45. (a) The links are numbered from bottom to top. The forces on the bottom link are the force of gravity mgG, downward, and the force GF21onof link 2, upward. Take the positive direction to be upward. Then Newton’s second law for this link is F2on1– mg= ma. Thus, F2on1= m(a+ g) = (0.100 kg) (2.50 m/s2+ 9.80 m/s2) = 1.23 N. (b) The forces on the second link are the force of gravity mgG, downward, the force GF12onof link 1, downward, and the force GF32onof link 3, upward. According to Newton’s third law 1on2FGhas the same magnitude as GFon. Newton’s second law for the second link is F3on2– F1on2– mg= ma, soF3on2= m(a+ g) + F1on2= (0.100 kg) (2.50 m/s2+ 9.80 m/s2) + 1.23 N = 2.46 N. (c) Newton’s second for link 3 is F4on3– F2on3– mg= ma, soF4on3= m(a+ g) + F2on3= (0.100 N) (2.50 m/s
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