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Unformatted text preview: Version 014 TEST02 TSOI (58160) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points An ore car of mass 37000 kg starts from rest and rolls downhill on tracks from a mine. At the end of the tracks, 28 m lower vertically, is a horizontally situated spring with constant 3 . 3 10 5 N / m. The acceleration of gravity is 9 . 8 m / s 2 . Ignore friction. How much is the spring compressed in stop- ping the ore car? 1. 9.86343 2. 6.7462 3. 8.05025 4. 5.34743 5. 5.55889 6. 7.94607 7. 5.00213 8. 5.0898 9. 7.84424 10. 5.63231 Correct answer: 7 . 84424 m. Explanation: Energy is conserved, so the change of po- tential energy from when the car is at rest to when it just hits the spring is mg h = 1 2 mv 2 . The kinetic energy is then converted to po- tential energy in the spring as the cart comes to rest. When the spring is fully compressed by an amount d , all of the kinetic energy has been converted to potential energy so 1 2 mv 2 = 1 2 k d 2 . Thus, 1 2 k d 2 = mg h, and solving for d we have d = radicalbigg 2 mg h k = radicalBigg 2 (37000 kg) (9 . 8 m / s 2 ) (28 m) (3 . 3 10 5 N / m) = 7 . 84424 m . 002 10.0 points According to some nineteenth-century geo- logical theories (now largely discredited), the Earth has been shrinking as it gradually cools. If so, how would g have changed over geo- logical time? 1. It would not change; the mass of the Earth remained the same. 2. It would decrease; the Earths radius is decreasing. 3. It would increase; g is inversely propor- tional to the square of the radius of the Earth. correct Explanation: The acceleration g 1 r 2 of gravity would increase if the Earth shrank but its mass stayed the same. 003 (part 1 of 2) 10.0 points The two blocks are connected by a light string that passes over a frictionless pulley with a negligible mass. The block of mass m 1 lies on a rough horizontal surface with a constant coefficient of kinetic friction . This block is connected to a spring with spring constant k . The second block has a mass m 2 . The system is released from rest when the spring is unstretched, and m 2 falls a distance h before it reaches the lowest point. Note: When m 2 is at the lowest point, its velocity is zero. m 1 m 2 k m 1 m 2 h h Version 014 TEST02 TSOI (58160) 2 Consider the moment when m 2 has de- scended by a distance s , where s is less than h . At this moment the sum of the kinetic energy for the two blocks K is given by 1. K = ( m 1 + m 2 ) g s + 1 2 k s 2- m 1 g s. 2. K = ( m 1 + m 2 ) g s- 1 2 k s 2 + m 1 g s. 3. K = ( m 1 + m 2 ) g s- 1 2 k s 2- m 1 g s....
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