How Do You Calculate the Components of Acceleration for a Car on a Curved Track?

AI Thread Summary
To calculate the components of acceleration for a car on a curved track, the car's acceleration can be determined using its speed and the radius of the track. The car's acceleration magnitude is found to be 1.07 m/s², but confusion arises regarding the tangential and radial angles at points A and B. The x and y components of acceleration can be calculated using trigonometric functions based on the angles provided. For a car moving in a circle at constant speed, the acceleration always points towards the center of the circle. Understanding these concepts is crucial for solving the problem accurately.
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A car is traveling around a horizontal circular track with radius r = 270 m at a constant speed v = 17 m/s as shown. The angle θA = 23° above the x axis, and the angle θB = 58° below the x axis.

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

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

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

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


I found the magnitude of the car's acceleration to be 1.07m/s^2. But all the tangential and radial angles are really confusing me at the moment =(. If anyone could help me or just briefly explain that would be great.

[PLAIN]http://www.smartphysics.com/images/content/mechanics/ch3/CarOnCurve2.png
 
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For an object traveling in a circle at constant speed, in what direction does the acceleration point? (If you don't know, there should be a discussion in your physics textbook that addresses my question.)
 
Use triangles.
 
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