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 = 15 m/s as shown. The angle A = 31° above the x axis, and the angle B = 66° 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 increasing, constant, or decreasing?

Explanation / Answer

given,

radius = 200 m

speed = 15 m/s

A = 31° above the x axis

B = 66° below the x axis

acceleration = velocity^2 / radius

acceleration = 15^2 / 200

acceleration = 2.25 m/s^2

the acceleration vector points toward the origin, so add 180º to the given angles

x component of the car’s acceleration when it is at point A = 2.25 * cos(180 + 31)

x component of the car’s acceleration when it is at point A = -1.928 m/s^2

y component of the car’s acceleration when it is at point A = 2.25 * sin(180 + 31)

y component of the car’s acceleration when it is at point A = -1.158 m/s^2

x component of the car’s acceleration when it is at point B = 2.25 * cos(180 - 66)

x component of the car’s acceleration when it is at point B = -0.915 m/s^2

y component of the car’s acceleration when it is at point B = 2.25 * sin(180 - 66)

y component of the car’s acceleration when it is at point B = 2.055 m/s^2

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