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oldhw30 - oldhomework 30 Turner(58185 This print-out should...

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This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A 6 kg watermelon is placed at one end of a 4 . 7 m, 272 N scaffolding supported by two ca- bles. One supporting cable is at the opposite end of the scaffolding, and the other is 0 . 81 m from the watermelon. How much tension is in the cable at the end of the scaffolding? The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 95 . 4375 N. Explanation: Rotational and Translational Equilibrium summationdisplay τ = summationdisplay τ cw - summationdisplay τ ccw = 0 Let the fulcrum be at the point of attach- ment of the cable closest to the watermelon. mg W T 1 The watermelon mg acts down (ccw) at a distance x from the fulcrum. The weight W acts down (cw) at a distance 2 - x from the fulcrum, and the rightmost tension T 1 acts up (ccw) at a distance - x from the fulcrum. Thus W parenleftbigg 2 - x parenrightbigg - m g x - T 1 ( - x ) = 0 . Multiplying by 2, W ( - 2 x ) - 2 m g x = 2 T 1 ( - x ) , T 1 = W ( - 2 x ) - 2 m g x 2 ( - x ) = (272 N) [4 . 7 m - 2 (0 . 81 m)] 2 (4 . 7 m - 0 . 81 m) - 2 (6 kg) (9 . 8 m / s 2 ) (0 . 81 m) 2 (4 . 7 m - 0 . 81 m) = 95 . 4375 N . 002 (part 2 of 2) 10.0 points How much tension is in the cable closest to the watermelon? Correct answer: 235 . 362 N. Explanation: Let the fulcrum be at the point of attach- ment of the rightmost cable. mg W T 2 The watermelon m g acts down (ccw) at a distance from the fulcrum. The weight W acts down (ccw) at a distance 2 from the fulcrum, and the tension T 2 acts up (cw) at a distance - x from the fulcrum. Thus T 2 ( - x ) - m g ℓ - W parenleftbigg 2 parenrightbigg = 0 .
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