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

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