11-098-satellite_and_junk.jpg

Question

A spherical satellite of radius 4.6 m and mass M = 195 kg is originally moving with velocity vsatellite,i = < 3000, 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 = 4.3 kg is initially moving toward the satellite with velocity vjunk,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 vjunk,f = < -1100, 500, 0 > m/s. Both before and after the collision, the rotation of the space junk is negligible.

MOMENTUM
1) After the collision, what is the final momentum of the satellite?
psatellite,f = kg·m/s

2) What is the final velocity of the satellite?
vsatellite,f = m/s

ANGULAR MOMENTUM
3) 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 = kg·m2

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

5) Which of the following statements about the translational angular momentum of the space junk, about location D, are true? Check all that apply:
Because the space junk is traveling in a straight line, its angular momentum is zero.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.(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 in the -z direction.

6) 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?
Ljunk,i
= kg·m2/s

7) 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?
Ljunk,f
= kg·m2/s

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

9) What is the new angular speed of the satellite?
omega_2 = radians/s

ENERGY
Consider a system consisting of both objects (space junk and satellite).

10) Before the collision, what was the total kinetic energy (translational + rotational) of the system?
Ki
= joules

11) After the collision, what is the total kinetic energy of the system?
Kf
= joules

12) 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".)
?Ethermal
= joules