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

N\cos\theta=mg

problems.proof.analysis

First identify the physical model and convention that match the stated setup. This fixes the signs used in the equations that follow.