1. The track of a roller coaster has an \"S\" shapedstructure. The structure can

Question

1. The track of a roller coaster has an "S" shapedstructure. The structure can support a maximum force of4000N, and has a radius of curvature of 15m for boths-curves. (a) Where with the maximum force be exerted and whatwill be the maximum speed of the 100kg car on this track? (b) At the top of the track what will be the maximum speed sothat the car does not leave the track? 1. The track of a roller coaster has an "S" shapedstructure. The structure can support a maximum force of4000N, and has a radius of curvature of 15m for boths-curves. (a) Where with the maximum force be exerted and whatwill be the maximum speed of the 100kg car on this track? (b) At the top of the track what will be the maximum speed sothat the car does not leave the track?

Explanation / Answer

Nm = 4000 N, m = 100 kg, r = 15 m a) The maximun force is at the bottom of the track. N - mg = mv2/r N = m(g + v2/r) Nm = m(g + vm2/r) vm = [r(N/m - g)] = 21.3 m/s b) at the top, N + mg = mv2/r N = m(v2/r - g) >= 0 v >= (gr) = 12.1 m/s

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