You're designing a "cloverleaf" highway interchange....

You're designing a "cloverleaf" highway interchange. Vehicles will exit the highway and slow to a constant $70 \mathrm{km} / \mathrm{h}$ before negotiating a circular turn. If a vehicle's acceleration is not to exceed $0.40 g$ (i.e., $40 \%$ of Earth's gravitational acceleration), then what's the minimum radius for the turn? Assume the road is flat, not banked (more on this in Chapter 5 ).

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Key Concepts

Unit Conversion

In physics problems, it is essential to work with consistent units. Speed measurements, for example, might be provided in kilometers per hour, but standard equations for motion require speeds in meters per second. Proper unit conversion ensures accurate calculations and meaningful results in engineering and physics analyses.

Circular Motion

Circular motion refers to the movement of an object along a circular path. This concept is essential in analyzing how forces act on objects in curved paths, such as vehicles turning on roads. Understanding the dynamics of circular motion helps in designing safe curves on highways or in any system involving rotations.

Centripetal Acceleration

Centripetal acceleration is the inward acceleration required to keep an object moving in a circle. It is calculated using the formula a = v²/r, where v is the object's speed and r is the radius of the circle. This concept is crucial when setting limits on how sharply a path can curve, ensuring that the forces experienced do not exceed safe thresholds.

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