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 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 G-FORCE RIDE

Orbiting Shuttle 0 G

The Moon .17 G

Mars .39 G

Jupiter’s clouds 2.64 G

Shuttle lift off 3.0 G

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

For a roller coaster find the lift motor horsepower,

the coaster weight, the coaster capacity, and the

first hill height. Figure out how long it will take for

a full coaster to reach the hilltop with the motor

running at full power (HINT: 1 Watt = 1 Joule/set)

VECTORS

Show how the GRAVITY and CENTRIPETAL

FORCE vectors combine at the top and at the

bottom of the loop below.

CENTRIPETAL FORCES

Let

v = velocity

Fc = centripetal force

ac = centripetal acceleration

r = radius of ride

Show that Fc = and that ac =

Calculate the centripetal acceleration for one ride.

Convert your answer to G’s using the fact that 1G =

9.8 meters/sec2.

PARABOLA PEAKS

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.

Plot parabolic curves for peak speeds of 2.2

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.

Let

v = velocity

m = mass

g = gravity acceleration

h = height of coaster

Potential energy = mgh

Kinetic energy = ½ mv2

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?

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 = radius of curve

Gravitational force = Ncos q = mg

Centripetal force = 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.

ANGLES AND ARCS II

90

0 An object on the horizon has an

angular height of 0

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.

Record your observations:

Time Sun Height

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 DISTANCE

8. Add this product to the height of the string hole.

_______ + ________________ = _______ the height of the tree or ride

PRODUCT HEIGHT OF STRING HOLE

Angle Tangent Value

0 .00

5 .09

10 .18

15 .27

20 .36

25 .47

30 .58

35 .70

40 .84

45 1.00

50 1.19

55 1.43

60 1.73

65 2.14

70 2.75

75 3.37

80 5.67

85 11.43

90 57.29

Safety First: Do not ever look directly at the sun!

tube

angle shown here is the

height of the sun

bright spot on ground

7

Accelerate

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.

Ride Information

Parallel Channels 2

Highest Point of Ride 2nd Hill

Number of Boats 24

Boat Capacity 6 adults

Decelerate

Greatest Gravitational

Potential Energy Spot

Banked

Curve

Forward

Leaning

Zone

Backward

Leaning

Zone

Weightless

Zone

Parabolic

Arc

Greatest Kinetic

Energy Spot

Greatest Gravitational

Potential Energy Spot

Inertia

Jerk Momentum

Roll

1

2

3 4

5

6

8

BAMBOOZLER

Describe a place where each sign should be placed.

Ride Information

Trip Time 1.5 Minutes

Drive Motor 1.5 – 7.5 kilowatts 480 V 3 phase

Capacity per Trip 42 adults

Hydraulic Pump 19 kilowatts 480 V 3 phase

Maximum Speed 15 rpm

Wheel Diameter 15 meters

Angle of Lift 54

Gravity at

Work

Greatest Gravitational

Potential Energy Spot

Greatest Kinetic

Energy Spot

Centripetal

Force at Work

High G-Force

Zone

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.

Ride Information

Total Height 21 meters

Ride Capacity 40 adults (665 newtons each)

Vertical Angle 88

Gondola Weight 887 newtons

Total Wheel Diameter 17 meters motionless, 20 meters in motion

Rotation Rate 12 rpm

3

5

7 3

4

1

2

6

Backward

Leaning

Zone

High G-Force

Zone

Banked

Curve

Greatest Kinetic

Energy Spot

Centripetal

Force at

Work

Forward

Leaning

Zone

Greatest Gravitational

Potential Energy Spot

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. 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?

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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.

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

Centripetal

Force at

Work

Greatest Kinetic

Energy Spot

Forward

Leaning

Zone

Backward

Leaning

Zone

Minimum

Speed

Driver who

will be thrown

sideways Car which

will change

direction at

the crash

Car which will

accelerate the

crash

Driver who

will be thrown

backward

Driver who

will feel the

strongest jolt

Car which will

decelerate at

the crash

Driver who

will be thrown

forward

faster car

slower car

Which car will bump the driver more, the faster

car or the slower car?

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.

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

Centripetal

Force at

Work

Inertia

Jerk

Minimum

Speed

Unbanked

Curve

Air

Resistance at

Work

Sideways

Leaning

Zone

Greatest Kinetic

Energy Spot

Rider’s path for 3 turns of center arm

Rider’s path for turn of center arm

1

2

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 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.

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 = F x d

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.

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.

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?

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.

A

B

C