#· #· ©Name· @Name· Date· Date· Midway Physics at the Fair #· (j) Name· Date· Chapin High School 2 Observing Rides Many interesting observations about science can be made while enjoying the State Fair, not all of them requiring calculations. In this section we have made a list of some of them. There are other observations also, and we hope you will keep a good sharp eye out for things we did not include. • Could you figure out the height of the rocket at the front gate using only its shadow and a yardstick? • As a Ferris wheel turns, a mark on the side moves in a circular path. Why is this so? As you sit in the moving seat of the Ferris wheel, sometime your feet are "inside" the wheel and sometimes they are "outside" Draw a diagram to represent the path of the mark and the path of your feet. Do your feet move in a circular path? • Try to diagram the paths of the more complicated rides. Mark where they are going fastest. Mark where the change in direction is sharpest and mark where the change in speed is greatest. • Ifyou carry a scale on the Ferris Wheel, do you expect things to weigh the same all around the trip? What would you expect at the top, bottom, and the two sides? Assume the wheel turns smoothly. Can you think of a way to test your ideas using a simpler method than riding a Ferris Wheel? • Ifyou carry a pendulum onto a merry-go-round would you expect its time-of-swing (period) to be different from that on the I ground? How about other rides - such as the Ferris wheel or a roller coaster? • What factors make it hard to toss a ring over a peg to win a prize? Look carefully at what happens, and see if you get some ideas. • Look in the mirror at the fun house. Is there a connection between the way the mirror is shaped and the way your image is shaped? Try your ideas for differently shaped ntirrors. • What will happen if a skinny driver in a bumper car runs head-on into a heavy driver in a bumper car? What happens if one or the other car is not moving? Why does the bumper car ride have a ceiling? Can you draw an electrical circuit diagram for the bumper car ride? • Are the rides and Midway illuminated primarily by incandescent or by florescent lamp bulbs? Why? 3 Ride Physics In this section we will discuss how you can apply physics principles to some of the rides at the South Carolina State Fair. Analyze several of the rides mentioned in this booklet and then use those rides as starting places for investigating other rides. One of the measurable aspects of fair rides is the force that they exert on you and the acceleration you feel. The force and acceleration are connected through Newton's second law; F =ma, where Fis the force in Newtons (N), ni is the mass in kilograms (kg) 1 and a is the acceleration in meters per second per second (mfs2). When the only force on you is the force of gravity your weight is W =mg, where g is the acceleration of gravity (9.81 m/s2l. When you feel "pushed down" at the bottom of a roller­ coaster loop you experience an apparent weight greater than your normal weight. When your apparent weight is twice your normal weight we say you experience a force of"two is". That is because you experience the acceleration of gravity plus the acceleration of the ride's motion. At another point on the ride you could be almost lifted from your seat. This is an example of less than one g because you feel lighter than your normal weight. The downward acceleration of gravity is the same, but your acceleration due to the ride cancels some of the effect of gravity. One of the objects of ride physics is to measure and calculate the acceleration of a rider. 3 3.1 Roller Coasters; Non-looping and Looping, Clothoids A roller coaster provides a good example of conservation of h = d(tan 8) +LS meters energy. The train is pulled to the top of a high hill and let go (Fig. v,oa"" = Jig(hA -h,) Bl). The train then plunges down the other side of the hill. It 4.n;2r then rises up another hill to plunge down again, perhaps with a..,," - g( tan 8) acalculat~d - y twists and turns to the left and right. A E F D c TABLE D-6 Trigonometric Functions ...,,, ... "" ... .... ... "" ... .. 0000 1.0000 .0000 .,. .7071 .7071 1.0000 1' .0175 .9'198 .0175 ... .719) .6947 1.0355 ,. .0)49 .9994 .OJ.49 ,,. .7314 •..&820 1.0724 ,. .0523 .9986 .0524 ... .7431 .6691 1.11()(> Figure Bl .u698 .9976 .0699 ... ..7547 .6561 1.1504 ••S' .0872 .9962 .0875 SO'­ .7660 .6428 1.1918 We can understand the motion of a roller coaster by ,. .10-15 .9945 .1051 51' .7771 .6293 1.23-49 ,. ,1219 .9925 .1228 ,,. .7880 .6157 1.2799 .. .1392 .9903 .1405 ,,. .7986 .6018 1.J270 considering conservation of mechanical energy. Assume the car is .. .1564 .9877 .15&4 ... .8090 .5878 1.376-C 10' .1736 .9Mll .1763 ,,. .•8192 .5736 1.42111 hauled up to point A. At point A the total mechanical energy is 11' .1908 .9816 .19~ 56' .8290 .5592 1.41126 12' .2079 .9781 .2125 ,,. .8387 .S.«6 1.5399 ll' .2250 .97+4 .2309 ,.. .8480 ,5299 1.6003 equal to the total mechanical energy at point E, as it is at all of ,.. .2419 .9703 .2493 ,,. .8572 .5150 1.6&4) 15' .2588 .9659 .2679 ... .86b0 .sooo 1.7321 16' .2756 .961) .2867 61' .8746 .4648 1.8040 the points on the track. (For the purpose of getting a general 17" .2924 .956) .)057 ,,. .8829 .4695 1.8807 10' .)090 .951 l .3249 .,. .8910 .4540 1.9626 understanding, we are omitting the energy converted into heat by 1,. .3256 .9455 .J<Ml ... .8988 .43&4 2.0503 ,.. .3420 .9197 .36'0 65' -.9063 .4226 2.1445 ,,. .J584 .9)36 .)839 ... .9135 .4067 2.2460 friction. You may want to try to estimate the magnitude of ,,. .)746 .9272 .4040 ,,. .9205 .)907 2.3559 ,,. .3907 .9205 .4245 ... .9272 .)746 2.4751 ,.. .4067 .91)5 .+452 ,,. .9336 .3584 2.6051 frictional effects in a more refined analysis. However you can best .4226 ..... .4663 70' .9397 J420 2.7475 '",.. .4384 .8988 .4877 ,,. .9455 .3256 2.9042 understand things by leaving frictional effects out at the start.) 1r .4540 .8910 .5095 Tl' .9511 .)090 J.0777 ,.. .4695 .81.129 .5317 ,.,. .956) .2924 J.2709 ,,. .4848 .8746 .554) ,.. .9613 .2756 ).4874 Thus the sum of the potential energy (PE) and kinetic energy (KE) .5000 .0660 .5774 ,,. .9659 .2588 3.7321 ""31' .5150 .8572 .6009 ,.. .9703 .2419 4.0108 is the same at points A and E. ,,. .5299 .6249 77' .9744 .2250 4.3315 ,,. ·"""'.8187 .6494 78' .9781 .2079 4.7046 ,.. ·"''.5592 .8290 .6745 ,,. .9816 .1908 5.1+46 35• .5736 .8192 .7002 .... .9848 .1736 5.6713 KE,.,+ PE,.,"' KEE+ PEE ,.. .5878 .0090 .7265 ... .9877 .I 564 6.31)8 ,,. .6018 .7986 .75)6 ,,. .9903 .1392 7.11$4 ,.. .6157 .788-0 .781) ,,. .9925 .1219 !l.1+43 ; mv! + mgh,., ... ~mu~+ mgfir ,,. .6293 .7771 .8098 ... .9945 .1045 9.5144 ... .6428 .7WJ . 8391 ... .9962 .0872 , !.4)01 .,. .6561 .7S47 . 8693 ... .9976 .0698 14.3007 .,. .6691 .7431 ,,. .9986 .0523 19.0811 ,,. .61120 .7)14 ·""'.9325 ... .9994 .0)49 28.6363 ... .6947 .7193 .%57 ,,. .99911 .0175 57 .2900 ... .7011 .7071 1.0000 ... 1.0000 .0000 . Therefore we can calculate the speed at E if we know the heights A Appendices hA and hE. Ifthe train is moving slowly at the top of the first bill (A) we can neglect the term } mu~ to find A.1 Formulas VE -J2g(h, - hE) · Summary of kinematic equations for constant acceleration. The bar over the u means average. The initial values of time, To make the ride more exciting the roller coaster d'esigners position, and velocity to be 0, 0, and vo, respectively. may put a loop - or even two loops- in the track, as shown in Fig. B2. They must choose the maximum height of the loop, and also d .. ~ (v0 + v)t A f 2""\' v' \ T ) 4ir'r 2 u - v~ + 2ad a .. - .. -----,­ v- v0 +at " r r T D E h ' c 2 I' Formulas from dynamics and energy. (Use 9.8 m/s for g.) Figure B2 the shape of the loop. You can estimate the maximum height of m;-\f 2"" ' mu' \ T ) 4n'mr the loop, or to turn the question around, can you estimate what F-ma F--r-- r ·--;p­ fraction of the initial potential energy at A is lost to friction ifthe 1 car has a given speed at position E and height h£. KE--mJ W-Fd PE· mgh 2 Ifthe loops were circular the riders would experience 6 tfs at the bottom and would just barely hang on (0 g's) at the top of the Conversion Factors loop. This is under the assumption that the coaster enters the 1 inch= 2.54 cm (exact) 1h=3600.s loop at a given speed at C and is slowed by the force of gravity as 1d=86,400 s 1 ft= 30.48 cm (exact) it coasts up to the top of the loop at D. Humans can not tolerate 6 1 m =39.37 in. 1kg=1000 g g's in this situation so another shape rather than a circle is used 1 lb =4.45 N for the loop.