midterm 2 - Version 106/ABCCC midterm 02 turner (57340) 1...

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Unformatted text preview: Version 106/ABCCC midterm 02 turner (57340) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A car of mass 1500 kg is moving over a rounded hill of radius 100 m with a constant speed of 13 m / s. At the topmost point on the hill, what is the magnitude of the normal force exerted by the road on the car? Take g to be 9 . 8 m / s 2 . 1. 7440.0 2. 2940.0 3. 12885.0 4. 13740.0 5. 14160.0 6. 5325.0 7. 6060.0 8. 2085.0 9. 12165.0 10. 6765.0 Correct answer: 12165 N. Explanation: Given : M = 1500 kg , R = 100 m , v = 13 m / s , and g = 9 . 8 m / s 2 . Let F be the magnitude of the normal force exerted by the road on the car. Applying momentum principle at the top of the hill in the vertical direction (y-component)-- Mv 2 R = F- Mg F = Mg- Mv 2 R F = 1500 kg * parenleftbigg 9 . 8 m / s 2- (13 m / s) 2 100 m parenrightbigg F = 12165 N 002 10.0 points A circular pendulum of length l = 1 . 2 m goes around at an angle of = 36 to a line drawn perpendicular to the ground. Deter- mine the speed of the mass at the end of the string. 1. 1.74148 2. 1.94193 3. 2.62135 4. 1.45754 5. 1.84402 6. 1.76623 7. 1.65986 8. 1.40724 9. 2.24101 10. 2.05973 Correct answer: 2 . 24101 m / s. Explanation: The equations of motion in the x and y directions are given by: summationdisplay vector F x = T sin = mv 2 l sin summationdisplay vector F y = T cos - mg = 0 , where T is the tension along the string. Di- viding the first equation by the second (to eliminate the unknown T ) yields tan = v 2 gl sin . Solving this for v yields v = radicalBigg gl sin 2 cos = 2 . 24101 m / s . Version 106/ABCCC midterm 02 turner (57340) 2 003 10.0 points Two wires with equal length are made out of pure copper. The diameter of wire 1 is twice the diameter of wire 2. When the wire 1 is hung with a weight which is half of that hung on wire 2, find the ratio of the stretches L 1 L 2 . 1. 8 2. 2 3. 1 4. 4 5. 16 6. 1 16 7. 1 2 8. 1 8 correct 9. 1 4 Explanation: Youngs modulus is defined as Y = F A L L .Since both wires are made out of the same materials, their Youngs moduli should be the same. Thus for equal length wires F 1 A 1 L 1 L 1 = F 2 A 2 L 2 L 2 L 1 L 2 = F 1 A 1 F 2 A 2 = F 1 A 2 F 2 A 1 = F 1 ( d 2 2 ) F 2 ( d 2 1 ) = F 1 F 2 parenleftbigg d 2 d 1 parenrightbigg 2 = F 1 2 F 1 parenleftbigg d 2 2 d 2 parenrightbigg 2 = 1 8 . 004 10.0 points A scientific probe of mass 420 kg is orbiting the asteroid Eros in a circular orbit of radius 44 . 2 km and period 1 . 06 days. Calculate the mass of Eros. ( G = 6 . 7 10 11 N m 2 /kg 2 ) 1. 5.18654e+15 2. 5.81505e+15 3. 5.50635e+15 4. 6.36369e+15 5. 7.53009e+15 6. 6.53041e+15 7. 7.06e+15 8. 7.43518e+15 9. 7.67541e+15 10. 6.06614e+15 Correct answer: 6 . 06614 10 15 kg....
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midterm 2 - Version 106/ABCCC midterm 02 turner (57340) 1...

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