37. The magnitude of the acceleration of the car as it rounds the curve is given by v2/R,wherevis the
speed of the car and Ris the radius of the curve. Since the road is horizontal, only the frictional force
of the road on the tires makes this acceleration possible. The horizontal component of Newton’s second
law is f=mv2/R.IfNis the normal force of the road on the car and mis the mass of the car, the
vertical component of Newton’s second law leads to N=mg. Thus, using Eq. 6-1, the maximum value
of static friction is fs,max =µsN=µsmg. If the car does not slip, f≤µsmg. This means
v2
R≤µsg=⇒v≤µsRg .
Consequently, the maximum speed with which the car can round the curve without slipping is
vmax =µsRg =(0.60)(30.5)(9.8) = 13 m/s.