie one end to a
weight (a key or a heavy washer). Tie
the other end through the hole at the
top of the angle marker.
5. Let the string hang free. The angle it
marks off is the angular height of an
object seen through the tube.
For example:
An object directly overhead has an angular height of 900.
0
An object on the horizon has an
angular height of 0
90
ANGLES AND ARCS II
6
Use the angle marker to help you solve the following problems.
Sighting the Sun
To sight the sun with the angle marker, look at the tube’s
shadow on the ground. When a bright spot can be seen in the
middle of the tube, the tube is pointed toward the sun. The
string will then mark the sun’s height above the horizon.
Safety First: Do not ever look directly at the sun!
Record your observations:
Time
Sun Height
tube
angle shown here is the
height of the sun
bright spot on ground
Sighting Tress and Rides
1.
Measure the distance between you and the tree or ride.
You can walk off the distance or use the park map if the
ride is far away.
Distance: ________ meters
2.
Measure the height of the string hole in meters.
String hole height: ________ meters
3.
Observe the tree top or ride top.
4.
Read off the angular height.
Angular height: _______ degrees
5.
Look up the tangent value for the angle measured.
Tangent value: _______
6.
Multiply this tangent value by the distance from the tree or ride.
7.
___________ x _______= _______
TANGENT VALUE
8.
DISTANCE
Add this product to the height of the string hole.
_______ + ________________ = _______ the height of the tree or ride
PRODUCT
HEIGHT OF STRING HOLE
Angle
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Tangent Value
.00
.09
.18
.27
.36
.47
.58
.70
.84
1.00
1.19
1.43
1.73
2.14
2.75
3.37
5.67
11.43
57.29
7
VIKING VOYAGER
Pick the best place on the ride for each sign. Put the number in the box beside the sign.
You may use the place numbers more than once. There may be more than one good place for some of the signs.
Accelerate
Decelerate
Greatest Gravitational
Potential Energy Spot
Banked
Curve
2
5
4
3
1
6
Ride Information
Parallel Channels
2
Highest Point of Ride
2nd Hill
Number of Boats
24
Boat Capacity
6 adults
Weightless
Zone
Forward
Leaning
Zone
Parabolic
Arc
Backward
Leaning
Zone
Greatest Kinetic
Energy Spot
Momentum
Roll
Greatest Gravitational
Potential Energy Spot
Inertia
Jerk
8
BAMBOOZLER
Describe a place where each sign should be placed.
Gravity at
Work
High G-Force
Zone
Greatest Kinetic
Energy Spot
Greatest Gravitational
Potential Energy Spot
Trip Time
Drive Motor
Capacity per Trip
Hydraulic Pump
Maximum Speed
Wheel Diameter
Angle of Lift
Ride Information
1.5 Minutes
1.5 – 7.5 kilowatts
42 adults
19 kilowatts
15 rpm
15 meters
54
480 V
3 phase
480 V
3 phase
Centripetal
Force at Work
9
ZULU
Pick the best place on the ride for each sign. Put the number in the box beside the sign. You can use the place
numbers more than once. There may be more than one good place for the signs.
1
4
7
6
3
2
5
3
Total Height
Ride Capacity
Vertical Angle
Gondola Weight
Total Wheel Diameter
Rotation Rate
Greatest Gravitational
Potential Energy Spot
Ride Information
21 meters
40 adults (665 newtons each)
88
887 newtons
17 meters motionless, 20 meters in motion
12 rpm
Greatest Kinetic
Energy Spot
Forward
Leaning
Zone
Backward
Leaning
Zone
Centripetal
Force at
Work
Banked
Curve
High G-Force
Zone
10
FINNISH FLING
Read the following questions before you go to Worlds of Fun.
Be ready to write a response when you return to school.
Things to think about while spinning at top speed:
1.
2.
3.
4.
5.
6.
move your body up the wall while you are spinning?
people have more difficulty climbing upward?
sensations change when you close your eyes?
to feel as if you are lying down instead of spinning?
hand straight up in front of you. Does it take more effort to raise your hand or to lower it?
your leg by bending your knee. Does it take more effort to raise your leg or to lower it?
Can you
Do heavier
How do the
Do you begin
Hold your
Try raising
11
Ride Information
Ride Capacity
30 adults (665 newtons each)
Power of Motor
11.2 kilowatts
Diameter of Circle 4.25 meters
Rotation Rate
32 rpm
12
AUTOBAHN
Connect the arrows to the drivers, then describe where you would put each sign.
Driver who
will feel the
strongest jolt
Driver who
will be thrown
sideways
Car which
will change
direction at
the crash
Car which will
decelerate at
the crash
Car which will
accelerate the
crash
Driver who
will be thrown
forward
Ride Information
Number of Cars
35 average, 40 maximum
Air Pressure of Bumper 221 kilopascals
Weight of Car
1663 newtons empty
Operating Current
8 amps at 90V DC
Speed Limit
4.25 kph
Driver who
will be thrown
backward
Centripetal
Force at
Work
Greatest Kinetic
Energy Spot
Forward
Leaning
Zone
faster car
slower car
Which car will bump the driver more, the faster
car or the slower car?
Backward
Leaning
Zone
Minimum
Speed
13
SCRAMBLER
Find the 1 and 2 spots on the Scrambler. Put a 1 or 2 in the box by each sign to show where the sign should be
placed.
1
2
Rider’s path for turn of center arm
Ride Information
Length of Center Arm
4.4 meters
Length of Gondola Arm
3.4 meters
Rotation Rate of Center Arm
11.4 rpm clockwise
Width of Seat
1.2 meters
Rotation Rate of Gondola Arm 27 rpm counter clockwise
Round Trip Time
1.5 minutes
Power of Turning Motors
7.46 kilowatts
Speed Limit
40 kph
Weight of Gondola Pod
9760 newtons
Ride Capacity
36 adults
Rider’s path for 3 turns of center arm
Sideways
Leaning
Zone
Centripetal
Force at
Work
Inertia
Jerk
Air
Resistance at
Work
Minimum
Speed
Unbanked
Curve
Greatest Kinetic
Energy Spot
14
MAMBA
Solve the following problems related to the Mamba. You may want to use the Useful Formulas page to help you.
1. As you travel over the five “camelback” bumps on the Mamba, you will feel “lifted”
from your seat. Explain why you feel this sensation. You may want to use the terms
“inertia” and “negative G-force” in your explanation.
2. The first drop on the Mamba is approximately 63 meters. If the speed of the train is 32
meters per second at the bottom of the drop, how much energy must have been lost
to friction? Use 7,500 kilograms as an estimation of the mass of the loaded 36passenger train.
3. If the loaded train masses 7,500 kilograms and it must be lifted vertically 63 meters to
the top of the first hill, how much work is needed to do the job?
While you are at Worlds of Fun:
4. Measure the time (in seconds) on your wristwatch that it takes to reach the top of the
first hill. Using the data in #3, calculate the power needed to do the lifting in this
amount of time.
5. The Mamba turns 580 degrees as it turns to make its return trip. Change 580 degrees
into (a) revolutions and (b) radians.
6. The top speed of the Mamba is approximately 116 kilometers per hour. (a) Change this
speed to meters per second. (b) What is the momentum of the fully loaded Mamba
when it is at this maximum speed? Again, use 7,500 kilograms as the estimated mass
of the loaded train. Use the proper label for your answer.
15
RIPCORD
Solve the following problems related to the RipCord.
You may want to use the Useful Formulas page to help you.
1. At what point on the RipCord do you have the greatest
potential energy?
2. At what point on the RipCord do you have the greatest
kinetic energy?
3. If friction is considered negligible, does the weight of riders
affect the maximum speed reached on the RipCord? Explain
your answer.
4. Calculate the potential energy in joules at the start of the ride if the launch site is 50 meters above the lowest
point of the ride. Base your answer on your approximation of the weight of the riders plus the harness.
5. If the energy lost to friction on the way down is not considered, how fast should you be traveling at the bottom
of the swing? HINT: Think of energy being changed from one form to another.
6. Use your answer in #5 to calculate the centripetal acceleration of the riders at the bottom of the arc, assuming
the support cables to be 50 meters long.
7. What would be the tension in the cable where it attaches to the harness, during the instant of maximum
velocity? HINT: Think about two things that are creating tension in the cable. If you have answered the previous
questions, you already have all the data you need.
8. Something to think about as you ride or watch riders on the RipCord: Is the point of maximum acceleration the
same as the point of maximum speed? Is it possible that the point of maximum speed is the point of minimum
acceleration? Explain your answer.
16
BOOMERANG
Solve the following problems related to the Boomerang.
You may want to use the Useful Formulas page to help.
1. If the ride is 610 meters long and lasts 60 seconds, what is the average speed of the ride in meters per
second? Convert this answer to kilometers per hour.
2. If the initial vertical drop of the Boomerang takes 3.0 seconds and a speed of 25 meters per second is
reached, what is its average rate of acceleration? How does this rate of acceleration compare to a body in
free fall?
3. If the ride starts by dropping from a height of 38.1 meters, explain why the cars could not ever reach a
height of 38.4 meters, without help from an outside energy source.
4. Name two sources of friction that slow the cars of the Boomerang (or any roller coaster).
5. If the vertical loop of the Boomerang has a radius of 9.1 meters, what is the minimum speed necessary to
make it over the top?
6. True or False: If the radius of the vertical loop of the Boomerang was twice as big, then the minimum speed
to make it over the top would also be twice as big. Explain your answer.
7. Thought Question: If the Boomerang was located on the moon, would the ride go faster or slower? Why?
17
USEFUL FORMULAS
PE = mgh
KE = mv2
W=Fxd
P=
1 revolution = 2p radians
p = mv
ac =
Fc =
Vavg =
VARIABLES DEFINED
SI Unites in ()
a = acceleration (meters/sec2)
ac = centripetal acceleration (meters/sec2)
d = distance (meters)
F = force (newtons)
Fc = centripetal force (newtons)
g = acceleration due to gravity (9.8m/sec2 on earth)
h = height (meters)
KE = kinetic energy (joules)
m = mass (kilograms)
P = power (watts)
PE = potential energy (joules)
p = momentum (kg x meters/sec)
r = radius (meters)
t = time (seconds)
v = velocity (meters/sec)
W = work (joules)
18
Worlds of Fun Railroad
Useful to Know:
• Number of cars per train ________
• Number of seating rows per car _______
Ride Data:
• Eli’s Track Length: 5300 feet
• Empty Train Weight: 29.4 tons
• Weight of locomotive & fuel: 22.4 ton
• Maximum number of passengers per car is 78
A group of students decide to take a relaxing trip on the Worlds of Fun Railroad. They begin their
journey at the Train Depot. An approximate plot of their distance travelled vs. time is presented above.
1. How long after they are seated does the ride begin? ________________
2. How long is the train stopped at the Train Depot? _________________
3. How long does it take to get from leaving the Train Depot and returning? ___________________
4. What is the average speed of the train while it is in motion from the Train Depot and back, in miles per hour?
_______
5. What is the average speed of the train over its entire ride cycle, from getting on and off the train, in miles per
hour? _______
6. Make a graph of speed vs. time for one lap of the Worlds of Fun.
19
Worlds of Fun Railroad
1. Let’s take a closer look at the acceleration and forces involved with the Worlds of Fun Railway. While
leaving Train Depot, it was determined that it took 42 seconds to accelerate to a speed of 90mph. What was the
rate of acceleration of the train?
2. Find the total mass, in kilograms, of the empty train and it’s locomotive and fuel.
3. Use the information above, and F=ma, to determine the minimum amount of force needed to accelerate the
train.
4. Remember, this calculation does not take friction into account. If friction were accounted for, would the total
force be greater, or less than what you calculated above? ____________
5. On the way out of the Train Depot, it was determined that the train took 48 seconds while accelerating to a
speed of 3 meters per second. Is this acceleration larger or smaller than the one found for the train leaving the
Train Depot?
6. Observe the train to determine the number of seating rows per car, and the number of cars per train. Use this
information, and an average weight of 150 lbs per passenger, to determine the maximum mass of the people that
the train can carry. Though mass and weight are not quite the same thing, you may use 1 kg ≈ 2.2 lbs to
determine mass from weight.
7. Determine the total mass, in kilograms, of a fully loaded Worlds of Fun Railroad train including its
locomotive and fuel.
8. Use the acceleration you calculated for the train leaving the Train Depot, and the mass of the fully loaded
train, to find the minimum force needed to accelerate the train.
20
Worlds of Fun Railroad
While the Worlds of Fun Railroad runs on propane, other locomotives run on coal.
1. The chemical potential energy of coal becomes thermal (heat) energy
as the coal burns in the locomotive. The heat boils water to make pressurized
steam, which also has potential energy, but there is still something else that
must happen before the potential energy of the coal is transformed into the
kinetic energy of the train in motion.
The drawings at the right show a cylinder in various positions. A cylinder is a
tube containing a piston which moves in response to pressurized fluid pushing
on it. A rod extends through one end of the cylinder so the motion can be used
outside of the device. The fluid (steam is a fluid, but steam isn’t a liquid!) is put
into one or the other side of the cylinder through a port, which is selected by valves
(not shown) that help control the motion.
To which port would steam have to be added in order to cause
the cylinder rod to be retracted? ________
To which port would steam have to be added in order to
cause the cylinder rod to be extended? ________
2. Consider the simplified engine drawings to the right.
In the drawing to the right, if the cylinder extends, which
direction will the wheels turn (clockwise, or counter clock-wise)?
Will the locomotive move to the left, or to the right as a result? Draw an arrow to indicate the motion.
Which side of the cylinder must have pressurized steam applied to make this happen? Draw some steam
molecules in this area to illustrate. Show with an arrow where the steam is entering.
If steam is entering one side of the cylinder to push the piston and rod, what is happening to the gas on the other
side of the cylinder is it being compressed, or is it exiting somehow (hint - listen to the locomotive as it begins
to pull the train. The Mean Streak crossing area is a great place to listen to the engine as it takes off. Why does
it sound the way it does?
3. Use F=ma to determine the minimum amount of force needed
to accelerate the train.
4. What class lever is shown to the right?______________
How does this lever relate to the simplified engine drawing above? Label which part of the engine drawing
(track, wheel axle, cylinder) corresponds to each of the parts of the lever (force, fulcrum, load).
21
Worlds of Fun Railroad
The Worlds of Fun Railroad was first established in 1973. Since then, it has utilized the power of steam
produced by propane and water in order to pull the railcars. The Worlds of Fun locomotive used 600 gallons of
propane and 750 gallons of water in a 12 hour time period. In order for the steam to drive the locomotive, the
pressure of the boiler must be 180 psi. Can you finish these problems from for a round trip to and from the
Train Station? This journey takes 7 minutes of motion and 8 minutes of resting. If you get stuck, keep cho choo
choooing along!
1. What kind of energy does coal have? _________________
2. Water ,
is boiled by the heat of coal burning. What phase is water transitioning from and to?
3. Is this a physical or chemical change that occurs? _________________ Draw three water molecules
connected together.
4. How much water would the locomotive use during twenty minutes of operation (roughly the time of one
round trip from the Train Depot and back)? _________________
5. Middle School Challenge: Identify and label the following
in the Heating Curve shown;
a) Phase and corresponding temperature (in each textbox)
b) Phase Change Process (in the arrow)
6. Conclusion (Fill in the Blanks) In order to make the Worlds of Fun Railroad operation, there are several
energy transformations that must take place. First, coal has ______________ ______________ energy. When
the coal is burned, it produces _______________ energy. The heat causes water to boil, which breaks
intermolecular forces resulting in a change of _____________ that results in steam production. The steam is
allowed into a _______________ which has a rod that moves the wheels of the locomotive. When the
locomotive is moving, it has _____________ energy.
22
Detonator
Use the diagram below
1. How far does the Detonator drop its passengers?
2. How long (seconds) does it take to drop? (use your stopwatch or cell phone as a timer)
3. Vertical Change (Drop Side): (Ending Point – Starting Point) / Time (Seconds)
4. Vertical Change (Thrust Side): (Ending Point – Starting Point) / Time (Seconds)
5. Are the two sides the same or different? Explain?
200 ft
40 ft
23
Detonator
Ride Data:
• Height: 225 ft
• Vertical Distance Traveled: 150 ft
• Maximum Speed: 45 mph
Watch the drop side of Detonator in operation. Then answer the questions on this page. When you’re done,
reward yourself with a ride!
1. Which of the graphs shown at the right is the most
reasonably correct depiction of vertical position vs. time
for a ride on the drop side of Detonator?
Draw a rectangle around the correct choice.
A
2. The horizontal scale of each graph is in seconds
(minor tic marks), with a major tic mark every ten seconds.
Assume that the origin (0,0) is at the lower left.
B
3. At what time does the car begin its long climb up
the tower?
4. How long does it take for the car to ascend the tower?
C
5. How long does the car stay at the top of the tower before it descends?
6. Describe the motion of the car as it ascends the tower - does the velocity change much during the ascent, or is
it relatively steady?
7. What is the average speed of the car during the ascent?
8. How long does it take the car to make its first drop from the very top?
9. Does the position graph intercept the vertical axis at a height of zero, or is there an offset?
10. On the graph, clearly label the region when the Detonator car has the most gravitational potential energy.
Then, clearly label the region where the Detonator cart has the most kinetic energy.