Figure P6.57 shows a photo of a swing ride at an amusement park. The structure c

Question

Figure P6.57 shows a photo of a swing ride at an amusement park. The structure consists of a horizontal, rotating, circular platform of diameter D from which seats of mass m are suspended at the end of massless chains of length d. When the system rotates at constant speed, the chains swing outward and make an angle (theta) with the vertical. Consider such a ride with the following parameters: D = 8.00 m, d = 2.50m, m = 10.0 kg, and theta = 28.0 degrees.

a.) What is the speed of each seat?
b.)Draw a diagram acting on a 40.0 kg child riding in a seat and
c.) find the tension in the chain

Explanation / Answer

You need to write equations for the net horizontal force (centripetal force) and the net vertical forces acting on the seat. The only force acting horizontally here is the horizontal component of tension in the chain. Since we measure the angle from the vertical, the horizontal component of tension is Tsin?. From Newton’s 2nd law, the net centripetal forces are: ?F = ma(c) = Tsin?--------------->(1) The forces acting on the seat vertically are the upward component of tension in the chain, Tcos?, and the downward weight of the seat, mg. The equation is: ?F = 0 = Tcos? - mg mg = Tcos?--------------------->(2) You may recall that sin? / cos? = tan?, this suggests dividing (1) by (2): ma(c) / mg = Tsin? / Tcos? a(c) / g = tan? But centripetal acceleration, a(c), is equal to v² / r, (remember that diameter is given so the radius is half that) so:

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