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Science · Advanced Physics
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Why do we need to set Xcg=Xs?

Example 11.1 Walking the plank of gravity m and mass M -90kg rests s D/2. Well use Eqs. (11.3) to locate the center st on sawhorses separated by D 1.5m and equidistant from the of the center of the plank. Cousin Throckmorton wants to stand on the EXECUTE: From the in right-hand end of the plank. If the plank is to remain at rest, how massive can Throckmorton be? the first of Eqs. (11.3), M(O) +m(L/2)L M m 2 M+ m SOLUTION We set acg xs and solve for m IDENTIFY and SET UP: To just balance, Throckmortons mass m must be such that the center of gravity of the plank-Throcky sys- tem is directly over the right-hand sawhorse (Fig. 11.6). We take the origin at C, the geometric center and center of gravity of the plank, and take the positive x-axis horizontally to the right. Then the centers of gravity of the plank and Throcky are at xp 0 and T L/2- 3.0 m, respectively, and the right-hand sawhorse is at D(90 kg) 6.0 m 1.5 m 15 m m M EVALUATE: As a check, lets repeat the calculation with the congs at the right-hand sawhorse. Now xs* 0, Xp =-D/2, and 1.6 Our sketch for this problem. (L/2)-(D/2), and we require xcg = xs = 0: L-6.0m D= 1.5m 느- X cg M+ m m L/2)- (0/2-D3 kg M-90ka cge The result doesnt depend on our choice of origin. A 60-kg adult could stand only halfway between the righte- sawhorse and the end of the plank. Can you see why?
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