Solved Example & Practice Problems: Motion of Vehicles on Unbanked Curved Roads

Motion of Vehicles on Unbanked Curved Roads [Dynamics of Particles]

Solved Examples for Understanding

Example 9.11.1 

A vehicle of mass 1000 kg is rounding an unbanked horizontal curve of radius 300 m. If the left and right wheels are 1 m apart, C. G. of the vehicle is 0.8 m above the road level and coefficient of friction μ=0.2, find the maximum speed of the vehicle so that level and co it should neither skid nor overturn. For what value of u will the vehicle skid and overturn simultaneously?

Solution: 

For unbanked road, the maximum speed without overturning is

For no overturning,

⸫ Safe speed, which is smaller of the two, is 24.26 m/s = 87.34 km/h.

For simultaneous skidding and overturning.

Examples for Practice

Q.1

A vehicle having wheel base 1 m and height of C.G. 1.5 m above the ground suddenly enters a curved road of radius of curvature 200 m with a speed of 27.5 m/s. If the mass of the vehicle is 3 tons and μs = 0.5, determine whether the vehicle will be able to negotiate the turn safely. 

[Ans. : No, the vehicle will overturn]

Q.2

Determine the wheel base of a race car to be designed to safely negotiate a turn of radius of curvature 100 m at a speed of 126 km/h. Take the height of C.G. to be 0.5 m above ground level. 

[Ans. : 1.25 m]