3.3 Carousels and Roller Coasters THE VIPER (Six Flags Over Magic Mountain) 188 feet high 70 mph One of the largest looping roller coasters in the world Top Thrill Dragster (Cedar Point) 420 feet tall 120 mph 0 to 120 mph in 4 sec “ …free-falls back to Earth, reaching a speed of 120 mph for the second time…” $ 25 million Amusement park rides are fun when they make us accelerate around loops, twists, turns, etc. WHY? New ideas for today •Feeling of acceleration •Circular motion •Roller coaster physics! At the start of a NASCAR race… Office chair Cart Feeling of acceleration F •Which direction is the force on the driver? •Which way is the feeling of acceleration? What about at the end of a race? F Feeling of acceleration Which way do you feel the acceleration for circular motion? Feeling of acceleration Force But the cables pull you inward! A “stupid human trick” The human carousel Feeling of acceleration F Feeling of F acceleration Circular motion: force is toward center of circle Note: the kid in the middle feels no acceleration! v Tennis ball on string at Try this at home – acceleration always points toward the middle of the circle Uniform circular motion – constant speed 2 Ice table, record player v ac r Centripetal 2 r acceleration 2 v Fc mac m Centripetal r m r 2 force •Always points to center of circle •As you move to the edge of the carousel: is constant, force increases, speed increases Xmas lights So far: •Feeling of acceleration always opposite to acceleration: FOA = -ma •Uniform circular motion involves force toward center of circle The experience of weight The force of your weight causes a series of support forces between parts of your body Your body senses changes in these support forces as a change in weight! Force from accelerating elevator The Feeling of Acceleration and Apparent Weight AW = W + FOA Acceleration and Weight • Feeling of acceleration – Feeling is caused by your support forces acting on your body – It points in the direction opposite the acceleration – It has a strength proportional to the acceleration • “Apparent weight” is felt due to the combined effects of gravitational acceleration and the feeling of acceleration • Your body really can’t tell the different between acceleration and weight! • Neither can anything else…this idea led to theory of general relativity by Einstein “g-forces” are what Inside the Numbers make roller coasters G Force Example and carousels fun! 1 Standing. 1.2 Normal elevator acceleration (up). 1.5-2 Walking down stairs. 2-3 Hopping down stairs. 1.5 Commercial airliner during takeoff run. 2 Commercial airliner at rotation. 3.5 Maximum acceleration in amusement park rides (design guidelines). 4 Indy cars in the second turn at Disney World (side and down force). 10 Threshold for blackout during violent maneuvers in high performance aircraft. 10 The NASA g-force simulator is limited to 10 g for astronaut training. 11 Alan Shepard in his historic sub orbital Mercury flight experience a maximum force of 11 g. During this time he was unable to speak because he could not move his jaw. 20 The Colonel Stapp experiments on acceleration in Measure acceleration rocket sleds indicated that in the 10 to 20 g range there was the possibility of injury because of organs moving inside the body. in units of g = 9.8 m/s2 30 The design maximum for sleds used to test dummies with commercial restraint and air bag systems is 30 g. g-force = -a Clicker Question Rotating stool A woman is riding one of those “barrel of fun” rides at the amusement park. Feeling of acceleration Which one of the diagrams best shows the forces acting on the woman? Apparent weight A B C D E Leaky cup, bean bag NASA’s vomit comet look at the passengers! Clicker Question What has to be true about the acceleration a of the vomit comet (if the apparent weight of the passengers is zero)? A. a points upward B. a points downward C. a points towards the center of their circular trajectory Roller coasters You better believe in conservation of energy if you want to live! “Most people find this Loop sudden reduction in apparent weight terrifying.” Note: this is not uniform circular motion! Roller Coaster Loops At top of loop: – acceleration is large and downward – so feeling of acceleration is large and upward – apparent weight is therefore much less than equilibrium weight: can feel weightless or even feel force upward. Roller Coasters Hills • Just over the top of hill (think about descent), – acceleration is mostly downward – so feeling of acceleration is mostly upward – apparent weight is therefore less than equilibrium weight, and into the track. • Just past the bottom of hill (think about ascent), – acceleration is mostly upward – So feeling of acceleration is mostly downward – apparent weight is therefore more than equilibrium weight, and into the track. Why we want the last seat on the roller coaster The weight of the first cars combined accelerates the last cars over the hill For next class: Read Section 4.1 See you next class!