Question

A motorcyclist performs stunt along the cylindrical wall of a ‘Well of Death’ of inner radius 4 m. Coefficient of static friction between tyres and the wall is 0.4. Calculate the maximum period of revolution. (Use g = 10 m/s²)

Answer 1

Given: Radius (r) = 4 m

Coefficient of static friction (µ) = 0.4

g = 10 m/s²

To find: Maximum period (T_max) = ?

Formula: `T_(max) = (2 pi r)/(v_min)`

Let us find v_min

∴ `v_(min) = sqrt((rg)/µ)`

∴ `v_(min) = sqrt((4 xx 10)/(0.4))`

∴ `v_(min) = sqrt((4 xx 10)/(4 xx 10^(-1)))`

∴ `v_(min) = sqrt(100)`

∴ v_min = 10 m/s

∴ `T_(max) = (2 pi r)/(v_min)`

= `(2 xx 3.142 xx 4)/(10)`

= 8 × 0.3142

= 2.5136 s