Dynamics_Part68

Dynamics_Part68 - Problem Set 9 Problem 4 Problem A space...

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Unformatted text preview: Problem Set 9: Problem 4. Problem: A space probe of mass M is struck at Point A by a meteorite of mass m and initial velocity vo = V ( 3 i - 15 j + k). Point A is located at rA = 6R i + 1 R k. The coordinate axes shown are the 4 16 2 principal centroidal axes of inertia. The radii of gyration for the three principal axes are kx = 9 R, 8 ky = 5 R and kz = R. After passing through the probe's solar panel, the meteorite's speed is 80% of 4 its initial value and its direction is unchanged. Determine the angular velocity of the probe after the meteorite strike. Express your answer in terms of m, M , V and R. Solution: The position vector from the space probe's center of mass to the point at which the meteorite strikes the probe is 1 rA = 6R i + R k 2 Thus, the meteorite's linear and angular momentum vectors just before the strike are mvo = mV 15 3 i- j+k 4 16 j 0 - 15 mV 16 = k 1 2R 1 mV (12 i - 15 j + 16 k) 16 15 mV R(i - 12 j - 12 k) 32 rA mvo = i 6R 3 4 mV = mV After the strike, we know that vf = 4 vo . Thus, the meteorite's linear and angular momentum vectors just 5 after the strike are 1 mV (12 i - 15 j + 16 k) mvf = 20 rA mvf = 3 mV R(i - 12 j - 12 k) 8 Denoting the space probe's angular momentum just after the meteorite strikes it by HA , conservation of angular momentum tells us that rA mvo = HA + rA mvf Substituting for rA mvo and rA mvf from above, we conclude that HA = 3 mV R(i - 12 j - 12 k) 32 ...
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This note was uploaded on 05/12/2010 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.

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