Homework 4−SolutionCHANG1 The motion of the man is 1-D vertical motion downward. Since the platformalso travels downward along with the man, they move as one unit and we can take the man andthe platform together as the free body. Let the total mass for the man and the platform beM8020100 Kg, and the FBD is shown here:MgTTT+yaNote that the positivey−axis is downward, same as the direction of the acceleration. ApplyNewton’s 2nd law:FymayMg−3TMaTMg−a31009.8−.23320 NFrom Newton’s 3rd law the force exerted by the man equals the tension in the cable, soFT320 N.CHANG2 Since the marble settles at the same elevation on the inclined surface and ridesalong with the spinning cone, its motion is a horizontal uniform circular motion. The FBD ofthe marble is shown here:w=mgNanynSet upn−ycoordinate system withnaxis pointing to the left toward the center of thecircular motion. Apply Newton’s 2nd law along bothyandnaxes, withay0 (motion ishorizontal) and radiusRLcosfrom geometry:FymayNcos−mg0NmgcosFnmanNsinm42LcosT2LgT2sin42cos29.81.52sin30∘42cos230∘0.372 mY&F5.52 The motion of the rider on the giant swing is a horizontal uniform circularmotion, and the FBD of the rider (and the seat) is shown here:
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