Two small objects each of mass m = 0.2 kg are connected by a lightweight rod of

Question

Two small objects each of mass m = 0.2 kg are connected by a lightweight rod of length d = 1.4 m (see the figure). At a particular instant they have velocities whose magnitudes are v1 = 25 m/s and v2 = 59 m/s and are subjected to external forces whose magnitudes are F1 = 51 N and F2 = 25 N. The distance h = 0.2 m, and the distance w = 0.6 m. The system is moving in outer space v1 z (out of page) I- (a) What is the total (linear) momentum P total of this system? P total- -kgA-m/s (b) What is the velocity cm of the center of mass? vcm = | m/s (c) What is the total angular momentum LA of the system relative to point A? LA = kgÂ-m2/s (d) What is the rotational angular momentum Irot of the system? kgÂ-m2/s rot (e) What is the translational angular momentum Ltrans of the system relative to point A? Itrans kgA-m2/s

Explanation / Answer

c. angular momentum= mvr= 0.2 x25x1.4 = 7

d. total angular momentum = 0.2 x 25 x 0.7 - 0.2 x 59X0.7 = 4.76

e. translational angular momentum= Iw= mR^2 x (v2-v1)/d= 0.2 x 1.4^2 x (59-25) /1.4= 9.52

f. v1f= 25 +(51/0.2) x 0.18 = 70.9 m/s

momentum = 0.2 x 70.9 = 14.18 kg.m/s

v2f= 59 - (25/0.2) x0.18 = 36.5 m/s

momentum = 0.2 x 36.5 =7.3 kg.m/s

total momentum = 14.18+ 7.3 =21.48 kg.m/s

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