A spherical satellite of radius 4.7 m and mass M = 195 kg is originally moving w

Question

A spherical satellite of radius 4.7 m and mass M = 195 kg is originally moving with velocity v with arrowsatellite,i = < 2800, 0, 0 > m/s, and is originally rotating with an angular speed 1 = 2 radians/second, in the direction shown in the diagram. A small piece of space junk of mass m = 4 kg is initially moving toward the satellite with velocity v with arrowjunk,i = < -2300, 0, 0 > m/s. The space junk hits the edge of the satellite at location C as shown in the diagram, and moves off with a new velocity v with arrowjunk,f = < -1100, 490, 0 > m/s. Both before and after the collision, the rotation of the space junk is negligible.

a) MOMENTUM After the collision, what is the final momentum of the satellite? p with arrowsatellite,f = kg·m/s What is the final velocity of the satellite?

b) ANGULAR MOMENTUM Assuming the density of the satellite is uniform throughout, what is the moment of inertia of the satellite? (The moment of inertia of a uniform-density sphere is (2/5)MR2.) I =

c) What is the initial rotational angular momentum of the satellite, around location D (its center of mass)? (Be sure your signs are correct). L with arrowsatellite,i = kg·m2/s

d) An instant before the collision, when the space junk is almost at location C, what is the translational angular momentum of the space junk about location D? L with arrowjunk,i = kg·m2/s

e) An instant after the collision, when the space junk is just slightly beyond location C, what is the translational angular momentum of the space junk about location D?

f) At the same instant after the collision, what is the rotational angular momentum of the satellite? L with arrowsatellite,f = kg·m2/s What is the new angular speed of the satellite?

g) ENERGY Consider a system consisting of both objects (space junk and satellite). Before the collision, what was the total kinetic energy (translational + rotational) of the system?

h) After the collision, what is the total kinetic energy of the system?

What was the rise in thermal energy for the space junk and satellite combined? (Your answer will be judged correct if it is consistent with earlier work, even if there were mistakes in the earlier work -- "propagation of errors".)

Explanation / Answer

According to the given problem,

Satellite radius - 4.7
Satellite mass - 195
Satellite velocity - <2800, 0, 0>
Angular speed - 2
Space junk mass - 4
Space junk initial velocity - <-2300, 0, 0>
Space junk final velocity - <-1100, 490, 0>

a)Final momentum of satellite
<2800*195 - 2300*4 + 1100*4, -490*4, 0>
<541200, -1960, 0>

Final velocity of satellite
<541200/195, -1960/195, 0/195>
<2775.38, -10.05, 0>

b) Moment of inertia of satellite
I = (2/5)MR2
I = (2/5)*195*4.72
I = 1723.02 kg-m2

c)Initial rotational angular momentum
L = I x w
L = 1723.02*2
L = <0, 0, -3446.04>
Angular momentum is in the z direction and it is negative because the satellite is spinning clockwise.

(r_perp) is the same when the space junk is at locations A, B, and just before getting to C.
xp_y - yp_x is the same when the space junk is at locations A, B, and just before getting to C.
The translational angular momentum of the space junk is the same when the space junk is at locations A, B, and just before getting to C.

d)Initial translational angular momentum of space junk
L = I x w
L = m*v*r
L = 4*-2300*4.7
L = <0, 0, 43240>
Angular momentum is in the z direction and positive because of right hand rule

Only 4 Sub-Parts per question, Please Repost the remaining question again.

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