A uniform aluminum beam 9.00 m long, weighing303N, rests symmetrically on two su

Question

A uniform aluminum beam 9.00 m long, weighing303N, rests symmetrically on two supports5.35m apart (see figure). A boy weighing642N starts at pointAand walks toward the right.

(a) In the same diagram construct two graphs showing the upward forcesFAandFBexerted on the beam at pointsAandBas functions of the coordinatexof the boy. Let 1 cm = 100 N vertically, and let 1 cm = 1.00 m horizontally. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) From your diagram, how far beyond pointBcan the boy walk before the beam tips?

(c) How far from the right end of the beam should supportBbe placed so that the boy can walk just to the end of the beam without causing it to tip?

Explanation / Answer

L = 9.00 m, weight w = 303 N, a = 5.35 m, weight W' = 642 N,

b) just before the beam tips, FA = 0, net torque about B = w'*x - w*(a/2) = 0

x = wa/(2w') = 1.26 m

c) net torque about B = w'*x - w*(L/2 - x) = 0

x = Lw/[2(w + w')] = 1.44 m

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