A car is traveling around a horizontal circular track with radius r = 230 m at a

Question

A car is traveling around a horizontal circular track with radius r = 230 m at a constant speed v = 17 m/s as shown. The angle A = 39° above the x axis, and the angle B = 57° below the x axis.

1.What is the magnitude of the car’s acceleration?

2.What is the x component of the car’s acceleration when it is at point A?

3.What is the y component of the car’s acceleration when it is at point A?

4.What is the x component of the car’s acceleration when it is at point B?

5.What is the y component of the car’s acceleration when it is at point B?

Explanation / Answer

1) a = v² / r = (17m/s)² / 230m = 1.256 m/s²
Here the acceleration vector points toward the origin, so add 180º to the given angles.
2) a_xa = 1.25m/s² * cos219º = -0.976 m/s²
3) a_ya = 1.25m/s² * sin219º = -0.79 m/s²
4) a_xb = 1.25m/s² * cos123º = -0.684 m/s²
5) a_yb = 1.25m/s5 * sin123º = 1.053 m/s²

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