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Thursday, December 15, 2016

Motion of a car on banked road

The maximum permissible speed of a car on a banked rough road can be obtained as under.
Ncosθ = mg + fsinθ

Nsinθ + fcosθ = mv²/R 
          
If v = vmax then, f = fmax = μsN

On substituting then simplifying we get

vmax = {[(μs + tanθ)/(1 - μs tanθ)]Rg}¹/²

Example 1:- A small block of mass m is moving over a smooth horizontal surface on a circular path at some moment. Length of string is L and velocity of block at some moment behind the tension in the string.

Solution: Here Tension provides, the required centripetal force

T = mv²/r = mvₒ²/L

Example 2:- Find the tangential acceleration of the bob of mass m at a moment when string makes angle θ with vertical as shown.

Solution: Let us make F.B.D. of bob, tension is radial, only force along tangent is

FT = mgsinθ

aT = F/m = gsinθ

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