At the Six Flags Great America amusement park in Gurnee, Illinois, there is a ro

Question

At the Six Flags Great America amusement park in Gurnee, Illinois, there is a rollercoaster that incorporates some basic physics.Each vertical loop, instead of being circular, is shaped like a teardrop. The cars ride on the inside of the loopat the top, and the speeds are high enoughto ensure that the cars remain on the track.The biggest loop is 35 m high, with a maximum speed of 31 m/s at the bottom. Suppose the speed at the top is 11 m/s and the corresponding centripetal acceleration is 2.1 g (where g = free-fall acceleration). a) What is the radius of the arc of the teardropat the top? b) If the total mass of the cars plus people is 1676 kg, what force does the rail exert on it at the top? c) Suppose the roller coaster had a loop of radius 15 m. If the cars have the same speed (11 m/s) at the top, what is the centripetal acceleration at the top? d) What is the normal force at the top in this situation?

Explanation / Answer

a] a_centripidal = v^2 / R R = V^2 / a_c b] Sum Forces: j: N - mg = m*v^2 / R N = mg + m*v^2 / R c] a_c = V^2 / R d] N = mg + m*a_c just plugin the values the calculation part is for you

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