Question

ROLLER COASTER PROBLEMS NET Force TO THE CENTEZ EF A 50 kg person rides each of the looping coasters shown. For each position indicated find the rider's total energy, potential energy, kinetic energy and speed. Find the centripetal force needed to make the rider move along the arc of the coaster at the position shown. Calculate the force the seat must exert to keep the rider in the desired motion as well as the force factor the rider experiences. Remember that the forces exerted by gravity and the seat must combine to create the centripetal force. (ner Centre force, 1. This coaster has a circular loop. Think about how the rider will feel at the top and bottom of the loop. A force factor of more than 4 is uncomfortable. D: Top of coop ET = Ep = EK = V= m/s FC = Fseat = H force factor =_ 55 m ET 4: Release eleveTON B Bottom of Coop mis - EK = V= Om's Fc= Fseat force factor = Ep = EK = VE Fc = Fseat- force factor

Answer 1

At point A: The total energy is: E = KA +UA = 0 +26950 = 26950) The potential energy is: UA = mgH = (50) (9.8) (55) = 26950) The kinetic energy is. KA = 0 The velocity: v = 0 The centripetal force: {Fc = mv' = 0 Fseat = mg = (50) (9.8) = 490 N Force factor: 1 At point B: The total energy is: E = EA = 26950) The potential energy is: Ug = 0) The kinetic energy is. Kg = UA = 26950) The velocity: v = 2gH = V2 * 9.8 * 55 = 32.8" The centripetal force: [Fc = mp2 = 50 (32.8)2 = 2690 N Fseat = mg + Fc = (50)(9.8) + 2690 = 3180 N Force factor: SFC = 2690 At point D: The total energy is: E = Ep = 26950) The potential energy is: Un = (50)(9.8)(20) = 9800 J The kinetic energy is. Kp = E – U, = 17150 ) The velocity: v = E= 12 + 17450 = 26.2 " The centripetal force: [Fc = my2 = 50(26.2)2 = 1716.1 N Fseat = {Fc - mg = 1716.1 – (50) (9.8) = 1226 N Force factor:Fc = 1716.1 = 3.5 factor. mg 50-9.8 = 3.5 20 mg509. 85.5 V mv