Question

A man is driving a cycle with a speed of 1.2km/min over a turn of radius of curvature 40m find out its centripetal acceleration and slope with the vertical​

Answer 1

Given info : A man is driving a cycle with a speed of 1.2km/min over a turn of radius of curvature 40m.

To find : The centripetal acceleration and slope with the vertical are ....

solution : speed of man driving a cycle, v = 1.2 km/min = 1.2 × 10³m/60 sec = 20 m/s

radius of curvature, r = 40 m

centripetal force = ma

⇒mv²/r = ma

⇒a = v²/r = (20)²/40 = 400/40 = 10 m/s²

Therefore the centripetal acceleration is 10 m/s²

see free body diagram,

Ncosθ = mg

Nsinθ = mv²/r

so, tanθ = v²/rg

⇒tanθ = (20)²/(40 × 10) = 1

⇒θ = 45°

Therefore slope with vertical is 45°