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?

Respuesta :

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= [tex]\frac{mv^2}{r}[/tex]..................(2)

dividing equation (2) by (1) we get

tanθ=[tex]\frac{v^2}{rg}[/tex]

[tex]\theta=tan^{-1}(\frac{v^2}{rg} )\\\theta=tan^{-1}(\frac{24.5^2}{120\times 9.81} )[/tex]

θ=26.98°

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

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