HW 03-solutions

# HW 03-solutions - cooper(mlc4285 HW 03 florin(55245 This...

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cooper (mlc4285) – HW 03 – florin – (55245) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001(part1of3)10.0points A spring has a stiffness of k = 531 . 9 N / m. Find the magnitude of the vector spring force exerted by the spring when the spring is a) stretched 0 . 0451 m from equilibrium. Correct answer: 23 . 9887 N. Explanation: BasicConcept: F spring = k * s Given: k = 531 . 9 N / m s 1 = 0 . 0451 m Solution: F spring = k * s 1 = 531 . 9 N / m * 0 . 0451 m = 23 . 9887 N 002(part2of3)10.0points b) compressed 0 . 0281 m from equilibrium. Correct answer: 14 . 9464 N. Explanation: Given: k = 531 . 9 N / m s 1 = 0 . 0281 m Solution: F spring = k * s 2 = 531 . 9 N / m * 0 . 0281 m = 14 . 9464 N 003(part3of3)10.0points c) unstretched. Correct answer: 0 N. Explanation: Given: k = 531 . 9 N / m s 3 = 0 m Solution: F spring = k * s 3 = 531 . 9 N / m * 0 m = 0 N 004 10.0points The stiffness of a particular spring is 42 N / m. One end of the spring is attached to a wall. A force of 2 N is required to hold the spring elongated a total length 16 cm. What was the relaxed length of the spring? Correct answer: 0 . 112381 m. Explanation: The spring force is given by vextendsingle vextendsingle vextendsingle vector F spring vextendsingle vextendsingle vextendsingle = k s | L - L 0 | , where k s is the stiffness, L is the stretched or compressed length, and L 0 is the relaxed length of the spring. Since the spring is elon- gated, which implies that L > L 0 , we have L - L 0 > 0 , which means | L - L 0 | = L - L 0 . Thus we have vextendsingle vextendsingle vextendsingle vector F spring vextendsingle vextendsingle vextendsingle = k s ( L - L 0 ) , or L 0 = L - vextendsingle vextendsingle vextendsingle vector F spring vextendsingle vextendsingle vextendsingle k s = 0 . 16 m - 2 N 42 N / m = 0 . 112381 m .

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cooper (mlc4285) – HW 03 – florin – (55245) 2 005 10.0points A spring of relaxed length of 20 cm is first extended to 24 cm. The spring is then com- pressed to a length of 12 cm. It is then extended again to 32 cm. If the forces ex- erted by the spring are given by vector F 1 , vector F 2 and vector F 3 , which of the following relations is true? 1. vector F 1 = - 2 vector F 2 = 3 vector F 3 2. 3 vector F 1 = ( - 3 / 2) vector F 2 = vector F 3 correct 3. vector F 1 = vector F 2 = vector F 3 4. vector F 1 = 2 vector F 2 = ( - 2 / 3) vector F 3 5. 3 vector F 1 = (3 / 2) vector F 2 = vector F 3 6. vector F 1 = - vector F 2 = vector F 3 7. vector F 1 = 2 vector F 2 = (2 / 3) vector F 3 8. vector F 1 = 2 vector F 2 = 3 vector F 3 Explanation: Let : L 0 = 20 cm , L 1 = 24 cm , L 2 = 12 cm , and L 3 = 32 cm .
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