Question

Moment of a Force: Vector Formulation 6 of 6 Mz, My, M175,-138,226 N-m Learning Goal evious Ans To understand the concept of moment of a force and how to calculate it using a vector formulation A man wishes to spin a merry-go-round in the x-y plane centered at the origin (0.000, 0.000,0.000). (Figure 1) Because he must pull upward and cannot stand on the merry-go-round, he must apply a force in the direction of the unit vector u (-13)it (2/3jj + (2/3)k. He pulls with a force F 188 N from point A (1.10,1.40,0.000) m] All attempts used; correct answer displayed free to rotate about the z axis, a moment about the x or y Because a merry-go-round is axis is easily overlooked. Just because a body is not free to rotate in a direction does not mean that a moment's component does not exist in that direction. For example, a moment about the x or y axis on a poorly designed merry-go-round can cause the merry-go-round to wobble up and down Part B Figure 1 of 1 Find M, the magnitude of the moment, and θ, the angle between r and the force F Express your answers in Newton-meters and degrees to three significant figures separated by a commia View Available Hint(s) vec M 32,70.5 M.θ N·m,degrees SubmitPrev evious Answers Request Answer

Answer 1

Mo - VOA F = [ 1.100 + 1.40 ] + o ook] x 188 [(-/ ) " + 2 } + 2 ] Moſ 1.10 1.40 0.00 -188 1-188 188 +2 188x2 188 * 2 188x2 Mo = 175.4667 ? - 137.8667 J+ 225.65 with three signficant figures My Mo = 175 - 138 g + 226² Nom Mx - My My Magnitude of the moment, M. M = √(175)2 + (-138) 2 + (226)2 3 And 317.4 - 1314 Nm

CROSS PRODUCT 1 x FI - Irl(Fl sino 8 = [top] = lli + 1.4 i .: 171 = √(1.12 + 11.4) 2. 181= 1.78 m IFI = 188 N 1rxF1 = M = 317 N.m 317 = (1.78) (188) sino sino = 0.947 = 317 (1.78 × 188) Ans. M = 314 Nm o = sin- (0.947) To = 71.3 degrees 10 = 71-3 Degrees