Physics 12 ASOlG Practice Problems Name: Part A 01 Bugs drives a race car at 180 kin-"h around a at circular Track of radius 90 m. Determine the centripetal acceleration of the car. 02 7 Daffy Duck drives a cycle with centripetal acceleration of 19.6 m-"'s2 around a at circular curve of radius 0.245 km. Determine the speed of the motorcycle. 03 7 Porky Pig and Tweety Bird feels 1 g at the top of a circular roller coaster loop for a total centripetal acceleration of 2 g's. The coaster diameter is 14.7 In. How fast are they moving? 04 Elmer Fudd and Sylvester the Cat twirl a 50 cm long sling 120 times in 10 seconds. Determine the period and frequency of the sling. How fast is the rock on the edge of the sling moving? 05 Buster Bunny drives a 1.176 tonne car at 29.4 m/s around a at. icy curved road of radius 320 m. A) Determine the coefficient of static friction. B) If the road was dry and ideally not covered in ice the coefcient would be 0.97 nd the maximum safe speed for Buster Burmy. 06 Wile E. Coyote rides a daring horizontal circular loop roller coaster. To complete a loop he must enter at 72 krn/h. A) If he feels 4g's at the top then his acceleration 3.: is Sg's. Find the radius of the loop. B) What speed would be needed on a clothoid loop? 07 Marvin the Martian stands on the outer wall of a space station with his head pointed towards the centre of the space station. His speed is 36 km/h. Determine the radius of the space station if he feels exactly 1.0 g. Part B 08 7 Road Runner ies a jet plane at 1434 kin-"h in a loop-de-loop of radius 1 km. Determine the normal force in terms of mg of the seat on the pilot at A) the top (upside-down), B) bottom (upside-right) and sides C) facing up and D) facing down of the loop. 09 Foghorn Leghorn has a mass of 60 kg and is standing on the planet Terra which has a mass of 5.98 x 1024 kg and radius of 637'0 km. Determine his weight on the surface of this mysterious planet. 10 Pepe Le Pew has a weight of 220 lbs on the surface of the planet Earth. A) He visits the planet Monde-T with twice the mass. and triple the radius. Determine his new weight. B) Later he visits the planet Mundo-E which has ?5% less radial length and one third the mass of the Earth. Determine his new weight. 11 Yosemite Sam has a weight of 784 N when standing by the ocean on the mysterious planet LooneyToon. He climbs to the top of a nearby mountain and has a weight of 783 N. Determine the altitude of the mountain in terms of the radius of the planet (example answer: 11 = 0.025 Rpm.\" or 2.5% of planet radius). You do not know the planet's mass or radius. Based on your answer what would the height be on the planet Earth which has a radius of 6380 km? 12 Speedy Gonzales orbits the Earth in a 10 tonne spacecraft with an orbital radius of 10 000 km. Determine the force of gravity acting on the space ship. 13 Tasmanian Devil orbits the Earth in geosynchronous orbitjust like a cell phone or teleconmnunications satellite does. Determine the speed of his ship and the radius of his orbit. Part C 14 Babs Bunny drives a l 200 kg car at 20 m/s around a frictionless banked curved road of unknown radius r km and angle 30 above the horizontal. A) Determine the radius of the curve. B) What speed would be safe for Babs if the road was at with an ideal coefcient of friction of 0.97? 15 The Warner Brothers and Sister Yakko. Wakko. and Dot drive a 250 kg bike around a banked curved road of radius 50.0 m. coefficient of friction 0.98 and angle 20.l above the horizontal. Determine the tangential velocity of the bike if the force of friction keeps the bike from moving A) up the hill B) down the hill C) up the hill and there is a micro-singularity or mini-black-hole of mass 1015 kg at the centre of the curve D) down the hill and there is a micro-singularity or mini-black-hole of mass 1015 kg at the centre of the curve. 16 Roger Rabbit is standing in a subway car moving at 10 mfs. A 1.5 kg ball is suspended from the ceiling on a l m long string and the ball has a height of 2 in. An instant later the subway car then accelerates forward. A) Determine the angle of deection if the subway accelerates at 1.96 m/sz. B) Determine the acceleration needed to deflect the ball 30. C) If the ball is deected from 2.00 in to a new height of 2.10 m determine the acceleration of the subway car. Also determine the magnitude of the fictitious force acting on the ball according to an observer on the subway car. To calculate the determine the magnitude of the ctitious force acting on the ball according to an observer on the subway car. To calculate the angle of deection you may wish to use a diagram to show h = L L COS 9 where L is length of the string. h is the change in height and 6 is the angle of deection (angle at the ceiling). 17 Jessica Rabbit has a mass of 50 kg and travels from the North Pole to the Equator. The Earth has a radius of 6 380 km and period of 24 hours. A) What is her apparent weight loss in Newtons and Pounds due to the centrifugal force? B) What would the apparent weight loss be for a Monty Python's vorpal rabbit of mass 5 kg at the equator (N 0 need to start over use ratios and proportions)? C) Find the apparent weight loss for Monster Bugs Bunny of mass 100 kg at the equator (Once againjust use ratio and proportions no need to start over)? D) Find the apparent weight loss for Jessica Rabbit at the equator of Planet 51 (radius 2 000 km. period of 3h:56min:32sec)? @ Answers 01 - Bugs: 27.8 m/s2 02 - Daffy Duck: 249 km/h 03 - Porky Pig and Tweety Bird: 12 m/'s 04 - Elmer Fudd and Sylvester the Cat: 136 km/h 06 - Buster Bunny: 0.276 (icy) vs dry pavement of 0.97 Eventually derive the formula: - = ug 06 - Wile E. Coyote: 51 km/h clothoid loop and circular loop radius is 8.16 m. 07 - Marvin the Martian: 10.2 m 08 - Road Runner: top 15.19 g, bottom 17.19 g, side down 16.19 g, side up 16.22 g Eventually derive the formula: N = mg -+ (+1 Bottom, O SideDown, -1Top rg 09 - Foghorn Leghorn: 590 N or 132 lbs 10 - Pepe Le Pew: Monde-T 48.9 lbs & Mundo-E 1173 lbs. 11 - Yosemite Sam: 0.0638 % of planet radius, on Earth that would be 4.07 km or 46% of Mt Everest. Eventually end up with a quadratic:Eventually end up with a quadratic: R2 1 h2 + 2R h- =0 which provides the roots h = R -1+ SeaLevel 783 F gHighAltitude 12 - Speedy Gonzales: 39 887 N or 8 954 lbs or 4.48 tons 13 - Tasmanian Devil: Location r = 6.62 Earth radii and tangential speed v = 11 061 km/h Eventually derive Kepler's 30 Law which is the formula: GM 14 - Babs Bunny: A) 70.7 m Eventually derive the formula: B) Use formula derived in question 07 with eqn -=g Tano = ug 15 -Yakko, Wakko, and Dot: Eventually derive the formula: V (Sin8 + /Cose) GM g (Cose + using) A & B -+ no speed required to avoid sliding down the ramp but 32.1 m's or 115 km/h maximum speed to avoid sliding up the ramp. C&D + 48.6 m/s or 175 km/h and 33.4 m/s or 120 km/h are the maximum and minimum speeds respectively. 16 -A) 11.30, B) 5.658 m/s or 0.577 g, C) 25.80 17 - A) 1.69 N or 0.379 lbs, B) 0.169 N or 0.0379 lbs, C) 3.37 N or 0.757 lbs, D) 49 N or 11 1bs