Physics. Force & Torsion. Please Answer Metiulously With Detailed & Complete Sol
ID: 1308904 • Letter: P
Question
Physics. Force & Torsion. Please Answer Metiulously With Detailed & Complete Solution
Celebrity rotary tug-of-war A charity decidas to televise an athletic competition between two teams of celebrities. One team consists of three female movie to stats (who nil completed Physics 7A). mass density on "tug-of-war," Ench team pushen on a rotating bar of uniform mass density, length 8L, and mass M that is tree to rotate horizontally about a frietionless hinge at its center, as shown from above in the diagram. The goal of each team is to rotate the bar by one quarter of a lull rotation (90degree) men can individually push with force F. whereas each of the three women cun may assume that every contestant pushes with a constant magnitude i force that is al - ay s perpendicular to the bar, and you can assume that the thicknesses of (lie bar and the hinge are both negligible. 1: the men spread themselves out so one is a distance / from the end ol the bur, one is 21, from the end, and one is 3L from the end. what is the magnitude of the combined torque all three men exert together on the bar? Take the center of the bar as the pivot point. If the women all push on the very end of their side of the bur, what is the net torque on the bar due to all forces acting on it including all six of the contestants? State whether this is clockwise or counterclockwise as viewed in the diagram. Immediately after all six of the contestants begin pushing on the bar, what is the direction and magnitude of the force from the hinge on the bar ? Given that the bar starts from rest, how long does it take for the bar to rotate by 90degree, one way or the other? Durum the time the bar rotates through 90degree, how much work is performed on the bar by the man closest to the middle of the bar?Explanation / Answer
Men torque: F*L + F*2L + F*3l = 6FL
Women torque: 2F/3 * 3 * 4L = 8FL
Net force: (2F/3+F)*3 => hinge reaction = 5F against backwards (against the contestant's force)
Net torque = 2FL anticlockwise (girls are winning)
Moment of inertia of bar = M*64L^2 / 12 = 16ML^2 /3
Angular acceleration = Torque/Moment of Inertia => alpha = 3F/8ML
Time = (2*theta/alpha)^1/2 = (8MLpi/3F)^1/2
Work done by man closest to hinge = -FLpi/2