Back to the playground.
A group of children are playing on a merry-go-round.
1. Compare the torque required to accelerate the merry-go-round to the same final angular velocity for the following two cases: (a) when the children are all at the outside edge of the merry-go-round and (b) when the children are all near the center of the merry go round.
2. The merry-go-round is spinning freely and all of the children are near its outside edge. Suddenly they all lean in toward the center of the merry-go-round. How does its angular velocity change? Why?
3. The merry-go-round is again spinning freely and all of the children are near its outside edge. Suddenly one of them lets go (without pushing off of the merry-go-round). She will of course accelerate toward the ground due to gravity, but what will the horizontal component of her velocity be (descriptive answer please)?
4. Compare her kinetic energy immediately before and after letting go. If she lands on wet grass (no friction) what will her kinetic energy be after landing?
Let's say you've decided to try bungee jumping. You are standing at the top of a tall platform with one end of a bungee cord tied to you and the other end tied to the platform. When you step off the platform you don't push off or jump up so you begin falling straight down. After falling a certain distance the bungee cord becomes taught and begins to stretch. Finally, your fall begins to slow and you come to a complete stop just above the ground before being sent back up by the acceleration provided by the stretched bungee cord.
5. Assuming that the bungee cord is perfectly elastic (no energy is converted into thermal energy) and neglecting air resistance how high will you go after the first bounce? Describe why using energy conservation.
6. If you use two identical bungee cords (both with one end attached to you and the other end attached to the platform) when you stop briefly at the bottom will you be lower or higher than with one bungee? Why?
7. In a real bungee jump some energy will be wasted in heating up the bungee cord and in moving the air as it resists your motion. You will eventually stop bouncing and come to rest in a stable equilibrium. At this equilibrium position how does the length of the bungee cord compare to its length when you were standing on the platform?
8. At this equilibrium position what force is the bungee cord exerting on you? What force do you exert on the bungee cord?