5. 0/3 points Previous Answers MI4 11.7.051 My Notes A thin metal rod of mass 1.

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5. 0/3 points Previous Answers MI4 11.7.051 My Notes A thin metal rod of mass 1.4 kg and length 0.9 m is at rest in outer space, near a space station (see figure below). A tiny meteorite with mass 0.05 kg traveling at a high speed of 225 m/s strikes the rod a distance 0.2 m from the center and bounces off with speed 60 m/s as shown in the diagram. The magnitudes of the initial and final angles to the x axis of the small mass's velocity are ?? = 26" and ?,-82? 4y (a) Afterward, what is the velocity of the center of the rod? (Express your answer in vector form.) CM 13.16 X m/s (b) Afterward, what is the angular velocity o of the rod? (Express your answer in vector form.) rad/s (c) What is the increase in internal energy of the objects? Additional Materials Section 11.7

Explanation / Answer

(A) applying momentum conservation for collision,
  
(0.05)(225)(cos26i + sin26j) = (0.05)(60)(-cos82i + sin82j) + (1.4)v

v_cm = 7.52i + 1.40 j m/s ....Ans

(B) Applying angular momentum conservation about the center of mass,

-(0.05 x 225 x 0.2 x cos26) + 0 = (0.05 x 60 x 0.2 x cos82) + (1.4 x 0.9^2 / 12) w

w = - 22.3 rad/s

Ans: 0i + 0j - 22.3 k rad/s

(C) Ki = (0.05 x 225^2 / 2) = 1265.625 J

Kf = (0.05 x 60^2 / 2) + (1.4 (7.52^2 + 1.40^2)/2) + ((1.4 x 0.9^2 / 12)(22.3^2)/2)

Kf = 154.45 J

thermal energy = Ki - Kf = 1111.2 J

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