A mechanic uses a crowfoot wrench to loosen a bolt at C. The mechanic holds the

Question

A mechanic uses a crowfoot wrench to loosen a bolt at C. The mechanic holds the socket wrench handle at points A and B and applies forces at these points. Knowing that these forces are equivalent to a force-couple system at C consisting of the force C = - (8 lb)i + (4 lb)k and the couple Mc = (360 lb in.)i, determine the forces applied at A and at B when Az = 2 lb. Fig. P3.122

Explanation / Answer

Ax+Bx = -8------(1) Ay+By = 0=>Ay= -By-----------(2) Az+Bz = 4 and given that Az = 2=>Bz = 2lb and M = rA x FA+rB x FB M = (8i+8k) x (Ax i+Ay j+ Az k) + (8i-2k) x (Bx i+By j+ Bz k) 360 i = 8Ay k-8Azj+8Axj-8Ayi + 8By k-8Bzj-2Bx j+2Byi equating coefficients of i,j and k terms on both sides =>360 = -8Ay+2By from (2) 360= 8By+2By By = 36 lb and Ay = -36lb 0 = -8Az+8Ax-8Bz-2Bx =>0 = -8*2+8Ax-8*2-2*Bx 8Ax-2Bx = 32----------(3) from (1) and (3) Ax = 1.6 lb Bx = -9.6 lb So, FA =[Ax2+Ay2+Az2] FA=[1.62+362+22] FA=36.1 lb FB =[Bx2+By2+Bz2] FB=[9.62+362+22] FB= 37.3 lb (check for calculations)

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