2015 Physics Guide

Physics Activity
Guide
2015
TABLE OF CONTENTS
Earthbound Astronauts
2
Mechanics of Motion
3
Angles and Arcs
4
Angles and Arcs II
5
Viking Voyager
6
Bamboozler
7
Zulu
8
Finnish Fling
9
Autobahn
10
Scrambler
11
Mamba
12
RipCord
13
Boomerang
14
The Physics Day Lesson Guide was originally compiled by the Informal Science Study of the University of Houston.
1
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 G-force 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
Orbiting Shuttle
The Moon
Mars
Jupiter’s clouds
Shuttle lift off
G-FORCE
0G
.17 G
.39 G
2.64 G
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.
2
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
௠௩ మ
௩మ
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
meters/sec and 11.2 meters/sec. Pick a hill from
9.8 meters/sec2.
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.
Let
v=
velocity
m=
mass
g=
gravity acceleration
h=
height of coaster
Potential energy =
mgh
Kinetic energy =
½ mv2
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.
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 =
௠௩ మ
௥
Write an equation for q.
On what two factors does q depend?
3
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.
90°
0°
An object on the horizon has an
angular height of 0°
4
ANGLES AND ARCS II
Use the angle marker to help you solve the following problems.
Sighting the Sun
Safety First: Do not ever look directly at 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.
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
5
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
6
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
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
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
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.
Can you move your body up the wall while you are spinning?
2.
Do heavier people have more difficulty climbing upward?
3.
How do the sensations change when you close your eyes?
4.
Do you begin to feel as if you are lying down instead of spinning?
5.
Hold your hand straight up in front of you. Does it take more effort to raise your hand or to lower it?
6.
Try raising your leg by bending your knee. Does it take more effort to raise your leg or to lower it?
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
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
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
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 36-passenger 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.
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.
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?
USEFUL FORMULAS
PE = mgh
ଵ
KE = mv2
ଶ
W=Fxd
ௐ
P=
௧
1 revolution = 2p radians
p = mv
ac =
Fc =
௩మ
௥
௠௩ మ
௥
Vavg =
ௗ
௧
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)