Question

To practice Problem-Solving Strategy 6.1: Circular motion A highway curve with radius R = 274 m is to be banked so that a car traveling v = 25.0 m/s will not skid sideways even in the absence of friction. At what angle should the curve be banked?

Answer 1

The curve should be banked at an angle of 13 degrees.

Step-by-step explanation:

We have,

Radius of a highway curve is 274 m

Speed of car on this curve is 25 m/s

Let
`\theta` is the banking angle. On a banked curve, the angle of safe diving is given by following expression.

`\tan\theta=(v^2)/(Rg)`

g = 10 m/s²

Plugging all the values in above formula,

`\tan\theta=((25)^2)/(274* 9.8)\\\\\theta=\tan^(-1)\left(((25)^(2))/(274*9.8)\right)\\\\\theta=13^(\circ)`

So, the curve should be banked at an angle of 13 degrees.