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10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

Cycloidal MotionIn Exercises 45 and 46, consider the motion of a point (or particle) on the circumference of a rolling circle. As the circle rolls, it generates the cycloid

where

Find the maximum speed of a point on the circumference of an automobile tire of radius 1 foot when the automobile is traveling at 60 miles per hour. Compare this speed with the speed of the automobile.

To determine

**To calculate:** The maximum speed of a point of an automobile tire on its circumference when the travelling speed of the automobile is 60miles/hour and the radius is 1 foot granted that the as the circle rolls it generates a cycloid

Explanation

**Given:**

The maximum speed of a point on the circumference of an automobile tire when the travelling speed of the automobile is 60miles/hour and the radius is 1 foot granted that the as the circle rolls it generates a cycloid

**Formula used:**

The path followed is:

The trigonometric identity:

**Calculation:**

Consider the path function as:

Now, differentiate the function with respect to *t* to obtain the velocity as shown below.

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P-10PSCh-12 P-11PSCh-12 P-12PSCh-12 P-13PSCh-12 P-14PS

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