# hw9 - Overton Mays – Homework 9 – Due 4:00 am – Inst...

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Unformatted text preview: Overton, Mays – Homework 9 – Due: Feb 11 2005, 4:00 am – Inst: Turner 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 2) 10 points In a stage production of Peter Pan, the 51 kg actress playing Peter has to fly in vertically, and to be in time with the music, she must be lowered, starting from rest, a distance of 4 . 3 m in 2 . 4 s. Backstage, a smooth surface sloped at 48 ◦ supports a counterweight of mass m , as shown in figure below. The acceleration of gravity is 9 . 81 m / s 2 . 51 kg m μ = a 48 ◦ What is the mass of the counterweight that must be used? The pulley is of negligible mass and is fricionless. Correct answer: 48 . 2921 kg. Explanation: Let : m p = 51 kg , θ = 48 ◦ , h = 4 . 3 m , t = 2 . 4 s , μ = 0 , and W counterweight = m 2 g W Peter = m p g = (51 kg)(9 . 81 m / s 2 ) = 500 . 31 N . Applying the kinematics equation, y = y o + v o t- 1 2 at 2 0 = h- 1 2 at 2 a = 2 h t 2 = 2(4 . 3 m) (2 . 4 s) 2 = 1 . 49306 m / s 2 . W k N W ⊥ m 2 a W k θ Applying X F x = ma x to each mass, T- mg sin θ = ma. (1) m p g- T = m p a. (2) Adding the equations, mg- m p g sin θ = ( m p + m ) a m ( g- a ) = m p ( a + g sin θ ) m = m p ( g- a ) a + g sin θ = (51 kg) h (9 . 81 m / s 2 )- (1 . 49306 m / s 2 ) i (1 . 49306 m / s 2 ) + (9 . 81 m / s 2 )sin48 ◦ = 67 . 9905 kg . 002 (part 2 of 2) 10 points What is the tension in the wire? Correct answer: 424 . 164 s. Explanation: Overton, Mays – Homework 9 – Due: Feb 11 2005, 4:00 am – Inst: Turner 2 Using equation (1), T = m ( a + g sin θ ) = (67 . 9905 kg) h (1 . 49306 m / s 2 ) +(9 . 81 m / s 2 )sin48 ◦ i = 424 . 164 N . Note: The weight of Peter ( w p = 500 . 31 N) is slightly greater than the tension in the wire. 003 (part 1 of 2) 10 points Consider the 693 N weight held by two cables shown below. The left-hand cable had tension 600 N and makes an angle of θ with the wall....
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## This note was uploaded on 03/22/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.

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hw9 - Overton Mays – Homework 9 – Due 4:00 am – Inst...

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