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\sin\theta=mv^2/r

problems.proof.analysis

This equation expresses the physical law governing the system. It incorporates the stated constraint rather than treating the relevant quantities as independent.

problems.proof.pitfall. Check the sign convention and physical case carefully; do not use a formula for a different motion or geometry.