Question

A truck of 10000kg approaches a curved path with radius of 5000cm. Determine the speed limit of the angle of banking of the curves is 15°

Answer 1

Given:

$R=5000\:\rm cm=50\: m$

$\theta=15^{\circ}$

The Newton's second law says:

$$ma_x=N\sin\theta\\ ma_y=N\cos\theta-mg$$

or

$$m\frac{v^2}{R}=N\sin\theta\\ 0=N\cos\theta-mg$$

From these equations we get

$$v=\sqrt{gR\tan\theta}=\sqrt{9.8*50*\tan 15^{\circ}}=11.5\:\rm m/s$$