Obtain an expression for the angle of lean when a cyclist taken a curved path
Answers
Answered by
1
The reaction R can be resolved into two rectangular components.
a) R cosθ, acting vertically upwards,
b) R sinθ, acting horizontally i.e, along the radius and towards the centre of the circular track horizontal component R sin θ provides the necessary centripetal force. Hence:
R cos θ=mg………………(1)
Rsin θ = mv2/r ………..(2)
Dividing eq.(2) by eq. (1), we have
R sin θ/R cos θ=(mv2/r)/mg or tan θ v2/rg
Or
θ = tan-1(v2/rg)
a) R cosθ, acting vertically upwards,
b) R sinθ, acting horizontally i.e, along the radius and towards the centre of the circular track horizontal component R sin θ provides the necessary centripetal force. Hence:
R cos θ=mg………………(1)
Rsin θ = mv2/r ………..(2)
Dividing eq.(2) by eq. (1), we have
R sin θ/R cos θ=(mv2/r)/mg or tan θ v2/rg
Or
θ = tan-1(v2/rg)
Similar questions