Upon arriving at a playground a child immediately runs to the swing set.
1. He climbs onto the swing and is initially sitting motionless with the swing hanging straight down. To get him started swinging his mother gives him a horizontal push from behind. If the boy were standing on the seat of the swing instead of sitting would it be easier or harder for his mother to push him? Why?
2. Now that the boy is swinging back and forth freely, what is his angular velocity about the swings pivot point when he is at his highest position behind the swing's pivot, at his lowest point directly under the pivot, and at his highest point in front of the pivot?
3. While he is swinging the ropes supporting the swing suddenly break when he is at the highest point in his motion. Where will he land?
4. The ropes are actually more likely to break at the bottom of the swing's motion. Why?
Having broken the swing the child moves on to the slide. This slide has a steep downward slope followed by a short flat horizontal section at the bottom and is very smooth (no friction).
5. Describe the boy's velocity at the top of the slide. How is his velocity changing in the middle of the slide? How is his velocity changing on the flat section at the bottom of the slide?
6. If the slide had a more gradual downward slope, but still started from the same height how would the boy's velocity differ at the bottom of the slide?
7. How would his velocity differ if he slid down the slide carrying a heavy rock?
8. If he dropped the rock over the side of the slide when he was half way down, would they hit the ground at the same time (assume the flat section at the bottom of the slide is at ground level)? Why?
In answering these questions you will no doubt have used many vector quantities. Remember, a complete description of these quantities requires both an amount and a direction as well as a point of reference. I am sitting three feet to the left of the table.
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