I really wish that I can understand these type of difficult problems. Please hel
ID: 1916388 • Letter: I
Question
I really wish that I can understand these type of difficult problems. Please help!!!
The next two problems are more difficult. You can use your book if you 'd like for help. These are extra credit problems. How should you throw a super ball so that trajectory below results, moving back and forth between the two points on the ground. The super ball undergoes perfectly elastic collisions with the ground and docs not slip. The moment of inertia for the super ball is I=2/5*MR2. (Specify the initial velocity vector). Someone once considered hanging a rope, (of density p), above the Earth so that it hangs slightly above the ground, (see diagram). How long docs the rope need to be? (Use Me = 5. 98 x 1024 kg, Re=6. 37 x 106 m, omega for Earth's rotation, and rho = 0. 33 kg/m). The rope has both ends free.Explanation / Answer
If the ball is rotating at rate around a horizontal axis
that is perpendicular to its plane of motion, and it is traveling with horizontal velocity v,
then its angular momentumaround the point of impact is
L = MRv + (2/5)MR².
Since the force of impact has 0 moment arm around the point of impact, L is conserved through the collision. So
L/(MR) = v + (2/5)R = v' + (2/5)R',
where the prime values are after the collision.
By symmetry, v' = -v and ' = -. So v + (2/5)R = 0.
Conversely, if v + (2/5)R = 0, then the motion will be oscillatory.