Curves on some test tracks and race courses, such as the Daytona International Speedway in Florida, are very steeply banked. This banking, with the aid of tire friction and very stable car configurations, allows the curves to be taken at very high speed. To illustrate, calculate the speed at which

Question

Curves on some test tracks and race courses, such as the Daytona International Speedway in Florida, are very steeply banked. This banking, with the aid of tire friction and very stable car configurations, allows the curves to be taken at very high speed. To illustrate, calculate the speed at which a 100 m radius curve banked at 65.0° should be driven if the road is frictionless.

Strategy
We first note that all terms in the expression for the ideal angle of a banked curve except for speed are known; thus, we need only rearrange it so that speed appears on the left-hand side and then substitute known quantities.

Accepted Answer

Starting with

[latex] tan θ = \frac{v^2}{rg} [/latex] (6.37)

we get

[latex] v = (rg tan θ)^{1 / 2} [/latex] (6.38)

Noting that tan 65.0º = 2.14, we obtain

[latex] v = \left[(100 m)(9.80 m/s^2)(2.14)\right] ^{1 / 2} [/latex] (6.39)

= 45.8 m/s.

Discussion
This is just about 165 km/h, consistent with a very steeply banked and rather sharp curve. Tire friction enables a vehicle to take the curve at significantly higher speeds.

Calculations similar to those in the preceding examples can be performed for a host of interesting situations in which centripetal force is involved—a number of these are presented in this chapter’s Problems and Exercises.

Question 6.5: Curves on some test tracks and race courses, such as the Day...

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