Problem 3: (33 points) The cantilever of a chair swing as depicted in the picture has an angle of 0 = 30° and a total le

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Problem 3 33 Points The Cantilever Of A Chair Swing As Depicted In The Picture Has An Angle Of 0 30 And A Total Le 1 (106.28 KiB) Viewed 75 times

Problem 3: (33 points) The cantilever of a chair swing as depicted in the picture has an angle of 0 = 30° and a total length OT of L = 5m and is attached to the mast of the ride in point 0. The passenger seat is connected to the free end of the cantilever with a chain of the length 1 = lm. The mast of the ride is propelled with a constant angular velocity ♡ by a motor. The passenger seat is rotating with a constant radius. Consider all parts of the carousel ride to be massless. Furthermore, the carousel has a computer controlled adjustable rope system (CCARS), which allows for a variation of e. Uz 9 CCARS T mp (a) Draw a free body diagram of the passenger seat. (b) Calculate the angular velocity of the carousel so that for an idealized passenger of mp = 75kg the seat has a constant angle of a = 40° in regard to the rotational axis of the carousel. (c) Calculate the tension force in the chain for this passenger. (d) Calculate the velocity of the passenger. The carousel has a mechanism of retracting and extending the cantilever during operation. No other external force or moment is applied to the system during retraction and extension, (e) Calculate the maximal allowed extension of the cantilever for a maximal allowed increase of the inclination angle of the passenger seat of 30%. (f) Does the tension in the chain increase or decrease for an increasing inclination angle of the cantilever? Justify mathematically.