Question

A 600-kg car traveling at 24.5 m/s is going around a curve having a radius of 120 m that is banked at an angle of 20°. (a) Is the curve properly banked for the car's speed?

Answer 1

Answer:

No curve is not banked properly.

Explanation:

Free body diagram is given below in the attachment.

for the figure we can clearly observe that

N cosθ= mg....................................................(1)

N sinθ= $\frac{mv^2}{r}$..................(2)

dividing equation (2) by (1) we get

tanθ=$\frac{v^2}{rg}$

$\theta=tan^{-1}(\frac{v^2}{rg} )\\\theta=tan^{-1}(\frac{24.5^2}{120\times 9.81} )$

θ=26.98°

hence calculated θ is more than the given hence it is not banked properly.