In the figure, a stunt car driver negotiates the frictionless track shown in suc

Question

In the figure, a stunt car driver negotiates the frictionless track shown in such a way that the car is barely in contact with the track at the top of the loop. The radius of the track is 9.9 m and the mass of the car is 1500 kg. a) Find the magnitude of the force of the car on the track when the car is at point A. You can treat the car as a point mass. b) Find the speed of the car at the bottom of the loop. c) If the car is launched from rest on a horizontal spring, compressed 3 m, just before reaching the bottom of the loop, find the spring stiffness k.

Explanation / Answer

Vt/R = g ? Vt = R*g where Vt is the velocity at the top of the loop.

Energy considerations: mVi = m*g*H = 2m*g*R ? Vi = 4*g*R

Also, m*(Vi - Va) = m*g*R ? Va = Vi - g*R = 4gR - gR = 3*g*R ?
Va/R = 3*g

Fa = m*aa = 1500*Va/R = 1500*3*g = 44550N

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