# physic

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An SUV is negotiating a horizontal unbanked turn. The radius of the turn is 20m, the center of gravity of the vehicle is 1m above the ground and in the middle between the left and right side. The seperation of the left and right wheels is 1.8m

What is is the greatest speed at which the SUV can negotiate the turn without rolling over?

• physics -

Consider the case where there is no force on the two wheels closest to the cetnter of the turn. Compute the speed at which that can happen by taking moments about the outer pair of wheels. Let the distance between right and left wheels be L = 1.8 m. The gravity torque M g L/2 must equal the centripetal torque
M V^2*h/R, where h = 1m is the height of the CM. M cancels out.
g L/2 = V^2 h/R
V = sqrt [R g L/(2h)

A wide wheelbase (L) and a low center of mass (h) helps prevent high speed flipping.

At higher values of V, dynamic equilbrium cannot be maintainewd.

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