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ENG102_SL7

# ENG102_SL7 - DATE DUE ENG102 Solution to homework set#7...

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DATE: November 6, 2011 DUE: November 11 14 (before Noon), 2011 ENG102, Solution to homework set #7. 1. Look at Problem 3/354 on page 266 in the book. a. Solve the problem with the additional information that each mass is a solid sphere with radius r = 0 . 1 m . Both momentum and angular momentum are conserved. The change from the original problem is that the moment of intertial around G is now: I = 2 mR 2 + 4 5 mr 2 , where R = 0 . 4 m . Thus: H G = m ( v A + v B )0 . 4 m = I ˙ θ (1) ˙ θ = H G I = v A + v B 2 · 0 . 4 m + 4 5 r 2 0 . 4 m = 9 . 756 s 1 (2) p = m ( v A - v B ) = 2 mv (3) v = v A - v B 2 = - 1 m/s (4) b. What is the loss in kinetic energy? Initial and Final kinetic energy are: E k = 1 2 mv 2 A + 1 2 mv 2 B (5) E k = 1 2 I ( ˙ θ ) 2 + m ( v ) 2 = 1 2 H 2 G I + m 4 ( v A - v B ) 2 (6) Δ E k = 1 2 H 2 G I - 1 4 m ( v 2 A + v 2 B + 2 v A v B ) = = 1 2 H 2 G I - 1 4 m ( v A + v B ) 2 (7) = 1 4 m ( v A + v B ) 2 bracketleftBigg 1 1 + 2 5 r 2 R 2 - 1 bracketrightBigg = - 0 . 390 m (m / s) 2 (8) Notice that r 0 gives Δ E k = 0 .

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ENG102_SL7 - DATE DUE ENG102 Solution to homework set#7...

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