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Unformatted text preview: 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 ℓ 2- x from the fulcrum, and the rightmost tension T 1 acts up (ccw) at a distance ℓ- x from the fulcrum. Thus W parenleftbigg ℓ 2- x parenrightbigg- mg x- T 1 ( ℓ- x ) = 0 . Multiplying by 2, W ( ℓ- 2 x )- 2 mg x = 2 T 1 ( ℓ- x ) , T 1 = W ( ℓ- 2 x )- 2 mg x 2 ( ℓ- x ) = (272 N) [4 . 7 m- 2 (0 . 81 m)] 2 (4 . 7 m- . 81 m)- 2 (6 kg) (9 . 8 m / s 2 ) (0 . 81 m) 2 (4 . 7 m- . 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 mg acts down (ccw) at a distance ℓ from the fulcrum. The weight W acts down (ccw) at a distance ℓ 2 from the fulcrum, and the tension T 2 acts up (cw) at a distance ℓ- x from the fulcrum. Thus T 2 ( ℓ- x )- mg ℓ- W parenleftbigg ℓ 2 parenrightbigg = 0 ....
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This note was uploaded on 05/02/2009 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.
- Spring '08