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GETTING STARTED
MAKING MEASUREMENTS
Time:
The times that you are required to work out problem can be measured using a digital watch with a stopwatch or with a
second hand. When measuring the period of a ride that involves harmonic or circular motion, measure the time for
several repetitions of the motion. This will give a better estimate of the period of the motion that just measuring one
repetition. In any case, measure multiple occurrences and then the average.
Distance:
Because of the locations and normal operation of the rides, you will not be able to directly measure heights, diameters,
etc. All but a few of the distances can be measured remotely using one or another of the following methods. They will
give you a reasonable estimate. Consistently use one unit of distance – meters of feet.
1. Pacing: Determine the length of your stride by walking at your normal rate over a measured distance. Divide the
distance by the number of steps – thus giving you the average distance per step. Knowing this, you can pace off
horizontal distances to help with calculating the heights of rides.
2. Ride Structure: Distance estimates can be made by noting regularities in the structure of a ride. For example, tracks
may have regularly spaced cross members. The length of the track can be estimated by estimating the length of one of
the regularly spaced cross members of the track and then multiplying this by the number of cross members of track. This
can be used for both vertical and horizontal distances of track.
3. Triangulation: A horizontal accelerometer can be used as a sextant to measure the height (h) of a ride. Triangulation
where you cannot measure the distance to the base of the ride may be done by sighting the top of the ride from two
different positions on the ground. Sight the top of the ride from one location and obtain one angle. Pace off a distance D
toward the ride and sight the same part on the ride to obtain another angle. Use the Law of Sines to obtain the height of
the ride.
Speed:
The average speed of an object is simply the distance the object travels divided by the time it takes to travel that
distance. To calculate the average speed of an object traveling in a circle , divide the circumference by the time for one
revolution. To measure the speed of a train as it passes a particular point, time how long it takes the train to pass the
chosen point. You may have to estimate the length of one car on the train and then multiply this length by the number
of cars in the train to get an estimate of the train’s length.
ON YOUR WAY TO THE PARK
PART A: STARTING UP
Things to Measure:
As you pull away from school or from a stop light, find the time it takes to go from stopped to 20 miles per
hour. You may have get someone up front to help out on this. T = __________seconds.
Things to Calculate:
Show equations used and unit cancellations:
1. Convert 20 mph to m/s. (1.0 mph = 0.44 m/s).
v = __________m/s.
2. Find the acceleration of the bus in m/s².
a = __________m/s
3. At a second stop, set up your accelerometer and record the maximum acceleration that the bus
experiences.
a = __________ m/s
4. Using your mass in kilograms, calculate the average force on you as the bus starts up. (1 kg of mass
weighs 2.2lbs.).
F = __________N.
5. Using your mass in kilograms, calculate your weight in Newtons. (W = mg).
W = __________N.
6. How does this force (#3) compare to the force gravity exerts on you (your weight in Newtons – (#4))?
Circle one: (more, less )
7. How many g’s are you experiencing during the bus’ acceleration?
# g’s = Force experienced (#3) .
Force gravity normally exerts (your weight in Newtons)
#g = __________g’s.
PART B: GOING AT A CONSTANT SPEED
Things to Notice:
8. Describe the sensation of going at a constant speed. Do you feel as if you are moving? Why or why not?
(You will have to try to ignore the effects of the bumps in the road).
9. Are there any forces acting on you in the direction that you are moving ? Explain what is happening in terms
of Newton’s First Law.
PART C: ROUNDING CURVES
Things to Notice:
10. If your eyes are closed, how can you tell when the bus is going around a curve? Try it and report what you
notice.
11. As the bus rounds a curve, concentrate on a tree or a building that would have been straight ahead.
See if you can sense that you are going straight but are being pulled into the curve by a centripetal force.
12. What is supplying the centripetal force that is helping you round the curve?
13. How does this change when the curve is tighter or if the bus is going faster?
RIDES THAT GO IN HORIZONTAL CIRCLES
DATA:
Time for 10 revolutions of the Carousel®: __________seconds.
Angle measured by horizontal accelerometer: __________degrees.
Acceleration measured using accelerometer: _________m/s².
QUESTIONS AND CALCULATIONS:
1. Where would you need to sit if you wanted to experience the greatest speed? Why?
2. If you were on a horse and were to drop a coin while the ride was in motion, where would it land relative to you?
Describe the path of the coin until it reaches the floor.
3. Now suppose you stood near the edge of the Carousel® and dropped the coin off the side. When the coin hits the
ground, where would it be relative to you?
4. Would you ride the Carousel® on the outermost horse if the frequency of the Carousel® were 1 Hz? Why / Why not?
5. Which direction would you imagine the force acting on you would be trying to push you…toward the center of the
Carousel® or away from the center of the carousel? Is there really force acting on you in this manner? What is the cause
of feeling this way?
6. Find the frequency in rpm’s (revolutions per minute) and in hertz.
7. Calculate the linear (tangential) velocity of your horse.
8. Calculate your centripetal acceleration. Would it be the same for all horses or does it changes from center to outer
horse?
9. What is the direction of the net force acting on your horse?
10. Notice the way the floor tilts. What could be the reason for this tilt?
11. Your mass in kilograms is __________(found from the ON YOUR WAY TO THE PARK section of this packet) and your
weight in Newtons is therefore __________. What is the net force acting on you?
12. What is your tangential acceleration?
13. What is your kinetic energy?
RIDES THAT GO IN HORIZONTAL CIRCLES
BEFORE YOU RIDE:
Locate the large horizontal curve. As you stand facing the ride (at the entrance to the ride’s queue line), the large
horizontal curve will be to your right. You may need to observe the train as it travels to locate this curve.
DATA:
Your mass = __________kg.
Your weight = __________N.
Time for entire train to pass point P at the side of the loop = __________s.
Angle of the train to the vertical () = __________degrees (estimated)
Length of train = 12m.
What would happen to the angle of the train, , if the train were moving faster?
How would be affected if the radius of the curve were larger?
R = 8.5m
WHILE YOU RIDE:
Observations: While going around the curve…
1. Sensation: Circle One: (Normal, Heavier, Lighter)
2. On what part of your body did you feel forces being exerted as you rounded the curve? ____
3. Even though the train was at such a great angle as it came around the curve, did you ever feel as if you were falling
out?
4. Explain.
Maximum Acceleration Value = __________ m/s2.
QUESTIONS AND CALCULATIONS:
(while rounding the large horizontal curve)
5. Use the length of the coaster and the time it took to pass point P (in the previous diagram) to calculate the average
speed of the coaster as it rounds the far turn. v =__________m/s.
6. What type of force keeps you going around the curve?
Fy
Fseat
7. What provides you with this force?
Two forces act on you as you ride, your weight and the seat force. They are shown at the right in
Fx
bold. The seat force has two components. The vertical component balances your weight. The
horizontal component provides the centripetal force needed to make you follow the arc of the
turn. Combined as vectors they give the force you were feeling.
8. Calculate the centripetal force on you. Fc = mv² / r.
W
Fc = __________Newtons.
9. Draw to scale on the diagram given.
a. your weight (in Newtons) pointing down.
b. the vertical component of the seat force pointing up (it is the same size as your weight!)
c. the horizontal component which is the centripetal force you calculated above.
10. Complete the vector diagram: Find the resultant
a. by approximating the length and angle of the on the diagram and
b. by calculation:
Seat Force = __________N @ angle ()_________degrees.
11. How does your calculated seat force angle compare to the angle and seat force you measured? How can you account
for discrepancies?
RIDES THAT GO IN VERTICAL CIRCLES
BEFORE YOU RIDE:
Estimate the diameter of the Wheelie® by triangulation or by scaling with a known sized object:
r1 = __________degrees
2 = __________degrees
h = __________meters
Diameter = __________meters
Radius = __________meters
1. Note the Angle each car makes with the vertical as the wheel approaches full speed while still rotating horizontally. Is
each car uniformly the same angle, regardless of its position around the wheel?
Carefully observe the angle of each car relative to the suspension point as it rotates after the Wheelie® is completely
raised vertically.
2. Why is it different when approaching the very top from when it is approaching the very bottom?
DATA:
Time for 10 revolutions (when traveling at full speed): __________seconds
Period (at full speed): __________seconds
Frequency (at full speed): __________hz
WHILE YOU RIDE:
Accelerometer readings: (Best estimate from time stamp)
a. at full speed, but while still horizontally oriented: __________g’s.
b. at the top: __________g’s.
c. halfway down: __________g’s.
d. at the bottom: __________g’s.
e. halfway up: __________g’s.
QUESTIONS AND CALCULATIONS:
3. Calculate the circumference of the ride. Then calculate the linear (tangential) speed of the car at full speed, but still
horizontally oriented.
v = __________m/s.
4. What is your centripetal acceleration at this phase of the ride?
ac = __________m/s2
5. How does your calculated result compare to the measured value?
6. Draw a free body diagram showing the forces acting on you:
a. at the top
b. at the bottom
c. halfway down
7. Where is the net force the greatest? Is this calculation collaborated with your accelerometer data? How did you feel
at this part of the ride?
RIDES THAT GO IN VERTICAL CIRCLES
BEFORE YOU RIDE:
*Use triangulation to determine the height (h1) of the first hill and the height (h2) of the largest loop.
r1= __________degrees (hill)
r2 = __________degrees (hill)
r1= __________degrees (loop) r2 = __________degrees (loop)
h1 = __________meters
h2 = __________meters
Step back and look carefully at the loop. It is not really circular. For safety’s sake, the car is going faster than the absolute
minimum speed at the top of the loop – so even when friction is a factor, this additional speed would make the rider
uncomfortable at the bottom of the loop is avoided by using what is called a clothoid loop in place of a circular loop.
1. Sketch the loop as you see it.
2. The radius of curvature is changing. Does this increase or decrease as you go from the bottom to the top of the loop?
WHILE YOU RIDE:
Use your accelerometer to measure the g’s at the various points during the ride.
Minimum acceleration _________g’s experienced at the (bottom, midway, top) of the loop.
Maximum acceleration _________g’s experienced at the (bottom, midway, top) of the loop.
QUESTIONS AND CALCULATIONS:
3. What happens to the gravitational potential energy on your way down the first hill?
4. Describe (in detail) the transition between gravitational potential energy and kinetic energy as the coaster goes
through a loop.
4. What two forces are acting on the train at the top of the loop? Give the direction of each force.
5. Why doesn’t the rider fall out of the train at the top of the loop and land on his head?
6. Using the data collected above, calculate the value of the gravitational potential energy at the top of the highest hill
and at the top of the loop.
7. From conservation of energy considerations use the change in height from the top of the first hill to the top of the
loop to calculate the speed of the train as it goes through the highest point in the loop. Does this satisfy the critical
speed criteria? Vc = √(rg)
8. Assume that the loop is circular. From your measure of the height – calculate the critical velocity and the kinetic
energy at the top of the loop.
9. From the potential energy calculated in #1 and from the kinetic energy calculated in #2, calculate the velocity of the
train at the top of the loop. Does the train have enough speed to travel in a circle?
10. What force would be exerted on you at the bottom of the loop if the loop were circular? How many g’s would this
be?
Since most people begin to feel uncomfortable beyond 3.5 g’s and some even pass out just over 4.0 g’s, do you see why
a clothoid rather than a circular loop is used?
RIDES THAT GO IN VERTICAL CIRCLES
BEFORE YOU RIDE:
*Use triangulation to determine the height (h1) of the first hill and the height (h2) of the largest loop.
r1= __________degrees (hill)
r2 = __________degrees (hill)
r1= __________degrees (loop) r2 = __________degrees (loop)
h1 = __________meters
h2 = __________meters
Step back and look carefully at the loop. It is not really circular. For safety’s sake, the car is going faster than the absolute
minimum speed at the top of the loop – so even when friction is a factor, this additional speed would make the rider
uncomfortable at the bottom of the loop is avoided by using what is called a clothoid loop in place of a circular loop.
1. Sketch the loop as you see it.
2. The radius of curvature is changing. Does this increase or decrease as you go from the bottom to the top of the loop?
WHILE YOU RIDE:
Use your vertical to measure the g’s at the various points during the ride.
Minimum acceleration _________g’s experienced at the (bottom, midway, top) of the loop.
Maximum acceleration _________g’s experienced at the (bottom, midway, top) of the loop.
QUESTIONS AND CALCULATIONS:
3. What happens to the gravitational potential energy on your way down the first hill?
4. Describe (in detail) the transition between gravitational potential energy and kinetic energy as the coaster goes
through a loop.
5. What two forces are acting on the train at the top of the loop? Give the direction of each force.
6. Why doesn’t the rider fall out of the train at the top of the loop and land on his head?
7. Using the data collected above, calculate the value of the gravitational potential energy at the top of the highest hill
and at the top of the loop.
8. From conservation of energy considerations use the change in height from the top of the first hill to the top of the
loop to calculate the speed of the train as it goes through the highest point in the loop. Does this satisfy the critical
speed criteria? Vc =√(rg)
9. Assume that the loop is circular. From your measure of the height – calculate the critical velocity and the kinetic
energy at the top of the loop.
10. From the potential energy calculated in #1 and from the kinetic energy calculated in #2, calculate the velocity of the
train at the top of the loop. Does the train have enough speed to travel in a circle?
11. What force would be exerted on you at the bottom of the loop if the loop were circular? How many g’s would this
be?
Since most people begin to feel uncomfortable beyond 3.5 g’s and some even pass out just over 4.0 g’s, do you see why
a clothoid rather than a circular loop is used?
RIDES THAT ALLOW YOU TO FALL
BEFORE YOU RIDE:
A. Use the triangulation method explained in the “Making Measurements” section of this packet to determine the
height of the tower.
B. Record the time it takes for the ride to fall until the unit reaches the breaking point. You should time the ride for
several falls and use an average time in your calculations.
DATA:
r1 = __________degrees
r2 = __________degrees
Distance paced off (D) = __________meters
h =__________meters
Time of fall = __________seconds
Maximum Accelerometer Reading __________
QUESTIONS AND CALCULATIONS
Try to ride Acrophobia® twice (if you can stomach it). The first you ride it look out (away from the ride) and the second
time you ride it, look down.
1. Which is harder to do? Why?
2. Using the time of fall and the acceleration due to gravity, how fast is Acrophobia® traveling at the moment that the
breaks begin to slow the ride?
v = gΔt = __________m/s
3. The mass of the passenger-carrying ring is 10,542kg. How much kinetic energy does the ring have at the velocity that
you calculated in question 2?
4. Use conservation of energy to determine the height of the tower.
H = ½v2/g.
5. How does this value compare to your measured value in the DATA section above? Account for any discrepancies.
6. Are you moving toward the ground at this rate, or is the ground moving toward you at this rate? Discuss in terms of
frame of reference.
RIDES THAT ALLOW YOU TO FALL
BEFORE YOU RIDE:
1. Observe one log coming down the hill. You will notice that the very front of the log has an unusual shape (it is not
streamlined like the nose of an airplane). Why do you think the engineers designed the front like this?
2. Observe a number of logs going over the hills and make the following observations:
A. If there is a lot of mass up front, is the splash smaller or larger? Explain.
B. If the riders are the same height, who gets wettest, the first or the last person?
The final downhill slop (the big splash is about 36 meters long). The log starts basically from rest and shoots down the
hill. By measuring the time it takes the log to get to the bottom, you can determine the acceleration of the logs as well
as the final speed at which the log hits the water at the bottom of the hill.
3. Measure how long it takes for a log to descend the final chute. You should time several logs going down the hill to get
a good idea of the average time per log.
Tavg = __________seconds
4. Use the formula a = 2d/t2 to calculate the acceleration of the log.
a = __________m/s2
5. An object in free fall has an acceleration of 9.8m/s2. How does your answer to question #4 compare with this? What
factors contribute to the difference in your answer and the acceleration due to gravity?
6. Estimate how fast a log is going at the bottom of the chute?
_____5 m/s? _____10m/s? _____100 m/s?
(60 mi/hr = 88 ft/s = 26.8 m/s)
7. You can now determine the speed at the bottom of the chute by using the formula: v = at.
Speed at the bottom of the hill __________m/s.
8. How does your estimated speed compare to your calculated speed? Are you surprised?
AFTER YOU RIDE:
9. Does the log move through the water or does the water move with the log?
10. In some areas, your log slows down rapidly. What happens to the water here?
11. Does the water move uphill when the log goes uphill? Is the water at the high areas of the ride?
12. What keeps all the water from running down to the bottom parts of the flume?
DATA
Maximum Accelerometer Reading __________
Roller Coasters
CHOOSE:
1. Which coaster did you chose? Circle one: Great American Scream Machine or Georgia Cyclone
The Great American Scream Machine and the Georgia Cyclone are two examples of old time wooden roller coasters
engineered with modern technology. After riding both coasters, you should have a feel for which coaster goes faster.
Each one has different speeds at various points, however we can figure out which coaster has the greatest average
speed.
ESTIMATE:
2. Which coaster do you think has the greatest average speed? (Make your guess before you calculate numbers!)
The total length of track for the Great American Scream Machine is 3,800 feet. Using a stopwatch, time yourself on the
ride from point of departure (as soon as you start moving) until you return to the station (after completely stopping).
Total time of the ride: __________________ seconds
Average speed of the Scream Machine: ______________ft/s = ______________ mi/hr
The total length of track for the Georgia Cyclone is 3,434 feet. Using a stopwatch, time yourself on the ride from point of
departure
(as soon as you start moving) until you return to the station (after completely stopping).
Average speed of the Georgia Cyclone: ______________ft.s = ______________ mi/hr
3. Based on the above calculations, which ride has the greatest average speed?
4. Was your guess correct?
5. What factors influenced you to make the right or wrong decision?
BEFORE YOU RIDE:
Stand back and look at the shape of the hills. Sketch the basic shape of one of the curves. This shape is no accident. It
was chosen to give you the feeling of falling. Choose your seat carefully. You will calculate the average speed of the
coaster, however, the rider actually feels the instantaneous speed. So the rider in the first seat has a different ride than
the one in the last seat.
6. Which rider goes faster, the one in the front seat or the one in the back seat? Explain in terms of physics.
(Try to ride the ride twice--once in the front seat and once in the back seat).
DATA:
Height at the highest point of the ride: _______________ meters
Height at the lowest point of the ride: _______________ meters
Length of track (Scream Machine = 3,800 ft; Georgia Cyclone= 3,434 ft)
Length of train (Length of car x # of cars) = ________________ meters
Radius at the “dip” at the bottom of the first hill: ______________ meters
Height of the second hill: ___________________ meters
Time for the entire ride: ___________________meters
Time for train to pass a point at the top of the first hill: ________________ seconds
Time for train to pass a point at the bottom of the first hill: __________________ seconds
WHILE YOU RIDE:
Max acceleration ____________________ g’s experienced at ______________________
Min acceleration ____________________ g’s experienced at ______________________
QUESTIONS AND CALCULATIONS:
7. Calculate the average speed of the train for the total ride.
8. Speed at the top of the first hill.
9. Speed at the bottom of the first hill.
10. If all the GPE and KE at the top of the first hill is converted to KE at the bottom of the first hill, how fast is the train
going at the bottom of the first hill?
11. How dos the calculated speed in #4 compare to that in #3?
12. What is the centripetal acceleration (in g’s) in the dip (bottom of the first hill)?
13. What is the total acceleration (in g’s) in the dip? How does the total acceleration you calculated compare to your
measured value?
14. From your height measurements for the first two hills, estimated the energy lost to friction as a function of track
length?
15. Where on the ride did you experience the greatest acceleration? In which direction was it? Why there and not
another place?
16. Where on this ride did you feel like you were being lifted out of your seat? How did the ride create that feeling?
17. What force causes you to be thrown from side to side in the train car? (Describe the shape of the track when you are
experiencing this if it helps.)
18. Why are the curves banked (sloped toward the inside turn of the turn)?
19. What are the elements (in physics terms) that make the roller coaster “scary”?
ENGINEERING MARVELS
BEFORE YOU RIDE:
Notice that the wheels on Superman are not all the same.
1. Why do you think that different materials would be used to make the wheels? Come up with some physics reasons
that might explain these differences.
While waiting in line, record the time it takes for the train to complete its trip. Time several trips to get an average time.
Time #1 _______________ s Time #2 _________________ s Time #3 __________________ s
Average time of travel = __________________ s
AFTER YOU RIDE:
2. Where along the ride did you experience the largest g-force? What part of you experience the greatest pressure?
3. Draw a free-body diagram for this location on the ride.
4. Superman contains 2,759 feet of track. Using the average time of travel measured above, calculate Superman’s
average velocity.
v = ___________________ ft/s = ______________________ m/s
5. If the ride time were cut in half, how would this change the average velocity of the coaster?
6. How could this change in average velocity affect the amount of g-force that you feel during the portion of the ride
that you mentioned in question #2?
7. In terms of safety measures, what concerns do the engineers have to address when designing and building a ride of
this nature? Do you think that the different materials that make up the wheels of this ride come into play? How?
8. How much of a role does the mass of the passengers play in the average velocity of the ride? (Hint: Try to estimate the
mass of passengers on a full train vs. the mass of the train itself. - Would there be a huge difference?)
9. Do you notice a significant difference in the time it takes for the train to return to the loading dock with each ride?
10. What are the chances that the mass of passengers in a full train is exactly the same with each load?
ENGINEERING MARVELS
BEFORE YOU RIDE:
1. Where do you usually sit when you want the fastest ride? Why (in physics terms) do you sit there?
2. Observe the coaster as it travels – try to observe the front car’s velocity vs. the back car’s velocity. Which car seemed
to travel faster? (front, back)
Ride this ride twice if possible- once in the front seat and once in the back seat! Do your best to notice two things during
this ride:
3. First, notice how many times it seems as if you feel the sensation of being thrown out of the coaster ( you’re
experiencing vertical acceleration of less than 1 g).
3. Second, notice differences in velocity from your ride in the front sea from your ride in the back seat.
AFTER YOU RIDE:
4. In which seat did you get the faster ride? (front, back) Can you explain why (in physics terms).
5. How many times did you experience a vertical acceleration of less than 1 g?
6. How does the coaster create that sensation?