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 roller coaster that incorporates some of the latest design technology and some basic physics. Each vertical loop, instead of being circu- lar, is shaped like a teardrop (shown in the figure). The cars ride on the inside of the loop at the top, and the speeds are high enough to ensure that the cars remain on the track. The biggest loop is 35 m high, with a maximumspeed of 31 m/s (nearly 69.44 mph) at the bottom. Suppose the speed at the top is 16 m/s and the corresponding centripetal acceleration is 2.8g (where g is the free-fall acceleration).

The acceleration of gravity is 9.8 m/s2 .

What is the radius of the arc of the teardrop at the top?

Answer in units of m.

(2)If the total mass of the cars plus people is 2986 kg, what force does the rail exert on it at the top?

Answer in units of N.

(3)Suppose the roller coaster had a loop of radius 30 m.

If the cars have the same speed (16 m/s) at the top, what is the centripetal acceleration at the top? 2

Answer in units of m/s .

(4)What is the normal force at the top in this situation?

Answer in units of N.

Explanation / Answer

(1) v =16 m/s , a =2.8 g, g =9.8 m/s^2

a =v^2/r

r =v2/a = (16*16)/(2.8*9.8)

r= 9.33 m

(2) F =ma = (2986)(2.8)(8.8)

F = 81935.8 N

(3) a =v2/r = (16*16)/(30)

a =8.53 m/s2

(4) T =ma = (2986)*(8.53)

T = 25480.5 N

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