Problem 1

A car travels at

v=20\,\mathrm{m/s}

around a horizontal curve of radius

r=50\,\mathrm m

. The road is banked at angle

\theta

so that the horizontal component of the normal reaction alone provides the centripetal acceleration; there is no lateral friction. Take

g=10\,\mathrm{m/s^2}

. (a) Find the first requested quantity. (b) Find the second quantity. (c) Determine the final result and check its units. (a) Write v (a) Write vertical force balance. (b) Determine the required bank angle. (c) Evaluate it and check the limit as speed tends to zero.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\tan\theta=v^2/(rg)

problems.proof.analysis

Rearranging the governing relation isolates the first requested result. Keeping the signs explicit also checks that its direction and magnitude are physically sensible.