A 2000kg car has to take a turn on flat road whose radius is 70m. The coefficient of friction between the car and the road is 0.3. Is the road suitable for a speed 20m/s. If not so, by what angle the outer edge of the road should be banked for safe turn at 20m/s.

Solution

Given that,
$L i m i t i n g space f r i c t i o n comma space straight mu equals 0.3 R a d i u s space o f space t h e space r o a d comma space space r equals 70 space straight m$
The maximum safe speed on the flat road is,
$v subscript 1 equals square root of mu r g end root equals square root of 0.5 cross times 70 cross times 10 end root space equals space 14.49 space straight m divided by straight s$
The flat track is not suitable for speed 20m/s.
Let for safe turn bank the road at angle $straight theta.$
Thus,
$nu equals square root of r g fraction numerator straight mu plus tan theta over denominator 1 minus μtanθ end fraction end root$
$rightwards double arrow$ $space space 20 equals square root of 70 cross times 10 fraction numerator 0.3 plus tanθ over denominator 1 minus 0.3 space tanθ end fraction end root$
$rightwards double arrow$ $400 over 700 equals fraction numerator 0.3 plus tanθ over denominator 1 minus 0.3 space tanθ end fraction$
$rightwards double arrow$ $space space tan space straight theta space equals space fraction numerator 1.9 over denominator 8.2 end fraction$
$rightwards double arrow$ $straight theta space equals space 13 degree$ , is the angle of banking required.