39. The magnitude of the acceleration of the cyclist as it rounds the curve is given by v2/R,wherevis the
speed of the cyclist 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 bicycle and mis the mass of the
bicycle and rider, 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 bicycle does not slip, f≤µsmg.
This means v2
R≤µsg=⇒R≥v2
µsg.
Consequently, the minimum radius with which a cyclist moving at 29 km/h = 8.1 m/s can round the
curve without slipping is
Rmin =v2
µsg=8.12
(0.32)(9.8) = 21 m .