What is the smallest radius of an unblanked(flat) track around which a scooterist can safely it. Her speed is 30m/hr. Find the coefficient of static friction between tyre and track is 0.32.
Answers
Answer:
The magnitude of the acceleration of the cyclist as it rounds the curve is given by $$v^2
/R$$,
where v is the speed of the cyclist and R is 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 = $$mv^2
/R.IfF_N$$ is the
normal force of the road on the bicycle and m is the mass of the bicycle and rider, the
vertical component of Newton’s second law leads to F
N
=mg. Thus, using Eq. 6-1, the
maximum value of static friction is f
s,max
=μ
s
F
N
=μ
s
mg. If the bicycle does not slip, $$f ≤
μ_smg$$. This means
r
v
2
≤μ
s
g⇒R≥
μ
s
g
v
2
Consequently, the minimum radius with which a cyclist moving at 29km/h=8.1m/s can
round the curve without slipping is
R
min
=
μ
s
g
v
2
=
(0.32)(9.8m/s)
(8.1m/s)
2