Problem 7 Acceleration in Circular Motion: A car initially traveling eastward tu

Question

Problem 7 Acceleration in Circular Motion: A car initially traveling eastward turns north by traveling in a circular path at constant speed as in Figure P7.15. The length of the arc ABC in the picture is 235 m, and the car completes the turn in 36.0 s. a) Does the car have centripetal acceleration? Explain why or why not. b) Does the car have tangential acceleration? Explain why or why not. c) Determine the car's speed. d) Determine the magnitude and direction of the acceleration of the car when it is at point B in the picture Figure P7.15

Explanation / Answer

(a) Yes. Any body moves in a circular path has centripetal accerelation and has value v^2/R.

(b) Yes. The body has also tangential acceleration. It is the component of centripetal acceleration.

(c) Car's speed = Arc length / time = 235/36 = 6.53 m/s.

(d) Here, length of the arc ABC = 2*pi*r / 4 = 235

=> pi*r/2 = 235

=> r = (2*235) / pi = 149.6 m

acceleration at a uniform speed on a circular curve is
a = v²/r
a = 6.53² / 149.6 = 0.285 m/s^2

and the direction will be towards the center of the curve which will be perpendicular to the instantaneous velocity.

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