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min (mm64262) – Homework 1 – lee – (GEDB00864) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points A flat circular plate of copper has a radius of 0 . 277 m and a mass of 45 . 8 kg. What is the thickness of the plate? Correct answer: 0 . 0212767 m. Explanation: Let : m = 45 . 8 kg and r = 0 . 277 m . The density of copper is ρ = 8 . 93 × 10 3 kg / m 3 . ρ = m V , for a flat circular plate, so V = π r 2 h = m ρ h = m ρ ( π r 2 ) = 45 . 8 kg (8930 kg / m 3 ) π (0 . 277 m) 2 = 0 . 0212767 m . 002 10.0points An electron, starting from rest and moving with a constant acceleration, travels 5 . 3 cm in 8 . 3 ms. What is the magnitude of this acceleration? Correct answer: 1 . 53868 km / s 2 . Explanation: Let : d = 5 . 3 cm = 5 . 3 × 10 5 m and t = 8 . 3 ms = 0 . 0083 s . Starting from rest with constant acceleration, the distance is d = 1 2 a t 2 a = 2 d t 2 = 2 (5 . 3 × 10 5 m) (0 . 0083 s) 2 1 km 1000 m = 1 . 53868 km / s 2 . 003(part1of2)10.0points The rectangular and polar coordinates of a point are ( x, y ) and ( r, θ ), where x = 4 and θ = 33 . Determine the value of r . Correct answer: 4 . 76945. Explanation: x = r cos θ r = x cos θ = 4 cos 33 = 4 . 76945 . 004(part2of2)10.0points Determine the value of y . Correct answer: 2 . 59763. Explanation: y = r sin θ = (4 . 76945) sin 33 = 2 . 59763 . 005(part1of2)10.0points A skier squats low and races down a 16 ski slope. During a 4 s interval, the skier accelerates at 2 . 7 m / s 2 . What is the horizontal component of the skier’s acceleration (perpendicular to the di- rection of free fall)? Correct answer: 2 . 59541 m / s 2 . Explanation: Let : θ = - 16 and a = 2 . 7 m / s 2 . a y a x a θ
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min (mm64262) – Homework 1 – lee – (GEDB00864) 2 a x = a cos θ = (2 . 7 m / s 2 ) cos( - 16 ) = 2 . 59541 m / s 2 . 006(part2of2)10.0points What is the vertical component of the skier’s acceleration? Correct answer: - 0 . 744221 m / s 2 . Explanation: a y = a sin θ = (2 . 7 m / s 2 ) sin( - 16 ) = - 0 . 744221 m / s 2 . 007(part1of2)10.0points Use linear combinations to solve the system braceleftbigg - 6 x + 5 y = - 8 4 x + 4 y = 64 Find the value of y . (Answer with - 100 if there is no solution.) Correct answer: 8. Explanation: braceleftbigg - 6 x + 5 y = - 8(1) 4 x + 4 y = 64 (2) Multiply eq(1) by 4 and eq(2) by 6, then add: - 24 x + 20 y = - 32 (1) 24 x + 24 y = 384 (2) 44 y = 352 44 y 44 = 352 44 y = 8 .
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