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Physics: Principles with Applications | 6th Edition | ISBN: 9780321569837 | Authors: Douglas C. Giancoli
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A circular curve of radius R in a new highway is designed so that a car traveling at

Chapter 5, Problem 93GP

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QUESTION:

Problem 93GP

A circular curve of radius R in a new highway is designed so that a car traveling at speed v0 can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from vmin to vmax. Derive formulas for vmin and vmax as functions of μs, v0, and R.

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QUESTION:

Problem 93GP

A circular curve of radius R in a new highway is designed so that a car traveling at speed v0 can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from vmin to vmax. Derive formulas for vmin and vmax as functions of μs, v0, and R.

ANSWER:

Solution 93GP

Step 1 of 3

We are required to determine the maximum and minimum velocities of the car under the given conditions.

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