What is the magnitude of the centripetal acceleration of a car following a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h)? Compare the acceleration with that due to gravity for this fairly gentle curve taken at highway speed. See Figure 6.9(a).

Strategy
Because v and r are given, the first expression in $a_c = \frac{v^2}{r} ; a_c = rω^2$ is the most convenient to use.a

Question

What is the magnitude of the centripetal acceleration of a car following a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h)? Compare the acceleration with that due to gravity for this fairly gentle curve taken at highway speed. See Figure 6.9(a).

Strategy
Because v and r are given, the first expression in $a_c = \frac{v^2}{r} ; a_c = rω^2$ is the most convenient to use.a

Strategy
Because v and r are given, the first expression in [latex] a_c = \frac{v^2}{r} ; a_c = rω^2 [/latex] is the most convenient to use.a

Accepted Answer

Entering the given values of v = 25.0 m/s and r = 500 m into the first expression for [latex] a_c [/latex] gives

[latex] a_c = \frac{v^2}{r} = \frac{(25.0 m/s)^2 }{500 m} = 1.25 m/s^2. [/latex] (6.18)

Discussion
To compare this with the acceleration due to gravity [latex] (g = 9.80 m/s^2) [/latex] , we take the ratio of [latex] ac / g = (1.25 m/s^2) / (9.80 m/s^2) = 0.128 m/s^2 . [/latex] Thus, [latex] a_c = 0.128 g [/latex] and is noticeable especially if you were not wearing a seat belt.

Question 6.2: What is the magnitude of the centripetal acceleration of a c...

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