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Unformatted text preview: Answer, Key Homework 6 David McIntyre 45123 Mar 25, 2004 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page find all choices before making your selection. The due time is Central time. Chapters 5 and 6 problems. 001 (part 1 of 2) 5 points An amusement park ride consists of a rotating circular platform 11 . 4 m in diameter from which 10 kg seats are suspended at the end of 1 . 18 m massless chains. When the system rotates, the chains make an angle of 43 . 7 with the vertical. The acceleration of gravity is 9 . 8 m / s 2 . l d What is the speed of each seat? Correct answer: 7 . 81126 m / s. Explanation: In the vertical direction we have T cos = mg , where T is the tension in the chain. In the horizontal direction we have T sin = mv 2 r . Since r = sin + d 2 = (1 . 18 m)sin43 . 7 + 11 . 4 m 2 = 6 . 51524 m , we have v = p g r tan = q (9 . 8 m / s 2 )(6 . 51524 m)tan43 . 7 = 7 . 81126 m / s . 002 (part 2 of 2) 5 points If a child of mass 62 . 5 kg sits in a seat, what is the tension in the chain (for the same angle)? Correct answer: 982 . 756 N. Explanation: M = 62 . 5 kg From the first part we have T cos = ( m + M ) g T = ( m + M ) g cos = (10 kg + 62 . 5 kg)(9 . 8 m / s 2 ) cos43 . 7 = 982 . 756 N . 003 (part 1 of 1) 0 points A figure of a dancer on a music box moves counterclockwise at constant speed around the path shown below. The path is such that the lengths of its segments, PQ , QR , RS , and SP , are equal. Arcs QR and SP are semicircles. S R P Q Which of the following best represents the magnitude of the dancers acceleration as a function of time t during one trip around the path, beginning at point P ? 1. t P O a t Q t t R t S t P 2. t P O a t Q t t R t S t P 3. t P O a t Q t t R t S t P Answer, Key Homework 6 David McIntyre 45123 Mar 25, 2004 2 4. t P O a t Q t t R t S t P 5. t P O a t Q t t R t S t P correct Explanation: During RS and PQ , the acceleration is zero becausethevelocityisaconstantbothinmag- nitude and in direction. During QR and SP , even though the magnitude of the velocity is a constant, it changes its direction, which will result in an acceleration of v 2 r , where v is the velocity and r is the radius of the arc. So the acceleration is fixed at a non-zero constant during SP and QR . 004 (part 1 of 2) 0 points An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away (see figure). The coefficient of static friction between the person and the wall is and the radius of the cylinder is R ....
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