Question

Example 78. 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 is 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 the vehicle to negotiate the curve.
Will the vehicle skid or topple if this velocity is exceeded ?​

Answer 1

Answer:

Here , r=60m,μ=0.5,h=0.3m,

distance between the wheels , 2×=0.8m,

x=0.4m

For no skidding, tanθ=μ=v^2/rg

v=√μrg = √0.5×60×9.8 = √17.15m/s

For toppling , mυ^2 / r×h=mgx

υ=√grx / h=√ 9.8×60×0.4 /0.3=28m/s

Hence the maximum safe velocity for negotiating the curve is 17.15m/s Beyond this speed , skidding starts until the car topples at v=28m/s .

Answer 2

Answer:

Solution :

Here , r=60m,μ=0.5h=0.3m,

distance between the wheels , 2×=0.8m,

x=0.4m

For no skidding, tanθ=μ=v2rg

v=μrg−−−√=0.5×60×9.8−−−−−−−−−−−√=17.15m/s

For toppling , mυ2r×h=mgx

υ=grx−−−√h=9.8×60×0.4−−−−−−−−−−−√0.3=28m/s

Hence the maximum safe velocity for negotiating the curve is 17.15m/s Beyond this speed , skidding starts until the car topples at v=28m/s

Explanation: