In a case of virtual reality run amok, your ebook version of the classic children’s story “Peter Pan” has somehow taken over your life. Even more troubling is the fact that Captain Hook and his pirates have captured you and will soon make you “walk the plank.” Projecting horizontally from the side of Hook’s ship is a flexible wooden board several meters long and it is this “plank” that you will have to walk out on before stepping off into space. After noticing a huge pile of mattress lying on the dock just under the board, you realize that the pirates aren’t so bad after all and that they’re just trying to have a little fun. Since no one is really getting hurt, you begin to enjoy the adventure.
1. There is a line of other victims ahead of you, so you can relax for the moment and watch the other people walk onto the board, one by one. You notice that as a victim walks out onto the board, the board gradually bends downward. Since the victim is losing altitude, she is also losing gravitational potential energy. Where is her gravitational potential energy going?
2. As the victim stands motionless at the end of the board, you observe that the board is bent downward by an amount that is exactly proportional to her weight; the previous victim was twice her weight and the board bent downward twice as far. Explain why the board’s downward deflection is proportional to the victim’s weight.
3. It’s now your turn to go. You walk bravely off the board and drop onto the pile of mattresses below. To your relief, you plunge into the soft heap, come to a stop deep in the mattress pile, and then rebound upward. After a couple more bounces, you come to rest. You then climb off the mattresses and walk off in search of Peter Pan himself. What was the direction of your acceleration (a) just before you reached the deepest point in the pile and (b) just after you reached the deepest point in the pile?
4. What forms did your energy take as you bounced up and down in the pile of mattress and at what moment was each form of energy at its maximum?
You’re playing racquetball with a friend. Each of you has a metal racket with nylon strings and you’re taking turns smacking the ball against the front wall of a hard-surfaced room. The ball ricochets back from the front wall after every hit and the two of you are working up quite a sweat trying to keep it bouncing off that front wall.
5. You swing your racket forward and hit the ball forward. You notice that your racket slows down slightly as a result of the collision. Use the concept of momentum to explain why the racket must slow down during this sort of collision.
6. Instead of swinging forward as the ball approaches him from the front wall, your opponent swings his racket gently backward (away from the front wall). The ball hits the racket and bounces remarkably weakly. In terms of energy and work, why did allowing the ball to hit the racket as the racket moved away from the front wall cause the weak bounce?
7. You let the racquetball drop from rest onto the rigid floor and observe that it rebounds to 72% of its original height. What fraction of the ball’s kinetic energy at the moment before it hits the floor has been returned to the ball by the moment after it rebounds from the floor? What became of the missing energy?
8. You hold the racket face horizontal and drop the ball onto its surface. To your surprise, the ball bounces higher from the racket face than it does when dropped directly onto the rigid floor. Why does the racket’s nylon-mesh surface allow the ball to bounce better than it would from a solid surface?