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 the track. The biggest loop is 40.0 m high. Suppose the speed at the top is 10.8 m/s and the corresponding centripetal acceleration is 2g. (a) What is the radius of the arc of the teardrop at the top

5.95 m

Explanation:

Given that the biggest loop is 40.0 m high. Suppose the speed at the top is 10.8 m/s and the corresponding centripetal acceleration is 2g

For the car to stick to the loop without falling down, at the top of the ride, the centripetal force must be equal to the weight of the car. That is,

(MV^2) / r = mg

V^2/ r = centripetal acceleration which is equal to 2g

2 × 9.8 = 10.8^2 / r

r = 116.64 /19.6

r = 5.95 m

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