The “Giant Swing” at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a cable 5.00 m long, and the upper end of the cable is fastened to the arm at a point 3.00 m from the central shaft (?Fig. E5.50?). (a) Find the time of one revolution of the swing if the cable supporting a seat makes an angle of 30.0o with the vertical. (b) Does the angle depend on the weight of the passenger for a given rate of revolution?

Solution to 46E Step 1 Length of the supporting shaft=3m Length of the arm holding the passenger=5m 0 Angle the arm makes with vertical =30 Step 2 Freebody diagram, Total radius of the swing=(3+5sin30)=5.5m Centripetal force Fc=Tsin ………………………………(T=tension in the arm) We know that , Fc=(mv )/r 2 (mv )/r=Tsin …………………………………………………………….(1) mg=Tcos ………………………………………………………………..(2) Dividing (1) by (2) 2 tan = (v )/rg …………………………………………………………….(3) v = r g tan v=5.57m/s