A roller coaster at the Six Flags Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop (Fig. P5.22). The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure the cars remain on the track. The biggest loop is 40.0 in high. Suppose the speed at the top of the loop is 13.0 m/s and the corresponding centripetal acceleration of the riders is 2g. (a) What is the radius of the arc of the teardrop at the top? (b) If the total mass of a car plus the riders is M, what force does the rail exert on the car at the top? (c) Suppose the roller coaster had a circular loop of radius 20.0 m. If the care have the same speed, 13.0 m/s at the top, what is the centripetal acceleration of the riders at the top? (d) Comment on the normal force at the top in the situation described in part (c) and on the advantages of having teardrop-shaped loops.
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- A roller coaster at the Six Flags Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop. The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure that the cars remain on track. The biggest loop is 40.0m high. Suppose the speed at the top is 14.4m/s and the corresponding centripetal acceleration is 2g. (a) What is the radius of the arc of the teardrop at the top? (b)If the total mass of a car plus the riders is M, what force does the rail exert on the car at the top? (c) Suppose the roller coaster had a circular loop of radius 21.4 m. If the cars have the same speed, 14.4 m.s at the top, what is the centipetal acceleration at the top?arrow_forwardA 0.1 kg ball is attached to a string and whirled around in a circle overhead. The string breaks if the force on it exceeds 60 N. What is the maximum speed the ball can have when the radius of the circle is 1 m?arrow_forwardA roller coaster at the Six FlagsGreat America amusement parkin Gurnee, Illinois, incorporatessome clever design technologyand some basic physics. Each verticalloop, instead of being circular,is shaped like a teardrop(Fig. P6.13). The cars ride onthe inside of the loop at the top,and the speeds are fast enoughto ensure the cars remain on thetrack. The biggest loop is 40.0 mhigh. Suppose the speed at thetop of the loop is 13.0 m/s andthe corresponding centripetalacceleration of the riders is 2g. (a) What is the radius of thearc of the teardrop at the top? (b) If the total mass of a carplus the riders is M, what force does the rail exert on the carat the top? (c) Suppose the roller coaster had a circular loopof radius 20.0 m. If the cars have the same speed, 13.0 m/sat the top, what is the centripetal acceleration of the ridersat the top? (d) Comment on the normal force at the top inthe situation described in part (c) and on the advantages ofhaving teardrop-shaped loops.arrow_forward
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- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning