Question

A motor car of mass 1000kg runs under a bridge at 48km/h the roadway in the form of an arc of radius 20m the reaction between the car and road at lowest point of road is

Answer 1

see figure, here a tough diagram is shown of given situation.

at equilibrium,

horizontal component of Normal reaction is balanced by centripetal force.

i.e., Nsinθ = mv²/r .....(1)

similarly, vertical component of normal reaction is balanced by weight of motor car.

i.e., Ncosθ = mg.......(2)

from equations (1) and (2),

N²(sin²θ+ cos²θ) = (mv²/r)² + (mg)²

or, N² × 1 = (mv²/r)² + (mg)²

or, N = m√{(v²/r)² + g²}

putting values of m, v, r and g

v = 48km/h = 48 × 5/18 = 40/3 m/s

r = 20m , m = 1000kg and g = 10m/s²

so, N = 1000 × √[{(40/3)²/20}² + (10)²]

= 1000 × √[(80/9)² + 100]

= 1000 × √[6400 + 8100]/9

= 1000 × √[14500]/9

= (10000/9) √(145)

= 13379.5 Newton

hence, normal reaction between car and road of lowest point is 13379.5 Newton.