For a spinning amusement park ride, the velocity v in meters per second of a car moving around a curve with a radius r meters is given by the formula v=sqrt (ar), where 'a' is the car's acceleration in m/s^2.

a) For safety reasons, a ride has a minimum acceleration of 39.2m/s^2. If the cars on the ride have a velocity of 14m/s what is the smallest radius that any curve on the ride may have?

b) What is the acceleration of a car moving at 8m/s around a curve with a radius of 2.5m?

Question

15 September, 11:57

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Answers (1)

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Mckinley Reed · Answer 1

A)

v=sqrt (ar)

v^2=ar

r = (v^2) / a

r = (14^2) / 39.2

r=5

5 m

b)

v=sqrt (ar)

v^2=ar

a = (v^2) / r

a = (8^2) / 2.5

a=25.6

25.6ms^-2