HW07-solutions - lee (cyl327) HW07 gentle (56245) 1 This...

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Unformatted text preview: lee (cyl327) HW07 gentle (56245) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 2) 10.0 points An animal-rescue plane flying due east at 22 m / s drops a bale of hay from an altitude of 86 m . The acceleration due to gravity is 9 . 81 m / s 2 . If the bale of hay weighs 199 N , what is the momentum of the bale the moment it strikes the ground? Correct answer: 945 . 248 kg m / s. Explanation: Let : v plane = 22 m / s , h = 86 m , and W = 199 N . v plane v 86 m The bale strikes the ground at an angle, so its final velocity v will have both a horizontal and a vertical component, and v 2 = v 2 + v 2 h Vertically, conservation of energy gives us E kf = E po 1 2 mv 2 = mg h v 2 = 2 g h The horizontal component of the bale is v , the speed of the plane, so the speed of the bale as it strikes the ground is v = radicalBig v 2 + v 2 plane = radicalBig 2 g h + v 2 plane The momentum of the bale is thus p = mv = W g radicalBig 2 g h + v 2 plane = 199 N 9 . 81 m / s 2 radicalBig 2 (9 . 81 m / s 2 ) (86 m) + (22 m / s) 2 = 945 . 248 kg m / s . 002 (part 2 of 2) 10.0 points At what angle of inclination will the bale strike? Answer between 180 and +180 . Correct answer: 61 . 8274 . Explanation: When the bale strikes the ground, the ver- tical component is the side opposite the angle of inclination and the horizontal component is the side adjacent, so tan = v v plane = arctan parenleftbigg v v plane parenrightbigg = arctan parenleftbigg 2 g h v plane parenrightbigg = arctan parenleftBigg radicalbig 2 (9 . 81 m / s 2 ) (86 m) 22 m / s parenrightBigg = 61 . 8274 . keywords: 003 10.0 points Two blocks have mass m and M = 1 . 74 m , re- spectively. A light spring is attached to one of them, and the blocks are pushed together, lee (cyl327) HW07 gentle (56245) 2 compressing the spring between them. They are secured, in this compressed state, by a cord. They are then placed, at rest, on a hor- izontal, frictionless surface. The cord holding them together is burned, after which the block of mass M moves to the right with a speed of 2 . 82 m / s. m M m M Before After (a) (b) v What is the speed of the block of mass m ? Correct answer: 4 . 9068 m / s. Explanation: From conservation of momentum p = 0, in our case we obtain 0 = M v M mv m . Therefore v m = M m v M = (1 . 74) v M = (1 . 74) (2 . 82 m / s) = 4 . 9068 m / s . 004 10.0 points A uranium nucleus 238 U may stay in one piece for billions of years, but sooner or later it de- cays into an particle of mass 6 . 64 10 27 kg and 234 Th nucleus of mass 3 . 88 10 25 kg, and the decay process itself is extremely fast (it takes about 10 20 s). Suppose the uranium nucleus was at rest just before the decay....
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HW07-solutions - lee (cyl327) HW07 gentle (56245) 1 This...

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