A car is traveling around a horizontal circular track with radius r = 200 m at a

Question

A car is traveling around a horizontal circular track with radius r = 200 m at a constant speed v = 28 m/s. The angle ?A = 36° above the x axis, and the angle ?B = 51° 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
6)As the car passes point B, the y component of its acceleration is :
a-increasing
b-constant
c-decreasing

Explanation / Answer

The car posess centripetal acceleration. Centripetal acceleration, a = v^2 / r Direction: towards the centre of the circle (1) Centripetal acceleration, a = 28^2 / 200                                         = 3.92 m/s^2 (2) X-component of acceleration, ax = a cos a                                                    = 3.92 * cos 36                                                    = 3.17 m/s^2 (3) Y-component of acceleration, ay = a sin a                                                    = 3.92 * sin 36                                                    = 2.3 m/s^2 (4) X-component of acceleration, ax = a cos b                                                    = 3.92 * cos 51                                                    = 3.46 m/s^2 (5) Y-component of acceleration, ay = a sin b                                                    = 3.92 * sin 51                                                    = 3.04m/s^2 (6) As the car passes the point B, the angle b decreases, and sin b decreases. So, the y-component of acceleration ( a sin b) decreases.

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