A test track contains a circular curve of radius

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

220\,\text{m}

. Engineers want vehicles to take the curve without depending on friction when travelling at

25\,\text{m}\!\cdot\!\text{s}^{-1}

. Assume the curve is perfectly smooth and that

g=9.8\,\text{m}\!\cdot\!\text{s}^{-2}

. (a) Derive, from first principles, an expression for the banking angle

\theta

required for a vehicle of any mass to negotiate a frictionless curve of radius

r

at speed

v

. Express your final answer for

\theta

in terms of

v

r

, and

g

only. (b) Using your derived expression, determine the numerical value of

\theta

needed on the

220\,\text{m}

curve for the specified design speed.