Batman – Type B
MAGIC MOUNTAIN PHYSICS LABS – Fizx Phirst
This packet contains the labs that need to be completed and
returned to your teacher the Tuesday after we return. You will only
need to do FOUR of the labs in this packet plus the “Entrance
Exam”. The labs are listed as Type A, Type B, Type C labs; you must
do one lab from each type along with “the lab on the last page”.
Preview the labs and determine ahead of time which ones you plan to
complete as well as what information you will need to gather while
at the park. Your group will need to check out an accelerometer and
an angle-measuring device that you and your group will be
responsible for returning, in working order, to your instructor.
You will also need a stopwatch or digital watch that can double as
a stopwatch for timing (some iPODs have a stopwatch function). A
$20 replacement fee will be assessed to any group that loses or
breaks their school equipment. These labs must be completed in
groups of 3-6 students from the same teacher.
A note on measurements: sometimes we find large errors in the
data collected on or about the rides. We will be grading the
process more than the final answer so show everything – describe
(in sentence form) how you measured it, write out the equations
used, show all of your work and calculations (don’t forget units).
If this dreaded event happens to your group, you have a chance to
correct yourself. First, you must show me all data YOU collected
and the calculations completed WITH YOUR DATA. Then you may get
data from another source (another group, the Magic Mountain web
site, a knowledgeable park employee, even me), CREDIT THE SOURCE,
and again complete the calculations with the new data.
NAMES ________________________________ Period ________
________________________________ Period ________
________________________________ Period ________
________________________________ Period ________
________________________________ Period ________
________________________________ Period ________
Magic Mountain Measurement Lab Entrance Exam
The purpose of this exercise is to become familiar with the
double triangulation method of estimating height and correct any
errors in measuring techniques before entering Magic Mountain.
You must show all of your measurements and calculations and
obtain your instructor’s initials before entering Magic
Mountain
Objective: Determine the height of “X” - The Extreme from the
parking lot using the double triangulation method.
Apparatus: Horizontal Accelerometer, 10 meter long string
Procedure: Double Triangulation – From the parking lot of Magic
Mountain, use triangulation to find the height to the top of the
first hill of X-The Extreme. Since the fence keeps you from easily
and accurately pacing from directly beneath the structure, you will
need to use the double triangulation method to find the height.
Start from a location in the parking lot (watch our for cars and
buses) far away from X-The Extreme and measure the angle 1, then
move some distance D (the length of your string) closer to X-The
Extreme and measure the angle 2. Show all your work below for
determining the height to the top of X-The Extreme.
h1 = D sinsin
sin()
h1 H
1
2
h0
h0
D
Data
1___________
D________
2___________
h0 (your height) _________
Calculate h1 below
h1 =___________m
Calculate total height H of X-The Extreme
H=__________m
Instructor’s Initials_________
Colossus – Type A
Note - if Colossus is not open do these measurements for
Viper
Purpose Use the height of the first hill to describe the motion
of the car as it drops.
Data and Evaluation
Determine the velocity of the car at the bottom of the hill
(vf), using the methods in parts A and B (assume an initial
velocity (vi) of zero.):
Part A. Determine the velocity through direct measurement.
Measure the length of the train and the time for it to pass a
single point at the bottom of the first hill
Data / Calculation
Length of Train (m)
Time to Pass Point at bottom of 1st hill (s)
Average Time=
Calculate velocity at bottom of the first hill
Velocity of the car at the bottom of the hill: ___________
m/s
Determining Acceleration
Time the car from the top of the hill to the bottom Time
___________s
Assuming that your velocity at the top of the hill is zero and
using the final velocity calculated above, calculate your
acceleration down the hill (use kinematics equations).
Calculated acceleration ___________ m/s2
Part B. Determine the velocity using the conservation of
energy.
From the Magic Mountain website, record the height and convert
to meters.
Height of first hill in feet: ______________ ft
Conversion:
Height of the first hill in meters: ______________ m
Data / Calculation
Velocity of the car at the bottom of the hill: ___________
m/s
Assuming that your velocity at the top of the hill is zero and
using the final velocity calculated above, calculate your
acceleration down the hill (use kinematics equations).
Calculated acceleration ___________ m/s2
Part C. During the drop down the hill (NOT at the bottom of the
hill), use the
accelerometer to measure your vertical acceleration.
__________ g’s
Convert this to an acceleration in m/s2 by taking (1 – #
measured g’s) x 9.81 m/s2.
Measured acceleration ___________ m/s2
Analysis / Conclusions
How did your calculated acceleration compare/match your measured
acceleration down the first hill? Describe possible reasons for any
difference.
Part A vs. C
Write down your calculated acceleration from part A.
__________
Write down you measured acceleration from part C (in m/s2)
__________
Are the values similar or significantly different? Describe
possible reasons for any difference between the two values.
Part B vs. C
Write down your calculated acceleration from part B.
__________
Write down you measured acceleration from part C (in m/s2)
__________
Are the values similar or significantly different? Describe
possible reasons for any difference between the two values.
.
Describe your feelings from the top of the first hill to the top
of the next hill.
Compare your feelings from just before you rode the coaster to
just after riding the coaster
Batman – Type B
h d
(
Apparatus: stopwatch, triangulation device (horizontal
accelerometer)
Part A Calculate the average speed of the Batman train as it
travels up the first incline.
Procedure:
I - Determine the height of the first incline using the
characteristics of the ride. It may help you to know that the
height of one of the steps is 0.18 m, if you’re a VERY fast
counter! Otherwise, use triangulation.
II - Determine the angle of the incline by holding the
triangulation device so that the straw matches the surface of the
incline and reading off the angle.
III - Measure the time required for the train to reach the top
of the first incline.
Data:data for height calculation:
Angle of incline __________degrees Time ________s
Evaluation of Data:
Calculate height: (describe how you did this and show your
work)
height _________m
Calculate d:
d ________ m
Calculate average speed:
Speed ________ m/s
According to Magic Mountain, the height of the first hill is
32.0 m. How do your triangulated height and the given height of
32.0 m compare? Are the values similar or significantly different
(How close was your estimated distance to the actual distance)?
Describe possible reasons for any difference between the two
values.
Part B Determine the increase in gravitational potential energy
as the train moves from the bottom to the top of the first incline
(use the given height of 32.0 m) and determine the total energy of
the train at the top of the first incline.
Procedure: The mass of the unloaded train is 9440 kg. Count the
number of people on a train and assume that they each have a mass
of about 70. kg.
Data: # People on a single train _________
Analysis / Conclusions
Total mass of train + passengers:
Mass ________ kg
Change in gravitational potential energy:
change in Eg ________ J
Determine the kinetic energy of the car (using the speed from
Part A).
Ek ________ J
Determine the total energy of the car at the top of the track by
adding the potential energy and the kinetic energy you just
found.
Total Energy _________ J
How much does it cost to bring the car from rest at ground level
to the top of the first incline at the speed you calculated if
electricity costs $0.25 per kWh and there are 3.6 x 106 J in each
kWh?
Cost $ ________
Estimate (your best guess) how fast you are moving at the bottom
of the first hill.
Speed ____________m/s
Assuming the total energy of the train at the top of the hill is
converted to kinetic energy at the bottom off the first hill, how
fast would you be moving at the bottom of the first hill?
Speed ____________m/s
According to Magic Mountain, the top speed of Batman is 22 m/s.
How does this speed compare with your calculated speed above? Are
the values similar or significantly different (How close was your
estimated speed to the actual speed)? Describe possible reasons for
any difference between the two values.
Compare your feelings from just before you rode the coaster to
just after riding the coaster
Superman--the Ride – Type B
Purpose:Determine the velocity of the car and track efficiency
using the conservation of energy.
Data and Evaluation:
Use the double triangulation method to determine the full height
of the tower (hmax)[don’t forget to add your height in], the actual
height (note that the cars don’t reach the full height of the ride)
of one of the cars at its highest point (hactual). Also triangulate
the height of the track at its lowest point (hmin).
Show your measurements and result of each calculation:
Record you measurements
(1
(2
D
hmin
hactual
Show your calculations below for each of the following
heights
hmin ___________m hactual ___________m
(hcar _________m
How did your triangulated heights compare to the “real” heights?
The published heights are 126.5 meters for hactual and 26 meters
for hmin
Discussion of hactual
Discussion of hmin
Energy Conservation and Track Efficiency
The Magic Mountain website states that the car reaches a maximum
speed of 100 mi/hr (44 m/s) before going up the tower. Based on
this speed, calculate the maximum height the car should
theoretically reach using conservation of energy. (Note: Consider
the straightaway portion of the ride to be your zero line.)
htheoretical _______________m
How does htheoretical compare to (hcar? Explain why there is a
difference.
Use your theoretical and real change in height to calculate the
efficiency of the track.
(Eff = (hcar / htheoretical)
efficiency ____________
Using (hcar , determine the velocity of the car just as it
reaches the bottom of the curved path using conservation of
energy.
velocity ____________m/s
Cost
The mass of an unloaded car is 2300 kg. Count the number of
people on a car and assume that they each have a mass of about 70.
kg.
Data: # People on a single car _______
Total mass of car + passengers
Mass ___________kg
Calculate the change in kinetic energy of the car from when it’s
launched to when it hits its maximum speed of 44 m/s
Change in Ek ____________J
How much does it cost to accelerate a single car from rest to
its maximum speed? Assume electricity costs $0.25 per kWh and there
are 3.6 x 106 J in each kWh.
Cost $ ________
Analysis/Conclusions
Does it cost Magic Mountain more money to launch a loaded car or
an empty car? Explain
What did it feel like when you reached the highest point
(hactual)?
What did it feel like when you are being launched?
The Buccaneer – Type C
The Buccaneer rocks you back and forth experiencing changes in
g-force.
Problem:Predict the maximum centripetal force and compare it to
the measured g-force. Also compare g forces on different parts of
the ride.
Apparatus:Stopwatch Vertical Accelerometer
Procedure:
IThe maximum centripetal force occurs where the velocity is
fastest. This is at the bottom of the swing when The Buccaneer is
swinging at its maximum amplitude.
IIThe time for the boat to pass the bottom-most point can be
measured using a stopwatch. Start timing when one end of the boat
passes the bottom and stop timing when the other end of the boat
passes the bottom.
The radius is measured from the top pivot point (point of
rotation) to the bottom of the boat. You can determine this by
triangulation or by using uniformity in the structure.
The length of the boat can be approximated by pacing the length
of the deck.
.
What acceleration do you think (estimate) you will measure at
the highest and lowest (bottom) points?
Estimated acceleration Top _________g’s Bottom _________g’s
Data:
Time for the boat to pass the bottom (not the entire swing)
____________ s
Length of boat __________ m
How was this determined?
Measured g-force at the highest point __________ g’s
Measured g-force at the bottom _________ g’s
Show how you determined the radius
Radius __________ m
Evaluation of Data:
Calculate the average velocity across the bottom of the
swing.
velocity ____________m/s
Calculation of centripetal acceleration (aC = v2 / r)
centripetal acceleration = _______________ m/s2
Convert the centripetal acceleration into g’s by dividing by
9.81.
Calculated g’s _________ g’s
Analysis / Conclusions
What differences did you feel when you were at the top and
bottom of the swing?
Write down your measured g’s from the DATA section.
__________
Write down you calculated g’s from the EVALUATION OF DATA
section. __________
How does the calculated centripetal acceleration at the bottom
of the swing (calculated g’s) compare with the measured
acceleration (measured g’s) at the bottom of the swing? Are the
values similar or significantly different? Account for any
difference by describing any possible reasons for any difference
between the two values.
Are the maximum g-forces significantly different for riders in
different parts of the boat? How do you know? Hint – try riding it
in different positions.
Swashbuckler Type C
Problem: Predict the maximum centripetal acceleration and
compare it to the measured acceleration on Swashbuckler.
Apparatus: StopwatchVertical accelerometer
Procedure
Take data when The Swashbuckler is moving at its fastest since
this is when the centripetal acceleration is greatest.
The time of one revolution can be collected using a
stopwatch.
The diameter of The Swashbuckler can be measured next to the
ride with “String”
The "g-force" will be collected using the accelerometer (held
horizontally, pointing toward the center of the circle).
The data for the time of one revolution and diameter can be
collected while waiting for the ride. The g-force will have to be
collected while the ride is going.
Data:
Measured time of multiple revolutions ________ s Number of
revolutions you timed _________
Maximum measured g’s ______________ g’s
Calculated time of one revolution __________ s
Measured Diameter ________ m Radius __________ m
Describe how you measured the diameter or radius.
Evaluation of Data:
Calculation of tangential speed. The circumference of the circle
will be your distance.
speed __________ m/s
Using the speed and radius calculated above to calculate the
centripetal acceleration (aC = v2 / r)
centripetal acceleration ___________ m/s2
Convert the centripetal acceleration into g’s by dividing by
9.81.
Calculated g’s _________ g’s
Analysis / Conclusions
Describe how you felt when you were riding Swashbuckler from
start to finish.
Write down your maximum measured g’s from the DATA section.
__________
Write down your calculated g’s from the EVALUATION OF DATA
section. __________
How does the calculated centripetal g’s compare with the
measured g’s. Are the values similar or significantly different?
Account for any difference by describing any possible reasons for
any difference between the two values.
Goliath – Type C
Objective – Determine the g forces on the horizontal loop (helix
part) near the end of the Goliath ride and compare the measured and
calculated values. The helix is just after the area where they
brake the train to slow it down and it is a full horizontal loop.
If you’re not sure where it is, ride Goliath and when you start to
black out, you know you have found it (
Apparatus – stopwatch, accelerometer
Procedure - Stand at the right hand exit of Colossus where you
can clearly see the horizontal loop on the Goliath ride. You need
to be near the far end of the bridge for a clear view. Measure the
time for one of the trains to complete the entire loop.
From the same position, measure the time for a train to pass a
given point.
While riding Goliath, measure the g forces on you during the
horizontal loop (point the accelerometer toward the center of the
circle, and good luck!).
After riding Goliath, measure the length of the train with your
string.
This is the helix loop you are looking for!
Data
Record the maximum g-force measured on the train during the
helix loop _____________ g’s
Record the time for the train to complete the helix loop:
_________________ s
Record the time for the train to pass one point on the helix
loop: _______________ s
Record the length of the train. Use your string to measure:
Length ________ m
Record your mass in kilograms: _________________ kg
Calculations
Calculate the velocity of the train during the helix loop.
Velocity _________ m/s
Use the velocity of the train and the time for the train to
complete the helix loop to calculate the radius of the loop.
Circumference is 2(r
Radius ________ m
Use the velocity of the train and the radius of the loop to
calculate the centripetal acceleration you experience on the ride.
(aC = v2 / r)
Calculated Centripetal acceleration ___________ m/s2
Convert the centripetal acceleration into g’s by dividing by
9.81.
Calculated g’s _________ g’s
Analysis / Conclusions
How did you feel as went through the helix loop?
Why do some people lose vision (close to blacking out) at this
portion of the ride? Hint – look up why fighter pilots black
out.
Write down your maximum measured g’s from the DATA section.
__________
Write down your calculated g’s from the EVALUATION OF DATA
section. __________
Are the values similar or significantly different? Describe
possible reasons for any difference between the two values.
You Choose the Ride Lab Report
(A.K.A. the lab on the last page)
Name of ride _______________________________________ Rank (1-10,
ten being best) ______
Favorite part of the ride
___________________________________________________________
________________________________________________________________________________________________________________________________________________________
Physics of your favorite part
________________________________________________________
________________________________________________________________________________________________________________________________________________________
Least favorite part of the ride
_______________________________________________________
________________________________________________________________________________________________________________________________________________________
Physics of your least favorite part
__________________________________________________
________________________________________________________________________________________________________________________________________________________
Acceleration measurement
Where is the measurement being made?
_____________________________________________
How did you feel at the point where the measurement is to be
made? ______________________
____________________________________________________________________________________________________________________________________________________________
Measurement value _________ g’s Value in meters per second per
second ___________m/s/s
Work for conversion
Time of ride ___________s
Time in line ___________s
Divide the amount of time in line by the amount of time of ride.
Report the number with units.
Use a complete sentence to describe what the ratio found above
means.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
One word to describe ride _______________ Recommend to a friend?
_________
hmin
hactual
(hcar