4. 4.{a} What is the kinetic energy of our moon in its orbit around Earth? {Assume Earth's reference ame.) 4.03} What is the kinetic energy of our planet, Earth, around the sun? 4.{c} How would an answer to (a) have to be changed if we instead asked for the kinetic energy of the moon from the reference frame of the sun, instead of Earth? Show a labelled diagram to support your explanation and then calculate this new kinetic energy for the moon. How does this new kinetic energy amount compare to the result you obtained in (a)? 4.{d} What is the gravitational potential energy of our moon with respect to the Earth? Assume the surfaces of these two very large bodies are to remain intact -- (i.e. they cannot go past their respective radii in the sense that neither can 'erash through' the other, they would have to stop just as their surfaces are theoretically imagined to make contact}. 4.{e} If for some inexplicable reason Earth was to suddenly stop orbitting the sun, what would be its impact velocity,r at the point just as its surface contacted the sun's surface (assume massive melting or other damage occurs -- i.e. their respective radii stay intact, similar to part {d})? 5. 5.(a) A cart (#1) on a linear track collides with another cart (#2). Cart #1 has a mass of 2.50 kg and is travelling 5.40 m/s [E]. Cart #2 is initially stationary and has a mass of 7.50 kg. If the collision is perfectly elastic, with no energy losses, what are the final velocities of the two carts? 5.(b) Repeat the above part (a), but where Cart #1 now has double its original mass. 5.(c) Repeat the above part (a), but where Cart #1 now has double its original velocity. 5.(d) Repeat the above part (a), but where Cart #1 has double its original mass, AND, double its original velocity. 5.(e) What mass would Cart #2 have to be for otherwise same circumstances as in part (a), but where the magnitude of Cart #1's final velocity (after the collision), is half of the magnitude of its original 'incoming' (before the collision) velocity? (Is there only one answer or are there 2 or more possible answers?? Explain and show any additional solutions if any.) 5.(f) Repeat the question in part (a) where the two carts get stuck together after the collision. 5.(g) Is it possible for Cart #1 to come to a complete stop after its collision with Cart #2 for some different mass of Cart #2, given everything else is the same as originally describe in part (a)? If so, show how this calculation would work and determine both this other mass for Cart #2 as well as its final velocity. If not, prove with theory and/or examples why not. Use diagrams to help your explanations. 5.(h) If Cart #2 was travelling toward Cart #1 with the same magnitude of velocity as for Cart #1 in part (a), but in the opposite direction, then what will the final velocities be? 5.(i) If Cart #2 is initially (before collision) travelling at 90.0% of the same velocity vector as Cart #1 (same direction, but a little bit slower), then determine the final velocities if everything else is the same as in the original part (a)