A scooter and its rider, having a combined mass of 150 kg , are travelling at 36 km/hr and need to negotiate a turn of radius 30 m . What should be the proper angle of banking if the required horizontal force for the turn is entirely provided by the normal force from the road? (Take g = 10 m/s ^2 )

Step-by-step solution

Given: Mass m = 150 kg Velocity v = 36 km/hr = 36 5 18 m/s = 10 m/s Radius r = 30 m Acceleration due to gravity g = 10 m/s ^2 For banking without friction, the necessary centripetal force is provided entirely by the horizontal component of the normal reaction. N = mv^2 r N = mg Dividing the two equations: = v^2 rg Substituting the given values: = (10)^2 30 10 = 100 300 = 1 3 = ⁻¹ ( 1 3 )