Question

A truck drives with a constant linear speed v_iv i ​ v, start subscript, i, end subscript down a road with two curves. The first curve has a radius RRR and the second curve has a radius 3R3R3, R. How does the magnitude of the truck's centripetal acceleration change after the radius increases? Choose 1 answer: Choose 1 answer: (Choice A) A Increases by factor of 333 (Choice B) B Decreases by factor of 999 (Choice C) C Decreases by factor of 333 (Choice D) D No change

Answer 1

Answer:

(C) Decreases by factor of 3

Explanation:

Centripetal acceleration is given by

$a = \dfrac{v^2}{r}$

where v is the linear velocity and r is the radius of the curve.

Let the centripetal acceleration on the curve of radius R be $a_1$.

Then

$a_1 = \dfrac{v_i^2}{R}$

Let the centripetal acceleration on the curve of radius 3R be $a_2$.

Then

$a_2 = \dfrac{v_i^2}{3R} = \dfrac{1}{3}\dfrac{v_i^2}{R} = \dfrac{1}{3}a_1$

Here, we see that the acceleration decreases by a factor of 3.