2015 Physics Guide
Transcription
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)