Standard +0.3 This is a standard M3 banked curve problem requiring resolution of forces (weight and normal reaction) and application of circular motion (F=mv²/r). While it involves multiple steps and careful angle work, it follows a well-established method taught explicitly in M3 with no novel insight required—slightly above average due to the mechanics context and algebraic manipulation needed.
A car moves round a bend which is banked at a constant angle of \(10°\) to the horizontal. When the car is travelling at a constant speed of \(18 \text{ m s}^{-1}\), there is no sideways frictional force on the car. The car is modelled as a particle moving in a horizontal circle of radius \(r\) metres.
Calculate the value of \(r\). [6]
A car moves round a bend which is banked at a constant angle of $10°$ to the horizontal. When the car is travelling at a constant speed of $18 \text{ m s}^{-1}$, there is no sideways frictional force on the car. The car is modelled as a particle moving in a horizontal circle of radius $r$ metres.
Calculate the value of $r$. [6]
\hfill \mbox{\textit{Edexcel M3 2003 Q2 [6]}}