Three children an standing on a 5 X 5-m raft. If the weights of the diiklren at

Question

Three children an standing on a 5 X 5-m raft. If the weights of the diiklren at points A, B. and C arc 375 N. 260 N. and 400 N respectively, determine the magnitude and the point of application of the resultant of tin* three weights. Three children are standing on a 5 X 5-m raft. The weights of the children at points A. H. ami C an 375 N. 260 N. and 4(H) N respectively. If a fourth child of weight 425 N climbs onto the raft, determine where sIh* should stand if the other children remain in the positions shown and the line of action of the resultant of the four weights is to pass through tin* center of the raft.

Explanation / Answer

force equation

Total force = Fa + Fb + Fc + Fd = R

R = -375 j - 260 j - 400 j - 425 j

R = -1460 j N

total momentum in +z direction

Total Mz = Fa*za + Fb*zb + Fc*zc + Fd*zd = R*z

1460*2.5 = 375*3 + 260*0.5 + 400*4.75 + 425*zd

Solving above equation

zd = 1.164 m

total momentum in +x direction

Total Mx = Fa*xa + Fb*xb + Fc*xc + Fd*xd = R*x

1460*2.5 = 375*1 + 260*1.5 + 400*4.75 + 425*zd

Solving above equation

xd = 2.323 m

So the fourth child should stand at

(xd, zd) = (2.323 m, 1.164 m)

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