Physics 20 Amusement Park Physics @ WEM Page 1 of 6 Group Members: Mindbender Rollercoaster Materials Needed: Stopwatch Maximum Height: 41.5 m First Hill Drop: 38.7 m Radius of the 1 st Loop: 7.177 m Height of 2 nd Hill (1 st brake station): 35.0 m Drop Height after 1 st brake station: 31.0 m Your mass: kg Time for first car to reach top of first hill: s List the sensations at the following points in the ride. Use words like heavier, lighter, and normal. 1. At the first brake station just before descending: 2. At about half way down: 3. At the bottom of the second hill just before going into the loop: 4. At the top of the first loop 5. What is the advantage of a long, shallow first hill? 6. No matter what rollercoaster, why must the first hill always be the highest? 7. Why is the track of the roller coaster always banked in turns? 8. If you had a gravity meter, what part of the trip would read as zero? 9. Where would your gravity meter show its maximum reading? 10. Why is it at a maximum at that point?
Calculations: 1. What is your potential energy at the top of the first hill? Page 2 of 6 E p = mgh 2. What is your kinetic energy at the bottom of the first hill? (Note: Does the car end up at the same level as it started at? Does it matter what height it ends up at?) 3. What is the velocity of the car at the bottom of the first hill? E k = ½ mv 2 4. What is the power is needed to get you up to the top of the first hill? P = W / t After the car passes through the bottom of the first hill, it curves up a second hill and levels off as it passes through the first brake station. The car then moves slowly through another curve. Assume the energy it has at this point is due to the height of the car at this new position. 5. What is the E p at this point just after the first brake station? E p = mgh 6. What is your kinetic energy at the bottom of the hill just before the first loop? E k = ½ mv 2 = E p Merry Go Round Period: 20 s Space between horses in outer ring: 2.6 m Number of horses: 12 Space between horses in inner ring: 1.6 m Number of horses: 12 1. Calculate the circumference of the outer ring. 2. What is the radius of this ring? C = 2 r
3. Calculate the speed of an outer ring horse. Page 3 of 6 v = (2 r) / T 4. What is the circumference and radius of the inner ring? 5. What is the speed of an inner ring horse? 6. Calculate the centripetal force acting on you when you are on one of the outer horses. F c = (mv 2 ) / r 7. Calculate the centripetal force acting on you when you are on one of the inner horses. 8. How do the two centripetal forces you just calculated compare? Swing of the Century Materials Needed: Stopwatch Diameter of the ride at top speed: 20.8 m Maximum angle chain makes to the vertical: = 36 degrees Time for two revolutions at top speed: s Period: s 1. Sketch what happens to the swing as the ride gains speed: Start Slow Fast
2. How do you feel as the ride gains speed? Page 4 of 6 3. Compare the angle of the chain with respect to the vertical on an empty swing with that of an occupied one: Empty Occupied 4. Describe the change in motion that occurs as the ride gains speed. Calculations: 1. Calculate the maximum speed of the swings. v = (2 r) / T 2. Calculate the centripetal force acting on you on this ride at full speed. F c = (mv 2 ) / r 3. Sketch a free body diagram of all the forces acting on a person on this ride. 4. To find the tension in the chain do the following in the space below a) Draw to scale a horizontal vector representing the centripetal force pointed left. b) Add a vertical vector to it which is equal to the magnitude of your weight. These two are the components of your tension. c) Draw the equilibriant force vector (which is actually the tension in the chain) and determine its magnitude using the scale you chose. d) How does your angle in the drawing compare with the angle measured while observing the ride?
Page 5 of 6 Flying Galleon (Swinging Ship) Materials needed: Stopwatch Height: 7.3 m Period for the pendulum to complete one full swing : s Calculations: 1. Calculate the period of the ride if it was acting as a true pendulum. T 2 g 2. Does your calculation of the period agree with what the boat was actually doing? How can you account for the difference between your answer in #1 and what the boat was observed to be doing? Cosmo s Space Derby (Bumper Cars) It will be easiest to answer these questions if you are working with a partner in another bumper car that will help you perform these specific collisions. 1. What happens to each bumper car in a collision when a) one bumper car is not moving? b) a rear end collision happens with both cars moving? c) a head on collision happens with both cars moving? d) there is a collision with a stationary object (like a wall)? e) the cars sideswipe each other?
2. Answer these questions using the concepts of force, energy, momentum, and impulse. a) What is the reason for having rubber bumpers around the cars? Page 6 of 6 b) Why would you not design a car with very soft bumpers? c) If you were riding in the only bumper car having a smaller mass than the rest, how would your ride be different? Explain why. Space Shot Materials needed: stopwatch Maximum Height: 36 m Time to Maximum Height: s Your Mass: kg Calculations: 1. What is the acceleration of the ride as it goes up? d = v i t + ½ at 2 2. What force would the ride s acceleration cause on your body? F r = ma 3. What is your regular weight (force due to gravity)? F g = mg 4. If you were sitting on a scale as the ride went up, what would be the maximum reading it would show? Give your answer in Newtons and kilograms. F NET = Fr + F g 5. When the ride is coming back down in free fall, what would you expect the scale to read for a moment?