ENG102_SL6

ENG102_SL6 - DATE: DUE: ENG102, Solution to homework set...

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DATE: October 26, 2011 DUE: November 4, 2011 ENG102, Solution to homework set #6. 1. Look at Problem 3/354 on page 266 in the book. a. Solve the problem. Both momentum and angular momentum are conserved. Thus: H G = m ( v A + v B )0 . 4 m = 2 m (0 . 4 m ) 2 ˙ θ (1) ˙ θ = v A + v B 2 · 0 . 4 m = 10 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 kinetic energy: E k = 1 2 mv 2 A + 1 2 mv 2 B . Final kinetic energy: E k = m (0 . 4 m ) 2 ( ˙ θ ) 2 + m ( v ) 2 = 1 2 m ( v 2 A + v 2 B ) . Thus, the kinetic energy is conserved, and there is no energy loss in the process. c. Assume that the point G is held fixed (by a nail, or something) such that the object can rotate freely around G . Solve the problem (1a) with this change. Now momentum is not conserved. Angular momentum around the axis of the nail (G) is conserved. Thus H G = m ( v A + v B )0 . 4 m = 2 m (0 . 4 m ) 2 ˙ θ (5) ˙ θ = v A + v B 2
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ENG102_SL6 - DATE: DUE: ENG102, Solution to homework set...

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