Sample problems for the final

1. Take a look at this lovely picture of Wayne Gretzky, the greatest hockey player of all time, waving goodbye to the fans in Toronto (I think).   Looking at the photo, it may be hard to believe he didn't fall over just after this photo was taken, but in fact he did not. Why didn't he fall over? What in fact was his motion after this moment? (Be advised that the force exerted by the ice on Wayne was along the direction of his left leg.)

2. Cedric is standing in a padded cell and notices that each of his feet has depressed the padding by 8 mm. As he walks around, he notices that his footprints disappear right away. While Cedric ponders the physical significance of this, he gently bounces up and down. Cedric's mass is 75 kg. At what frequency does he bounce?

3. Tarzan (90 kg) wishes to make a very cinematic rescue of Jane (50 kg), who stands on a floating log surrounded by hungry crocodiles. Tarzan is on a tree branch on the west side of the river, 15 m higher than Jane. He grabs a vine that he usually uses to swing over to a branch on the east side of the river. This branch is 7 m higher than the log. His plan is to swing down, grab Jane, and then land with her on the other side of the river. Is this going to work? Or will they both end up as crocodile chow?

4. In Physics I lab one day the students are studying pendulum motion. They tie a bob onto a 1.1 m string, pull the bob back so that the string makes an angle of 36 degrees with the vertical, and let go. The bob swings down, just missing the floor, and continues to an angle of 15 degrees from the vertical, at which point the string breaks or the knot unties itself (witnesses disagree). Where does the bob land?

5. Consider a cylinder 20 cm in diameter, fitted with a massless piston, the outer side of which is attached to a spring of spring constant 3000 N/m. The cylinder is horizontal and contains helium gas. When our problem begins the gas occupies 40 cm of the cylinder, is at a temperature of 300K, and the spring is compressed by 2 cm, and everything is stable. Heat is added gradually to the gas until the spring is compressed by an additional 1.2 cm. What is the new temperature of the gas? How much heat was added to the gas? (Yes, the whole apparatus is in a room at sea level, so that the air pressure on the spring's side of the piston is 1 atm.)

6. Gwendolyn intends to make yogurt, and for that she needs milk at 110 degrees Fahrenheit. She puts 0.8 liters of milk into the microwave, and nukes it for a couple of minutes. When she removes it, the milk is at a temperature of 125 F. Fortunately she has a supply of ice at 0 F. How much of this ought she to add to the milk to get the milk down to 110 F?

7. Consider two collisions, both beginning with the same initial conditions - same two masses, same two initial velocities. In case A, the two masses stick together; in case B they do not. Is momentum conserved in case A? in case B? Is kinetic energy conserved in case A? in case B? Can you say for sure if the total kinetic energy after the collision is greater in one case, and if so, in which case?

8. Suppose that on the top of a flat-roofed building construction workers have left a 7 m long beam whose mass is 100 kg. The last two meters of the beam extends past the edge of the roof. Andrea (60 kg) begins walking out along the beam. Can she walk all the way to the end of the beam without it falling (presumably along with Andrea)? If not, how far can she walk before it begins to teeter?

9. Compute the rms speed of helium at room temperature and that of carbon dioxide. Comment on why helium is always escaping into outer space, while other molecules stick around.