two cars are on a circular track of radius r= 200m. they travel in opposite dire
ID: 1614548 • Letter: T
Question
two cars are on a circular track of radius r= 200m. they travel in opposite directions. the red car has a constant angular speed of 0.12 rad/s as it passes by the blue car at point A. the blue car starts from rest at point A and accelerates with a constant acceleration of 8m/s^2. they meet again at point B.
A) find the angular acceleration of the blue car.
B) Find the time it takes for either car to reach the point B.
C) find the angle theta shown in the figure
D) Find the centripetal acceleration of the red car
1BO bsA AExplanation / Answer
A)
for blue car
angular acceleration alpha = a/r = 8/200 = 0.04 rad/s^2
B)
for red car
angular displacement theta1 = w*t = 0.2*t
for blue car
angular acceleration alpha = a/r = 8/200 = 0.04 rad/s^2
angular displacement theta 2 = (1/2)*alpha*t^2
theta2 = (1/2)*0.04*t^2
theta2 = 0.02 t^2
theta1 + theta2 = 2pi
0.12*t + 0.02*t^2 = 2pi
t = 15 s
C)
theta = w*t = 0.12*15 = 1.8 rad = 1.8*360/(2pi) = 013.1 degrees
(D)
a = r*w^2 = 200*0.12^2 = 2.88 m/s^2 <<<----answer
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