Sandra drives a bus with a wheelbase of 2.6 meters. The center of gravity is in

Question

Sandra drives a bus with a wheelbase of 2.6 meters. The center of gravity is in center of the bus, 1.2 meters above the ground. You can treat the bus as if all of its mass was at its center of mass. Sandra turns right on flat ground. The center of mass has a turning radius of 47 meters. The bus moves at a constant speed V, and has a mass M. a) What is the acceleration of the bus? b) What is the total normal force on the bus? What is the frictional force? c) What is the torque on the bus about its center of mass from the force of friction? d) If all of the normal force comes from the left wheels, what is the torque on the bus about its center of mass from the wheels? e) At what speed V would these two torques be equal? f) What should Keanu do if he wants to make the turn at a slightly higher speed?

Explanation / Answer

given wheel base, 2a = 2.6 m

a = 1.3 m

heiht of center of gravity, h = 1.2 m

mass of bus = M

radius of curvature of center of mass while turn, r = 47 m

speed of bus = V

a. acceleration of the bus = V^2/r = V^2/47 m/s/s

b. total normal force = N

from force balance

N = Mg

N = 9.8M

c. force of friction = f

f = MV^2/r

then torque about center of mass = f*h

T = MV^2*h/r = 0.0255319148MV^2 Nm

d. if all the normal force comes form left wheels

torque form the wheels = Tw

Tw = N*a = 9.8M*1.3 = 12.74M

e. T = Tw

12.74 = 0.02553198148V^2

V = 22.3379057 m/s

f. for a slightly higher speed at the turn, ar/h has to increase

hence

either wheel base mush be widened, or radius of turn has to increase, or the height of center of mass form the ground has to decrease

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