12_P82InstructorSolution

# 12_P82InstructorSolution - 12.82 Model The clay balls are...

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12.82. Model: The clay balls are particles and undergo a totally inelastic collision. Linear momentum is conserved during the collision. Visualize: Solve: (a) The angle is measured counterclockwise from r G to . v G From geometry, () 1 1 180 tan 1 225 , β + and 1 2 1 tan 26.6 . 2 ⎛⎞ == ° ⎜⎟ ⎝⎠ So ( ) 12 1 1 1 1 2 2 2 2 2 sin sin 0.015 kg 2 m 2 m/s sin 225 0.025 kg 5 m 2.0 m/s sin 26.6 0.020 kg m /s. LL L m r v m r v ββ =++ + + ° = Note that the signs of 1 L and 2 L agree with those determined by the right-hand rule. (b) At the instant before the clay balls collide they are located at (1.5 m, 1.0 m). Here, 1 21 2 2 tan 33.7 180 146.3 3 ° = ° + = ° So ( ) ( ) ( ) ( ) ( ) 22 2 0.015 kg 1.0 m 1.5 m 2.0 m/s sin 213.7 0.025 kg 1.0 m 1.5 m 2.0 m/s sin33.7
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