Name: Centripetal and Centrifugal Force
Uploaded: 2019-07-19
Duration: 2 min 42 s
Description: The meaning of centrifugal force is the apparent force that is felt by an object moving in a curved path that acts outwardly away from the centre of rotation

Question

Why are circular roads banked? Deduce an expression for the angle of banking. Draw the free-body diagram. Derive a relation for the optimum velocity of negotiating a curve.

Accepted Answer

Motion of a car on a banked road

If we want to increase the maximum possible speed to move on a curved horizontal road, then the road should be banked as shown in the figure (this is the phenomenon of raising outer edge of the curved road above the inner edge) by this we can reduce the contribution of friction to the circular motion of the car safely.

Now, After free body diagram of vehicle

$Ncosθ = mg + fsinθ \Rightarrow Ncosθ - μ_{s} sinθ = mg . . . . . . (i)$

(as there is no acceleration along the vertical direction, which means the net force along vertical direction must be zero)

Centripetal force, $\frac{{mv}^{2}}{R}$ provides the horizontal components of $N$ and $f .$

$Nsinθ + fcosθ = \frac{{mv}^{2}}{R} \Rightarrow Nsinθ + μ_{s} cosθ = \frac{{mv}^{2}}{R} . . . . . . . (ii)$

Dividing equation $(i)$ by $(ii)$

$\frac{Ncosθ - μ_{s} Nsinθ}{Nsinθ + μ_{s} Ncosθ} = \frac{mg \times R}{{mv}^{2}} \Rightarrow v = v_{\max} = \sqrt{R g (\frac{sinθ + μ_{s} cosθ}{cosθ - μ_{s} sinθ})} \Rightarrow v_{\max} = \sqrt{Rg (\frac{tanθ + μ_{s}}{1 - μ_{s} tanθ})}$

Why are circular roads banked? Deduce an expression for the angle of banking. Draw the free-body diagram. Derive a relation for the optimum velocity of negotiating a curve.

Important Questions on Laws of Motion

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