test1 - Version 026 TEST01 tsoi(92940 1 This print-out...

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Version 026 – TEST01 – tsoi – (92940) 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 10.0points A 888 kg block is pushed on the slope of a 32 frictionless inclined plane to give it an initial speed of 50 cm / s along the slope when the block is 1 . 5 m from the bottom of the incline. The acceleration of gravity is 9 . 8 m / s 2 . 888 kg 1 . 5 m 32 What is the speed of the block at the bot- tom of the plane? 1. 3.8459 2. 3.36035 3. 3.97865 4. 5.21834 5. 4.35265 6. 3.78572 7. 4.1071 8. 3.93111 9. 4.56848 10. 4.76804 Correct answer: 3 . 97865 m / s. Explanation: Let : m = 888 kg , θ = 32 , and v 0 = 50 cm / s = 0 . 5 m / s . Note: It doesn’t make any difference whether the block is initially pushed up or down the slope. Consider the free body diagram for the block M g sin θ N = M g cos θ M g We therefore have a x = g sin θ . The final speed is v 2 = v 2 0 + 2 a x ( x x 0 ) = v 2 0 + 2 g sin θ ( x x 0 ) = (0 . 5 m / s) 2 + 2 (9 . 8 m / s 2 ) sin 32 (1 . 5 m) = 15 . 8296 m 2 / s 2 , so v = radicalBig 15 . 8296 m 2 / s 2 = 3 . 97865 m / s . 002 10.0points This question is typical on some driver’s li- cense exams: A car moving at 49 km / h skids 17 m with locked brakes. How far will the car skid with locked brakes at 147 km / h? 1. 64.0 2. 117.0 3. 108.0 4. 126.0 5. 135.0 6. 100.0 7. 56.0 8. 81.25 9. 48.0 10. 153.0 Correct answer: 153 m. Explanation: 147 km / h 49 km / h = 3 At 3 times the speed, it has 9 times the KE parenleftbigg 1 2 m v 2 parenrightbigg and will skid 9 times as far: 153 m. Since the frictional force is about the same in both cases, the distance has to be 9 times as great for 9 times as much work done by the pavement on the car.

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Version 026 – TEST01 – tsoi – (92940) 2 003 10.0points Take the mass of the Earth to be 5 . 98 × 10 24 kg. If the Earth’s gravitational force causes a falling 68 kg student to accelerate downward at 9 . 8 m / s 2 , determine the upward accelera- tion of the Earth during the student’s fall. 1. 1.50769e-22 2. 3.93311e-23 3. 8.19398e-23 4. 1.24548e-22 5. 9.01338e-23 6. 5.73579e-23 7. 6.71906e-23 8. 1.27826e-22 9. 9.17726e-23 10. 1.11438e-22 Correct answer: 1 . 11438 × 10 22 m / s 2 . Explanation: By Newton’s third law, the force F se ex- erted on the student by the earth is equal in magnitude and opposite in direction to the force F es exerted on the earth by the student.
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