Question

A motorcycle rides on the vertical walls around the perimeter of a large circular room. The friction coefficient between the motorcycle tires and the walls is µ. How does the minimum µ needed to prevent the motorcycle from slipping downwards change with the motorcycle’s speed, s?
a) µ ∝ s0b) µ ∝ s−1/2c) µ ∝ s−1d) µ ∝ s−2e) none of these

Answer 1

Answer:

option D

Explanation:

given,

coefficient of friction between wall and tire = µ

speed of motorcycle = s

friction force = f = μ N

where normal force will be equal to centripetal force

$N = \dfrac{mv^2}{r}$

for motorcycle to not to slip weight should equal to the centripetal force

 now,

$m g =\mu \dfrac{mv^2}{r}$

$\mu =\dfrac{rg}{s^2}$

where "rg" is constant

$\mu\ \alpha \ \dfrac{1}{s^2}$

$\mu\ \alpha \ s^{-2}$

Hence, the correct answer is option D