During the course of a turn, an automobile doubles its speed. How much additional frictional force must the tires provide if the car safely makes around the curve?
A
An increase in velocity by a factor of two must be accompanied by an increase in centripetal force by a factor of eight.
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B
An increase in velocity by a factor of two must be accompanied by an decrease in centripetal force by a factor of half.
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C
An increase in velocity by a factor of two must be accompanied by an increase in centripetal force by a factor of four.
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D
An increase in velocity by a factor of two must be accompanied by an increase in centripetal force by a factor of half
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Solution
The correct option is C An increase in velocity by a factor of two must be accompanied by an increase in centripetal force by a factor of four. Since F c varies with v 2 , an increase in velocity by a factor of two must be accompanied by an increase in centripetal force by a factor of four.