Question

When a car corners at speed one is relying on the friction between the tyres and the road to counter the centrifugal force tending to throw the car outwards. One way to reduce the dependence on friction is to ‘bank’ the corner. For a car travelling with a speed v entering a corner of radius r, show that the angle of the bank, θ, (measured from the horizontal) should satisfy tanθ = v2/(gr) if there is to be no reliance on friction. In the light of this result discuss the design of the ‘Wall of Death’ fairground attraction in which a motorbike is ridden at speed around the inner surface of a large vertical cylinder, with the bike and rider at a small angle to the horizontal plane. What role does friction play and why is a small angle necessary?

Answer 1

Free-body diagram for the car on the banked turn is shown above.

In the vertical direction there is no acceleration

so,

Ncos = mg

N = mg / cos ------------ (1)

In horizontal direction,

N sin = mv² / r

(mg / cos ) sin = mv² / r

g tan = v² / r

tan = v² / rg

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In wall of death play, the friction between the bike and wall keep the bike from sliding toward the center of the turn or down the wall. The normal force from the wall on the biker will have two components. The vertical component will balance the friction force acting between bike and wall and horizontal component will be equal to centripetal force.