27 - hernandez (ejh742) oldhomework 27 Turner (58120) 1...

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Unformatted text preview: hernandez (ejh742) oldhomework 27 Turner (58120) 1 This print-out should have 14 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 4 . 9 kg watermelon is placed at one end of a 7 . 2 m, 200 N scaffolding supported by two cables. One supporting cable is at the opposite end of the scaffolding, and the other is 1 . 1 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: 73 . 3079 N. Explanation: Let : m = 4 . 9 kg W = 200 N , = 7 . 2 m , x = 1 . 1 m , and g = 9 . 8 m / s 2 . 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 (CCW) 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 summationdisplay = summationdisplay CW- summationdisplay CCW = 0 W parenleftbigg 2- x parenrightbigg- mg x- T 1 ( - x ) = 0 W ( - 2 x )- 2 mg x = 2 T 1 ( - x ) T 1 = W ( - 2 x )- 2 mg x 2 ( - x ) = (200 N) [7 . 2 m- 2 (1 . 1 m)] 2 (7 . 2 m- 1 . 1 m)- 2 (4 . 9 kg) (9 . 8 m / s 2 ) (1 . 1 m) 2 (7 . 2 m- 1 . 1 m) = 73 . 3079 N . 002 (part 2 of 2) 10.0 points How much tension is in the cable closest to the watermelon? Correct answer: 174 . 712 N. Explanation: Let the fulcrum be at the point of attach- ment of the rightmost cable. mg W T 2 The watermelon mg 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 (CCW) at a distance - x from the fulcrum. Thus T 2 ( - x )- mg -W parenleftbigg 2 parenrightbigg = 0 . Multiplying by 2, 2 T 2 ( - x ) = 2 mg + W T 2 = 2 mg + W 2 ( - x ) = 2 (4 . 9 kg) (9 . 8 m / s 2 ) (7 . 2 m) 2 (7 . 2 m- 1 . 1 m) + (200 N) (7 . 2 m) 2 (7 . 2 m- 1 . 1 m) = 174 . 712 N . hernandez (ejh742) oldhomework 27 Turner (58120) 2 003...
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This note was uploaded on 06/14/2011 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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27 - hernandez (ejh742) oldhomework 27 Turner (58120) 1...

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