Physics of Fun offers students an adrenaline-fille adrenaline-filled d ride that tackles numerous experiments and links physical science theories to the real world.
Teacher's Notes
Duration: 23 min Years: 11-12
This video Teacher’ Teacher’s s Guide includes detailed The offers a lot of different physicsexplanations examples of examples the concepts presented, question-andwhere the theory is easilyalong linkedwith to experience in answerproblems. handouts.The Themarvel video’sofintroduction assembles simple it all is that there is a montage of is events that range from the simple, control, there prediction, there is safety. Or maybe it easy-to-understand easy-to-underst andout physics concepts to the more is that things aren't of control, we don't experience complex Use the program to excite students the totallyones. unpredictable, and no one gets hurt. aboutwe physics and toeach illustrate physicsthrilling, occurs in How experience eventhow is exciting, of Car Crashes everyday don’t pumping. miss Physics , and it getslife. theAnd adrenalin There is always that also produced distributed nervous feeling by as Classroom our senses Video tell us,and even scream atby CLEARVUE us, that we are/eav. unsure, even when we understand the physics. The introduction puts together a montage of physics Fun , students In Physics see:easily understood events thatofrange from the will simple, ones to the more complex ones that even when we • Conversion of potential energy (PE) to kinetic understand them, our senses describe them energy (KE) and back again; differently. • Conversion of PE to KEattotheheat straight My personal experience fun in park alwaysorhas me complex descents; head towards the little simple ones first, like Bam• Balance of a set of or force Bam's Balloon Race the vectors; little slide where mums and • Addition of tightly severaltoforce give with an dads hold on their vectors children.toThen acceleration in a on changing direction; confidence gained, to the next level. • Production of see projectile motion that traces a The physics we includes: Converting potential parabola; energy (PE) to kinetic energy (KE) and back again; • The parabola weightlessness; Converting PE topath KE and to heat in straight or complex • Radial acceleration get a horizontal descents; Balancing atoset of around force vectors; Adding corner; several force vectors to give an acceleration in a • Radial acceleration to get around a vertical changing direction; Producing projectile motioncorner; that • Changing rotational speeds and angular traces a parabola; The parabola path and momentum; Radial acceleration to get round a weightlessness; • The distribution massacceleration in rotating objection; and corner horizontally;of Radial to get round a • Rotational inertia. corner vertically; Using components of F g with banking tracks to make it easier to get around a corner; Changing rotational speeds and angular momentum; Students will view morein than 50 physics concepts in The distribution of mass rotating objects, rotational this program. To help navigate the content, the inertia. examples are assembled below the headings To help navigate through the overunder 50 examples we have where theythem appear video.statement below, assembled as in thethe content under the headings as they occur in the video.
Trapeze artists; Pirate Ship; Russian tumblers; Tumblers on see-saw, 1 jumper, 2 jumpers; Big Dipper; Roller Coaster loop; Water Slide into water. River Ride Slippery dip, walk up, slide down; Trapeze artist, man drops, woman drops. Tightrope; Cable car. Circle high ride; Horizontal ride; Ride with spin; Ship with 2 motions; La Bamba; human cannonball; Second shot into harbour; 2 from cannon; Fireworks missile path -> trajectory; Free fall tower, s v graph + sh graph, combined graph; Right quadrant of parabola; Fireworks shot horizontally; Fireworks shot vertically up; Complete parabola; Car on ramp; Tumblers on springboard; Bike off ramp. plane with engines off; Big dipper and weightlessness; Animated big dipper. Merry-go-round; Dummy off seat; Truck crash into wall. Merry-go-round animation; Merry-go-round at night, vector diagram; Tasmanian Devil circular ride; Circus horse rides; Big Dipper track banking; Witches Fury with attached accelerometer; Fast Ferris Wheel. La Bamba; Very fast Ferris Wheel; Looping Roller Coaster. Spinning Aerialist; Increasing angular velocity; Animation Animation on spinning seat. Aerialist Aerialist on rope; Trapeze artist swinging; Pirate Ship pendulum.
Page 4 KEY WORD LIST
Energy conservation, energy conversion, energy transfer, energy loss, potential energy (PE), kinetic energy (KE), fuel, inertia, heat, velocity, speed, acceleration, weight force or gravity force (Fg ), orbital speed, angular velocity (w), centripetal force (Fc), normal or reaction force (FN), tension force (Ft), centripetal acceleration ac, turbulence, frictional force Ffr , catapult, missile. POTENTIAL AND KINETIC ENERGY
As the trapeze artist swings, her initial potential energy is converted into kinetic energy. This conversion increases her velocity from zero to what it would have been in free fall. As KE is a scalar quantity, this velocity will take on the direction of the swing arc at any time. The vertical velocity changes are interesting as they lead to the concept of simple harmonic motion, SHM. (Q1, 2.) The Pirate ship shows the conversion of PE to KE to PE. But it is not a simple pendulum, and so the velocity at the bottom is not as fast as it could be. (Q3.) The same conversion is seen with the Russian tumblers. Notice the effect of starting with twice the amount of PE; the catapulted tumbler rises 2x as high. Again in the Big Dipper we see the same conversion. In the Roller Coaster the energy lost on each run has to be made up before the next journey, otherwise there would be a real problem. To stop the journey in the end, more energy has to be lost. The brakes are applied and things get noisy and hot. The Water Slide is a variation of this. (Q4, 5, 6.) PE->KE->HEAT
Both the river water and the boat are lifted to gain PE, the energy for the ride down. This is converted to KE during the ride. Luckily it is designed so the water quickly reaches terminal velocity as friction and turbulence constantly remove energy from the system. Again the water heats up.
Page 5 WORK=FORCExDISTANCE
When we walk up the stairs of the slippery dip, 3/4 of our food fuel is used in running our body and 1/4 is converted to PE. In walking up the stairs we are doing work by applying a force just larger than F g and moving it through the height of the stairs. At the top of the stairs our PE = Fgh = mgh. We will do the same work in sliding down and our PE is converted into KE and heat through friction; we reach a terminal velocity. The slide should be called the "friction dip".(Q7, 8.) As the trapeze artists fall into the safety net, we again see a force applied to stop them, and this force moves through a distance as the elastic rope stretches. So the work done by the rope = mgh = the average stopping force stopping distance = Fs. (Q9.) VECTORS
We could calculate this stopping force using a vector diagram. This same vector diagram is useful in working out the tension in a tightrope. (Q10.) COMPONENTS OF MOTION
Complex motion is made of several simple movements combined. Each of these are termed components and by examining them one at a time, the resulting motion can be better understood, and even better experienced! If La Bamba was a horizontal ride travelling at the same speed our experiences would be different; something is added by rotating in a vertical plane. Four different experiences are added: falling, stopping the fall, accelerating upwards, and being catapulted. (Q11.) The Human Cannon Ball also experiences complex motion, in fact each of the four sensations just listed above. But is this path part of a circle? We find out by dividing the trajectory into just 2 components, one looking at the vertical movement, and the other the horizontal movement.
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The Free Fall Tower takes you up and drops you down. The investigation starts by making a distance or displacement picture of its fall. Falling 1 2 from rest, the relationship s = at lets us find 2 how far it travelled in each time interval - each 1/25 th of a second, the time between each video frame, or each second. (Q12.) This becomes the vertical axis for our picture. To get the horizontal movement we add the second component, travelling the same distance horizontally each time interval, so no acceleration. By combining these 2 components, half a parabola is produced. The family of parabolas is produced by having a different horizontal velocity for each. Each falls the same vertical distance in the same time. The rules also apply to a missile shooting upwards. It is also accelerating downward and so its velocity is reduced by 9.8 ms-1 each second until it stops at the top of its flight. The complete parabola results when the missile has the same horizontal velocity on the way up as on the way down - our Human Cannon Ball, or the car jumping 3 cars using a ramp. The tumblers catapulted from the springboard also demonstrate this. There is something else to be seen as the bike rider launches from the ramp. Both paths, his and the bike's, are parabolic, they both have the same horizontal velocity (minus the little push). As they both fall, the rider will no longer feel the bike pushing up against his weight force. They are both in free fall together. (Q13.) An airplane with its engines off, and a minor adjustment to compensate for wing uplift, becomes a missile. It follows the path of a parabola as it falls. The passengers experience
this same weightlessness as they are free-falling together with the plane. They temporarily feel the sensation of zero gravity. Whenever the plane follows part of the inverted parabolic path, even when going up, the passengers experience free-fall. The track of the Big Dipper has this same parabolic path and so the riders will momentarily feel the fun of being weightless or freefalling with the carriage. At the bottom of the Big Dipper dips however, theres a payback, the carriage pushes back on the riders very hard. They have to stop falling and then be catapulted back up in a short time. This push changes the direction of travel very quickly. On a Merry-go-round we experience a continuous force causing us to constantly change direction, but we retain the same speed. This force, called a centripetal force, keeps pulling us sideways, horizontally towards the centre. Without this pull we would go straight ahead. But this centripetal force is different to the forces we experience in the dip. Three forces appear to act: the tension in the rope, Ft, and the gravitational force, Fg , are constantly balanced, to give the required centripetal force (Fc). Because Fc is a component of our weight force, the experience is similar to leaning into a corner to turn a pushbike. (Q14.) The vector diagram shows the 3 forces acting: F t + Fc = Fg. Such a combination, where the weight force is the resultant of the 2 others, gives a horizontal centripetal force that is not bone shattering. In fact it is very gentle as seen acting on the acrobats on horseback, constantly moving them in their circle. And it is the same for the fast train ride - the Witches Fury. By using the attached water tank as an accelerometer, a clearer picture emerges. As the car moves into the curved banked section of the ride, the water surface in the tank and the pendulum are no use in telling where the horizon is. But they do tell us other things, and help locate the same 3 forces again. The camera is attached to the car and as it banks, the EarthÕs horizon appears to tilt anti-clockwise. By pausing the video this new horizon and thus Fg can be
found. The banking appears "flat" as does the water surface. In text books the frame of r eference is usually the Earth and not the car. The only 2 forces acting ar e F and F and as the car doesn't slip on the N g bank, Fg must be balanced by an equal and opposite force, -Fg. But the only force in this direction is FN so Fg must be a component of FN with Fc, the centripetal force, being the other component. Fc is the unbalanced force acting towards the centre of the circular track. tan α =
F c or F = m.g.tan α m.g c
2 2 but F = mv ∴ m.g.tan α = mv c r r 2 or v = r.g.tanα
∴v =
r.g.tan α
Phew!! It would have been a real mess if "m" was still a variable. (Q15.)
T
= 4seconds, r = 8metres
2 2π ∴a c = rω 2 = 8 × = 19.7ms − 1 4 2π r and v = = 12.6ms −1 T
At the top, from F = ma F + mg = ma N ∴ FN = ma − mg or F = m[19.7 − 9.8], so F N N At the bottom, from F = ma F − mg = ma N ∴ F = ma + mg N or F = m[19.7 + 9.8], so F N N
= 10m newtons.
= 30m newtons.
VERTICAL RIDES.
In the La Bamba we experience 2 vertical events. Firstly the seat or ride has to accelerate us up, and to do this it has to apply a force greater than Fg, and then it has to launch us. If the top of the seat decelerates vertically faster than we do, then we float off the seat and free-fall. At the bottom, the seat slows us down to zero and then starts launching us again. On the Fast Ferris Wheel example, measurements can be made to show that at the bottom of the ride the push that the seat gives us is about 3x Fg, while at the top we stay pushed to the seat with a force of about Fg. (Q16.)
ANGULARMOMENTUM
The spinning aerialist, as her assistant applies a torque, spins faster and faster, gaining angular velocity and angular momentum. With no more help, her angular momentum, Iw, will not change. But by changing her radius of rotation, her angular velocity must change to conserve her angular momentum. (Q17.) I ω =I ω 1 1 2 2 But I = kmR 2 So if R increases then I will increase dramatically. Therefore w must equally decrease for Iw to remain the same. The animation works through the same logic.
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This has to do with the way rotating objects respond to an applied torque because of the distribution of their mass. As the trapeze artist changes the position of her centre of mass, she changes the period of the pendulum she is part of, and can thus speed it up or slow it down. The swing frequency of a physical pendulum is governed by this mass distribution. In a simple pendulum the mass is concentrated at the end, and the formula used to calculate the period is an approximation. (Q18.)
Producer
Editor/FX
Sound
For a physical pendulum the period, T, is given by : T = 2π
Executive Producer
I mgh
For a simple pendulum the period, T, is given by : T = 2π
Teachers notes
l g
If the Pirate Ship was not a compound physical pendulum then the period of the swing would be much less, and the speed at the bottom would certainly make us scream! (Q19.)
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Questions 1. Make measurements from the video to determine the speed of the trapeze artist. Remember the time between each video frame is 1/25 th seconds. Her height is about 1.6 metres, and her mass is about 60kg. 2. What are the units of Energy? How can we find out her PE? Calculate the PE lost as she falls. If all this PE converts to KE, use mgh = 1/2mv 2 to calculate her speed at the bottom of the arc. Does this value agree with your answer in Q1? 3. Calculate the speed of the Pirate Ship at the bottom of its arc. Does the ship work like a simple pendulum? 4. Try working out the speed of the Big Dipper at the bottom of its run if all its PE was converted to KE. 5. The Roller Coaster travels through a tear-drop loop. Why is it this shape? Its velocity or speed on entering this loop of 7 metres diameter is about 7ms 1. What is its speed at the top of the loop? Use measurements from the video and calculate its PE and KE to check. 6. Describe all the energy changes that occur with the Roller Coaster from getting on to getting off. Do the same for the Water Slide. 7. What would your PE gain be in walking up the stairs of the Slippery Dip? If 1 joule of fuel is contained in a 0.25 mm grain of sugar, how many sugar grains would you have used as fuel to climb the stairs? 8. What would your speed be at the bottom if all this PE was converted to KE? Show that your mass is not part of this calculation. OR: Why do all sliders reach the same velocities? I worked it out to be about 14 ms-1 or about 50 km/hr. Why would this be a problem at the end of the slide? What could be done? Why do they close this "friction dip" when it rains? 9. The trapeze artist falls 6 metres from her swing into the safety net. How long before she hits the net? How fast is she going when she hits? What is the stopping force she experiences if her mass is 60kg? There are several ways of finding this. Try others and see how closely they agree. o
10. The angle the tightrope makes to the horizontal is about 3 . Use a vector diagram and calculations to find the tension in the rope. Is this a small value or a large one?
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Questions (cont'd) 11. There is a lot we can find out from La Bamba! First list all the things that change during one revolution. Then record how you experience these changes, especially with your feet. What do you feel during each quarter of a revolution? What would you experience if La Bamba went slower? If it went faster? 12. There are rides in some Fun Parks where the ride is similar to La Bamba, but horizontal. Describe one such ride. What is the difference in what you experience? 13. This question refers to the Free Fall Tower. Try to work out things about the tower. How high is it? How long does the car take to fall? How is it stopped? 1 2 Given the equation s = 2 at , which tells us how far something falls under F g each second, calculate how far the car falls each 0.1 of a second. Can you find its final velocity? 14. Examine the bike rider launching from the ramp. Try to take some measurements from the video. Is it real time or has it been slowed down? If the video is in real time then the time of his fall is 2.4 seconds. Why is this probably not true? Find his horizontal velocity as he leaves the ramp. Why did he push back on the bike? Did the bike push on him? What would this change? Many old movies were shot at 16 frames per second, the video plays at 25 f/ps. 15. Draw a force diagram showing how a cyclist turns a corner without turning the handlebars. Include those forces between the horizontal road and the wheel as well. 16. As the Witches Fury moves into the fast section of the track, pause the video and examine the Earth's horizon and the water surface in the tank. Draw what you notice. What are the only 2 forces that act on the car? Draw the accelerometer from the EarthÕs frame of reference. Complete a force vector diagram to show th origin of the centripetal force Fc. Show that Fc does not depend on the masses involved. 2 17. Using the Fast Ferris Wheel footage determine T, the period of rotation, r, the radius of the wheel and use a = rω to determine the centripetal acceleration. c What is the velocity of the car? What are the forces on you at the top, sides & bottom of the ride?
18. Explain how tumblers change their angular velocity. 19. Locate examples of pendulums in action. Calculate their period, T. Place these results in a table together with the length of the pendulum. Draw a graph of length against the period of the swing. Comment on any examples where the results do not fit the general pattern. 20. Examine the Pirate Ship footage. Does the seat include a harness? Would a harness be necessary? Passengers fear losing things from their pockets. Comment on this. If all the PE that the Pirate Ship has at the top of its swing converted into KE, what would its final velocity be at the bottom of the swing? Why does this not occur? Page 14
