Assignment:
1. Review Problem: A frictionless mass is at the bottom of a hill, as shown below. The mass can be pushed against a spring so that when the mass is released, it goes a height h up the hill. What spring compression x is necessary for the mass to reach a given height h?
2. Use the impulse-momentum theorem to explain why landing on an air-filled bag (see https: //www.youtube.com/watch?v=YY6IMLOuaSo) is so much more comfortable than doing the same jump from 55 meters onto concrete.
3. An exploding grapefruit (sorry, it's late) is sitting on the floor when it explodes into exactly two pieces. One piece is twice as massive as the other. Compare their speeds immediately after the explosion.
4. After the grapefruit explosion in the previous problem, the two pieces (one twice the mass of the other) slide across the floor until they come to a stop. Compare the distances they travel.
5. Tough question: Calvin (mass m) is sliding down a snow-covered hill (height h) on his frictionless toboggan. Exactly halfway down the hill he hits Hobbes (also mass m) who lands in Calvin's lap and the two of them continue down the hill. How fast are they going at the bottom?
6. A mass m is attached to a spring k on a frictionless horizontal surface. The spring is stretched some initial distance x = xo, and then the mass is released. How fast is the mass going when it gets to x = xo/2?
7. In lab, a "frictionless" cart of mass M is on a horizontal track. A hanging mass m is attached by a string, over a frictionless pulley. How fast will the cart be moving after the hanging mass drops a distance h? Use force/acceleration methods.
8. Redo the previous problem, using energy conservation.
9. The world record for the men's indoor pole vault -6.15 meters- is held by Sergei Bubka of Ukraine. Pole vaulting is very much a "conservation of energy" sport: the kinetic energy of the vaulter is changed to spring potential energy in the pole and finally to gravitational potential energy as the vaulter clears the bar.
(a) What approach speed would Sergei have needed in order to clear the bar, assuming that his center of mass was initially at a height of 1.0 m?
(b) Sergei's measured approach speed was 9.9 m/s. Where did the extra energy come from?
(Data in this problem comes from Wikipedia.org, February 2007.)
10. How long would it take a ping-pong ball to fall 10 m, considering air resistance? Use the techniques you've learned in Python so far to find the answer.