Question

A road surrounds a circular playing field having radius of 10 m. If a vehical goes around it at an average
speed of 18 km/hr, find proper angle of banking for the road. If the road is horizontal (no banking), what
should be the minimum friction coefficient so that a scooter going at 18 km/hr does not skid.

Answer 1

Answer:

proper angle of banking for the road = tan⁻¹ (1/4)

coefficient so that a scooter going at 18 km/hr does not skid = 1/4

Explanation:

Given,

A road surrounds a circular playing field having radius of 10 m.

An average speed of 18 km/hr. = 5 m/s

To find: i) proper angle of banking for the road

             ii) the minimum friction coefficient so that a scooter going at 18 km/hr does not skid.

Solution:

i) Proper angle of banking is given by:

tan φ = v² / rg

where, v = average speed , r = radius of field , g = 10 m/s^2

substituting the values,

tanφ = (5)² / 10*10 = 1/4

φ = tan⁻¹ (1/4)

Therefore, proper angle of banking for the road = tan⁻¹ (1/4)

ii) miminum coefficeint of friction for no banking is given by:

μ = v²/rg = 5² / 10*10 = 1/4

μ = 1/4

Therefore, coefficient so that a scooter going at 18 km/hr does not skid = 1/4