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Unformatted text preview: Le (tl8426) – 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 31 m / s drops a bale of hay from an altitude of 74 m . The acceleration due to gravity is 9 . 81 m / s 2 . If the bale of hay weighs 177 N , what is the momentum of the bale the moment it strikes the ground? Correct answer: 886 . 282 kg m / s. Explanation: Let : v plane = 31 m / s , h = 74 m , and W = 177 N . v plane v ⊥ θ 74 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 = 177 N 9 . 81 m / s 2 × radicalBig 2 (9 . 81 m / s 2 ) (74 m) + (31 m / s) 2 = 886 . 282 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: 50 . 8692 ◦ . 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 θ = v ⊥ v plane θ = arctan parenleftbigg v ⊥ v plane parenrightbigg = arctan parenleftbigg √ 2 g h v plane parenrightbigg = arctan parenleftBigg radicalbig 2 (9 . 81 m / s 2 ) (74 m) 31 m / s parenrightBigg = 50 . 8692 ◦ . keywords: 003 10.0 points Two blocks have mass m and M = 3 . 99 m , re- spectively. A light spring is attached to one of them, and the blocks are pushed together, compressing the spring between them. They are secured, in this compressed state, by a Le (tl8426) – HW07 – gentle – (56245) 2 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 . 74 m / s. m M m M Before After (a) (b) v What is the speed of the block of mass m ? Correct answer: 10 . 9326 m / s. Explanation: From conservation of momentum Δ p = 0, in our case we obtain 0 = M v M − mv m . Therefore v m = M m v M = (3 . 99) v M = (3 . 99) (2 . 74 m / s) = 10 . 9326 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 α 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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This note was uploaded on 12/05/2011 for the course PHY 301 taught by Professor Swinney during the Fall '07 term at University of Texas at Austin.
- Fall '07