A car is traveling around a horizontal circular track with radius r = 290 m at a
ID: 1408010 • Letter: A
Question
A car is traveling around a horizontal circular track with radius r = 290 m at a constant speed v = 20 m/s as shown. The angle ?A = 30° above the x axis, and the angle ?B = 54° below the x axis.
A) What is the magnitude of the car’s acceleration?
B) What is the x component of the car’s acceleration when it is at point A
C) What is the y component of the car’s acceleration when it is at point A
D) What is the x component of the car’s acceleration when it is at point B
E) What is the y component of the car’s acceleration when it is at point B
F) As the car passes point B, the y component of its acceleration is:
-increasing
-decreasing
-constant
Explanation / Answer
Here ,
A) magnitude of acceleration , a = v^2/r
magnitude of acceleration , a =20^2/(290)
magnitude of acceleration , a =1.38 m/s^2
the magnitude of acceleration is 1.38 m/s^2
B)
at A
x - component of acceleration = - a * cos(30)
x - component of acceleration = -1.38 * cos(30)
x - component of acceleration = -1.195 m/s^2
the x - component of acceleration is -1.195 m/s^2
C)
y - component of acceleration = a * sin(30)
y - component of acceleration = 1.38 * sin(30)
y - component of acceleration = 0.69 m/s^2
the y - component of acceleration is 0.69 m/s^2
D)
at point B
x - component of acceleration = a * cos(54)
x - component of acceleration = 1.38 * cos(54)
x - component of acceleration = 0.811 m/s^2
the x - component of acceleration is 0.811 m/s^2
E)
y - component of acceleration = a * sin54)
y - component of acceleration = 1.38 * sin(54)
y - component of acceleration = 1.12 m/s^2
the y - component of acceleration is 1.12 m/s^2
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