HW 19 - Morby Grant Homework 19 Due Mar 8 2006 noon Inst...

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Morby, Grant – Homework 19 – Due: Mar 8 2006, noon – Inst: Drummond 1 This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Two ice skaters approach each other at right angles. Skater A has a mass of 64 . 5 kg and travels in the + x direction at 2 . 89 m / s. Skater B has a mass of 68 . 1 kg and is moving in the + y direction at 2 m / s. They collide and cling together. Find the final speed of the couple. Correct answer: 1 . 74104 m / s. Explanation: From conservation of momentum Δ p = 0 m A v A ˆ ı + m B v B ˆ = ( m A + m B ) v f Therefore v f = p ( m A v A ) 2 + ( m B v B ) 2 m A + m B = p (186 . 405 kg m / s) 2 + (136 . 2 kg m / s) 2 64 . 5 kg + 68 . 1 kg = 1 . 74104 m / s 002 (part 1 of 1) 10 points A student performs a ballistic pendulum experiment using an apparatus similar to that shown in the figure. Initially the bullet is fired at the block while the block is at rest (at its lowest swing point). After the bullet hits the block, the block rises to its highest position, see dashed block in the figure, and continues swinging back and forth. The following data is obtained: the maximum height the pendulum rises is 5 cm, at the maximum height the pendulum sub- tends an angle of 48 . 2 , the mass of the bullet is 61 g, and the mass of the pendulum bob is 897 g. The acceleration of gravity is 9 . 8 m / s 2 . 897 g 61 g v i v f 48 . 2 5 cm Determine the initial speed of the projec- tile. Correct answer: 15 . 5471 m / s. Explanation: Let : θ = 48 . 1897 , m 1 = 61 g , m 2 = 897 g , and h = 5 cm = 0 . 05 m . The final velocity is v f = p 2 g h . Using conservation of momentum m 1 v i = ( m 1 + m 2 ) v f , so v i = ( m 1 ) + ( m 2 ) m 1 v f = ( m 1 ) + ( m 2 ) m 1 p 2 g h = (61 g) + (897 g) (61 g) × q 2 (9 . 8 m / s 2 ) (0 . 05 m) = 15 . 5471 m / s .
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