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Unformatted text preview: Version 048 Midterm 02 florin (56930) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Three balls with masses: m , 2 m and 1 2 m , re- spectively are thrown from the top of a build- ing, all with the same initial speed v i . The first ball is thrown horizontally, the second at some angle 1 above the horizontal, and the third with some angle 2 < 1 below the hor- izontal. Neglecting air resistance, rank the speeds of the balls as they reach the ground, from the slowest to the fastest: 1. 1, 2, 3 2. 2, 1, 3 3. 1, 3, 2 4. 3, 2, 1 5. 3, 1, 2 6. All three balls strike the ground with the same speed. correct 7. 2, 3, 1 Explanation: Consider each ball and the earth as three separate systems. There is no work done on these systems by the surroundings so E sys = W surr = 0. Next, consider the system that consists of the ball with mass m and the earth. Ini- tially, it has a total energy (ignoring rest mass energy) of E sys,i = K i + U i = 1 2 mv 2 i + mg y i and a final energy of E sys,f = K f + U f = 1 2 mv 2 f + mg y f so E sys = 1 2 m ( v 2 f v 2 i ) + mg ( y f y i ) = 0 Solving this equation for v f gives v f = radicalBig g ( y f y i ) + v 2 i The result does not depend on the mass of the ball so the same expression can be derived for each one. All three balls begin with the same speed v i and experience the same change in height ( y f y i ) so the final speed for all three is the same . 002 10.0 points A bucket containing a rock of mass m is ro- tated in a vertical circle of radius 1 . 469 m. What must be the minimum speed of the pail at the top of the circle so that the rock wont fall out? 1. 3.0043 2. 3.05123 3. 3.20475 4. 3.79423 5. 2.49656 6. 2.54515 7. 2.87085 8. 2.68019 9. 3.74745 10. 3.6695 Correct answer: 3 . 79423 m / s. Explanation: The system is the rock. In order for the rock to move in a circle of radius 1 . 469 m, it ex- periences a net force equal to the centripetal force necessary to maintain the circular mo- tion. A free body diagram of the system includes only the force of gravity and the nor- mal force exerted by the bottom of the bucket, so F net = F N + F g . When moving with the minimum velocity, the rock is just about to fall out, so the normal force is zero and the centripetal acceleration is supplied by gravity alone. Version 048 Midterm 02 florin (56930) 2 F N + F g = mg = = ma centripetal = m v 2 r . Then, mg = m v 2 r and so, v = g r = radicalBig (9 . 8 m / s 2 ) (1 . 469 m) = 3 . 79423 m / s . 003 10.0 points The escape speed from a very small asteroid is only 28 m / s. If you throw a rock away from the asteroid at a speed of 48 m / s, what will be its final speed? G = 6 . 7 10 11 N m 2 kg 2 ....
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- Fall '08