A car is traveling around a horizontal circular track with radius r = 240 m at a

Question

A car is traveling around a horizontal circular track with radius r = 240 m at a constant speed v = 25 m/s as shown. The angle A = 29° above the x axis, and the angle B = 59° 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 magnitude of the car’s acceleration = v² / r .
The x component of acceleration = -( v² / r) cos and
The y- component of acceleration = -( v² / r) sin
where v is the tangential velocity and . the angle at the centre measured
anti - clockwise from +ve .x - direction.

1) The magnitude of the car’s acceleration = v ² / 240 = 25 ²/240 = 2.60 m / sec²

2) The x component of the car’s acceleration when it is at point A
= - (v² /r) cos (A) = - 2.60*cos(29) = -2.27 m / sec²

3) The y component of the car’s acceleration when it is at point A
= -( v² / r) sin (A) = -2.60* sin (32) = -1.377 m / sec²

4) The x component of the car’s acceleration when it is at point B
= -( v²/ r) cos (B) = -2.60*cos(-59) = - 1.33 m / sec²

5) The y component of the car’s acceleration when it is at point B
= - ( v²/ r)sin (B) = - 2.60*sin (-62) = 2.228 m / sec²

6) As the car passes point B, the y component of its acceleration is - Decreases.

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