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A train traveling at a constant speed rounds a curve of radius 250 m. A chandelier suspended from the ceiling swings out to an angle of 15.5° throughout the turn. What is the speed of the train?

what equation should i use?

  • physics -

    You need to think it through and solve two equations. The fixture or chain that holds the chandelier exerts a tension force T upon it that is inclined 15.5 degrees to the vertical. The vertical component supports the weight, M g, and the horizontal component provides the centripetal force, M V^2/R . Thus

    T cos15.5 = M g, and
    T sin15.5 = M V^2/R

    You can divide the last equation by the first to eliminate T and M

    tan15.5 = V^2/(gR) = 0.2173

    Solve for V, in m/s

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