4. c m start finish A car and a motorcycle start from the southern end of a circ

Question

4. c m start finish A car and a motorcycle start from the southern end of a circular racetrack of radius r. The car's speed is 10 and the angular acceleration of the motorcycle isa. Let r = 85 m, vo-35 m/s, and = 0.030 rad/s2. A) How long after they start will they first meet? B) Through what angle (in radians) will the motorcycle have traveled? C) When they meet what will be the angular velocity (in rad/s) of the car, wc? D) When they meet what will be the angular velocity (in rad/s) of the motorcycle wm? E) When they meet find the magnitude of the total acceleration (in m/s?) a of the motorcycle. a) 11.7 s, a) 1.67, a) 0.412, a) 0.470, a) 0.57, b) 7.50 s, c) 10.9s, d) 12.9s b) 1.79, c) 2.76, d 0.28 b) 0.3, c) 0.357, d) 0.800 b) 0.328, c) 0.258, d) 0.075 b) 4.88, c) 9.47, d) 22.4

Explanation / Answer

supose they meet after time t,

total angle revolved = by car + by motorcycle = 2 pi

wt + alpha t^2 /2 = 2 pi

(35/85)t + (0.030 t^2 / 2) = 2 pi

0.015 t^2 + 0.412 t - 6.283 = 0

t = 10.9 sec

Ans(C)

(B) by motorcycle = 0.03 x 10.9^2 /2 = 1.79 rad

Ans(b)

(C) w = 35/85 = 0.412 rad/s Ans(a)

(d) w = alpha t = 0.328 rad/s Ans(b)

(e) a_t = alpha r = 2.55 m/s^2

a_r = 0.328^2 x 85 = 9.14 m/s^2

a = sqrt(a_r^2 + a_t^2) = 9.49 m/s^2

Ans(c)

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