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qz9sol_3706Hs11 - stars We label them star 1 2 and 3 Star 1...

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TA: Tomoyuki Nakayama Tuesday, April 5, 2011 PHY 2048: Physic 1, Discussion Section 3706H Quiz 9 (Homework Set #11) Name: UFID: Formula sheets are not allowed. Do not store equations in your calculator. You have to solve problems on your own; memorizing final algebraic expressions from homework assignments and just plugging numbers into them will not give you full credit. Leave all your work. ________________________________________________________________________________ Three identical stars of mass M = 8.00 × 10 30 kg form an equilateral triangle that rotates around the triangle's center as the stars move in a common circle about that center. The triangle has edge length L = 3.00 × 10 10 m. a) What is the speed of the stars? By symmetry, all stars have the same speed. Thus it is enough to consider the motion of one of the
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Unformatted text preview: stars. We label them star 1, 2 and 3. Star 1 rotates in a circle. Therefore, it accelerates toward the center with magnitude v 2 /R, where R is the radius of the circular orbit. The radius of the circle and the edge length of the triangle are related as Rcos θ = L/2 ⇒ R = L/(2cos ), where = 30 º . The centripetal acceleration is provided by two gravitational forces from other 2 stars. The two forces have the same magnitude and each makes an angle = 30 to the radial direction. Newton’s 2 nd law yields M(v 2 /R) = F 1 M(v 2 /(L/(2cos θ ))) = F 12 cos θ + F 13 cos θ = 2(Gm 2 /L 2 )cos θ v = √ (Gm/L) = 1.334 × 10 5 m/s b) What is the period of the circular motion of the stars? The period of the circular motion is T = 2 π R/v = 2 π (L/(2cos θ ))/v = 8.16 × 10 5 s...
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