Question

Problem 1 A 20-kg base satellite deploys three sub-satellites, each of which has its own thrust capabilities, to perform research on tether propulsion. The masses of sub-satellites A, B, and Care 4 kg, 6 kg, and 8 kg, respectively, and their velocities expressed in m/s are given by: VA = 41 - 2] + 2k Vg = 1+4) Vc = 21+ 2) + 4k 35 m 25 m 1. At the instant shown, what is the angular momentum Ho of the system about the base satellite? 2. Assuming that the velocity of the base satellite is zero, determine: (a) The position vector i of the mass center G of the system, (b) The linear momentum L of the system, (c) The angular momentum Hg of the system about G. 15 m

Answer 1

Based on () Tse = figure position of sub-parts. 30 isë+2 s § + 35k 3 8B B a %ć 40 นุ๐ about the origin Ho rax min + = Angular momentum ox mou + P x me u H. - 30j x4(-; +22) +lescº +25; +35+X[ituj) + (400) x 8 c2u²+ 29 +4E) ŷ k ។ Ё (in h = of 0 30 l·li 25 35 yo 1 16 -8 8 24 o 16 16 32 H, - * (240-840) - 5 (-210 +1280) + K (-480+360-150 +640) -600 a 1070 ; + 370 kg mels 1 H.

(2) (@) mara + med + more fo matm r me P6 4 (302) + 6(15a + 25 g +35²) + 8 (402) of ll 4+ 6 + 8 ad = 22.78 tis g +11.67 Ê + (6) ĭ = MATA u + meu ī = 4c4a-2} + 2k) + 6( + 4 + 8(2 i + 2% + UR) TJ 38 + 32 + 40k J kg mlo (a) Ha= (rap) v moun + (78 -8 jy move+ (% -% x mc ue (30j - (22.781 +isz' +11.67 1ê) x4(ui*+2) *-29 +28) +15+25j +356 - (20.78i tusgº +11.67 ) x612 +4)) + (40 - (22-78 +15j +11.67 * l) x 862 i + 2;" +4k) 826.58 - 602-26 ; + 211.04 Å kg m/ ra Ha ) =