Answer to Question #114809 in Classical Mechanics for john

Question

A car is moving around a banked curve of radius 86 m at a constant speed. The road is banked at an angle of 11° and the car is moving at just the correct speed to ensure that there are no lateral frictional forces on the tyres - that is the only forces acting on the car are the force of gravity and the normal force from the road.

At what speed is the car moving? (in m s−1 to 2 s.f

Answer 1

As per the question,

Radius of the curvature of the road (R)=86m

The banking of the road $(\theta)=11^\circ$

Now, applying the force balance rule,

$mg\sin \theta =\dfrac{mv^2\cos \theta}{R}$

$\Rightarrow v=\sqrt{\dfrac{Rg \sin \theta}{\cos \theta}}$

Now, substituting the values,

$v=\sqrt{163.82}m/sec=12.79 m/sec = 12.8 m/sec$