1. bouncing behavior in springs, balls, and other elastic objects,
2. relative motion and the interactions between objects in relative motion,
3. connections between translational and rotational motions,
4. connections between acceleration and force,
5. the way we perceive acceleration.
   

1. One of the big hits among the braver members of your group is the free fall tower. You and your little charges are strapped into individual seats on a bench that is gradually hauled up to the top of a vertical tower by a cable. After hanging stationary at the top of this tower for a few moments, the bench is suddenly released. Though rails keep the bench from drifting away from the tower, the bench nonetheless drops freely for a terrifying second or two before brakes activate and slow the bench to a stop. When during this trip from the top of the tower to the bottom do you (A) feel the lightest and (B) the heaviest? In each case, briefly explain why you feel that way.

2. You move your gang along to the swinging pirate ship, a huge pretend boat that hangs from a central pivot high overhead. After you are all strapped into seats in the boat, it begins to swing back and forth, higher and higher. Eventually the boat swings so high that it travels over the top of the pivot. The boat and its occupants are upside-down for a few seconds. The motion is slow and during this time, loose change, hats, sunglasses, food, and other items come raining out of the boat onto the ground below. In the normal loop-the-loop of a roller coaster, everyone feels pressed into their seats and nothing falls out of the cars. Why in this case do the boat riders feel that they are hanging upside-down and why is this situation so different from that of the loop-the-loop?

3. Sickening though it is, the egg scrambler is still a favorite among 8-year-olds. You sit in your circular cars as this giant mixer throws each car back and forth across a large circle. Although the whole ride gradually pivots, the main motion is very simple: you begin almost at rest near the edge of the circle, then swing at tremendous speed through the center of the circle, and finish almost at rest near the opposite edge of the circle. Even when you close your eyes, you can't ignore the motion; you frequently feel it pressing you fiercely against your seat or against your fellow passengers. Briefly explain why this sideways squishing effect (A) is most severe during the start and stop of each swing and (B) vanishes briefly as your car passes through the center of the circle.

4. The skydiving ride isn't open to the children, but you take a turn anyway. They cheer you on and laugh as you scream on the way down. The ride resembles a 200-foot-tall playground swing, except that instead of being pushed gradually to greater and greater heights, you are pulled backward and upward just once and then released. You are so high at the start that you begin your descent in near free fall. During those first moments, you feel weightless and terrified, which explains why you are bellowing loudly enough for the kids to hear. But how do you feel as you swing through center and make your closest approach to the ground? Are you still weightless or is there some other apparent weight that you are experiencing?

5. You now enter the arcade part of the park and watch people try to win prizes by performing seemingly simple feats. Not surprisingly, most of those feats are deceptively difficult.

The first game you encounter is a ring-toss in which you must throw a small, rigid plastic hoop around the neck of a glass soda bottle. An array of motionless upright bottles fills the center of the booth and it looks as though it would be easy to toss a hoop so that it would fall down around one of the bottle necks. But in 10 minutes of watching, not a single hoop stays on a bottle neck. They all bounce up and off. (A) Use the concept of conservation of energy and the fact that both the hoops and the bottles have coefficients of restitution of almost 1.0 to explain briefly why the hoops can't stay on the bottle necks. (B) Why would replacing the rigid hoops with similarly shaped beanbag rings make this game relatively simple to win?

6. The next arcade game involves tossing quarters onto glass salad plates arranged horizontally in the middle of the booth. Those plates are almost flat and have a shiny, smooth surface. Not surprisingly, the quarters never stop on the plates and all end up on the floor below. Use the concepts of energy and momentum to explain briefly why this game is so nearly impossible to win.

7. Another game you enjoy watching involves tossing a basketball into a stiff fruit basket that's mounted with its bottom against a slanted wall. The basket is tipped back just enough that it can hold a basketball, but it doesn't take much to make that basketball roll out and fall to the floor. Over and over, people toss balls into the baskets only to watch them bounce or roll back out. You point out that this feat would be much easier if the baskets were moving when the balls landed in them. Which way should the basket be moving as the ball arrives for this feat to become easier and why that direction?

8. A final arcade game requires that you swing a huge mallet over your head and pound downward on the end of a lever. The other end of the lever then flies upward and strikes a block, which immediately slides up a tall vertical track toward a bell. If you hit the lever hard enough, the bell will ring and you'll win a prize.

All the kids are cheering you on as you swing the mallet and drive it violently into the lever. The far end of the level swings upward rapidly, smacks the block hard, and sends that block up the track so that it rings the bell. You're an instant celebrity. Of course, your chances for success were greatly improved when the game operator allowed you to stick whatever material you wanted to the top of the lever and the bottom of the block. You chose very elastic materials (coefficients of restitution of almost 1.0) for both surfaces and that made all the difference. Why is it so helpful to have highly elastic surfaces colliding in this case?