The car is towed up a ramp to position 1. A slight leftward horizontal force is

Question

The car is towed up a ramp to position 1. A slight leftward horizontal force is then applied to the car and it rolls down the track. All the dimensions of the car are small compared with the length and radii of curvature of the track. Thus, all rotation effects may be neglected, and the car may be assumed to move as a particle in translation. In addition, all friction effects may be neglected. The heights are h1 = 60ft, h2 = 25ft, h3 = 40ft, and radius of curvature at point 2 is h1-h2.

a. Find max acceleration a passenger experience at position 2.

b. Find min possible value of radius of curvature when car in position 3, if the wheels of the car are not to lose contact with track at that location.

park. The car is towed up a ramp to position 1. A slight leftward horizontal force is then applied to the car. and it rolls down the track. All the dimensions of the car are small compared with the length and radii of curvature of the track. Thus, all rotation effects may be neglected, and the car may be assumed to move asi particle in translation. In addition, all friction effects may be neglected. The heights are h1, = 60 ft, h2= 25 ft. and h3 = -40 ft. and the radius of curvature of the track at point 2 is h1-h2. Find the maximum acceleration which a passenger would experience when the car is in position 2. Find the minimum permissible value of the radius of curvature when the car is in position 3. if the wheeb of the car are not to lose contact with the track at this location.

Explanation / Answer

a) mg(h1-h2) = .5mv^2

v^2 = 2*9.8*35

max acc = v^2/r - g = 2*9.8 -9.8 = 9.8m/s^2

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