A car is speeding on a horizontal road curving round with a radius 60 m The coefficient of friction between the wheels and the road in 0.5 The height of centre of gravity of the car from the road level is 0.3 m and the distance between the wheels is 0 .8 m . Calculate the maximum safe velocity for negotiating the curve . Will the car skid or topple if this velocity is exceeded ?

Explanation

Here , `r = 60 m,mu = 0.5 h = 0.3 m`,
distance between the wheels , `2 xx = 0.8 m`,
`x = 0.4 m`
For no skidding, `tan theta = mu =(v^(2))/(r g)`
`v = sqrt(mu rg)= sqrt(0.5 xx 60 xx9.8) =17.15 m//s`
For toppling , `(m upsilon^(2))/(r) xx h = mg x`
`upsilon = sqrt(grx)/(h) = sqrt(9.8 xx 60 xx 0.4)/(0.3)=28 m//s`
Hence the maximum safe velocity for negotiating the curve is `17.15 m//s` Beyond this speed , skidding starts until the car topples at `v = 28 m//s` .