The roller-coaster track shown is contained in a verticalplane. The portion of t

Question

The roller-coaster track shown is contained in a verticalplane. The portion of track between A and B is straight andhorizontal, while the portions to the left of A and to the right ofB have radii of curvature as indicated. A car is traveling at aspeed of 72 km/h when the brakes are suddenly applied, causing thewheels of the car to slide on the track (uk = 0.25).Determine the initial deceleration of the car if the brakes areapplied as the car (a) has almost reached A, (b) is travelingbetween A and B, (c) has just passed B.

Explanation / Answer

72 km/hr = 20m/s Point A: F = ma -N = ma -(g - V2 / ) = a -0.25*(9.81 - 202 / 30) = 0.881 m/s2 Point A to B: F = ma -g = a -0.25*9.81 = -2.4525 m/s2 Point B: F = ma -(V2 / + g) = a -0.25(202 / 45 + 9.81) = -4.67 m/s2 Take notice: V2 / is centripetal force, andalways points towards the instantaneous center ofcurvature.

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