A classic 1957 Chevrolet Bel Air is a rear-wheel-drive automobile. Its mass is M

Question

A classic 1957 Chevrolet Bel Air is a rear-wheel-drive automobile. Its mass is M and its center of mass is a distance h above the road. With an empty trunk, the distances between the ceter of mass and the rear and front wheels are l_r = 3h and l_f = 2h, respectively. The kinetic-friction coefficient between the car's tires and the road is mu. A box of mass m loaded into the trunk rests just above the rear wheels. It causes no change in the vertical distance between the car's center of mass and the road. What is the ratio of the Chevy's maximum possible acceleration with the box loaded to that with an empty trunk? Express your answer in terms of M and m. Compute the ratio for M_g = 3300lb and mg = 500lb, where g is gravitation acceleration.

Explanation / Answer

normal reaction on front tires be N1 and rear wheel be N2, N1 + N2 = Mg, also,,from torque balance MgLr = N1*( Lr + Lf ) + ma, mu*N1 + mu*N2 = Ma, from here you can get all variables, frictional force on front wheels = mu*N1 and on rear mu*N2.

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