1. If a vertically-oriented string with machine screws attached is dropped, all of the machine screws will begin moving at essentially the same time.
2. If two machine screws, A and B, are dropped, and it is found that A takes less time to cover a given distance than B, then A's average speed while covering the given distance is greater than B's average speed while covering that distance.
3. When a machine screw falls from a ceiling of 5 meters to a floor at 0 meters, it passes through every possible height between 0 and 5 meters; put another way, any number you could ever possibly think of between 0 and 5 (such as 2.087112087112...) represents a height at which a screw that fell from 5 meters must spend at least one instant.
4. When metal machine screws "free fall" towards the earth's surface from heights less than or equal to 5 m, any possible influences from air resistance are too small to be noticeable.
5. A string with evenly-spaced machine screws produces a rhythm of decreasing times between beats when dropped from a height of 5 meters onto a cookie sheet.
6. The above claim implies that the machine screws speed up as they fall.
7. Average velocity is equal to change in position divided by time elapsed.
8. In "Pattern B," the differences between the distances between screws remained constant.
A. Imagine that your lab group (which may or may not be taking physics in an alternate reality) creates a string with screws at positions 1m, 2m, 3m, 4m, and 5m. You drop this string from a height of 5m, just as the lab instructions tell you to do, and you notice that the time intervals between screws hitting the cookie sheet get larger with each screw. The first two impacts are close together, then a little farther apart, then farther, and farther. Assume that all your measurements and observations are more or less accurate and that you performed your drop correctly. What would you conclude from your data about the behavior of objects in free fall?
B. Now imagine that you are living in a world where free-falling objects have an upwards jerk (i.e. a negative jerk if down is positive). In other words, they accelerate downwards, but the downwards acceleration gets smaller and smaller with each beat.
i. Design a pattern of bolt positions that might produce a steady rhythm in this imaginary world. Think hard. This is hard.
BIG Hint: to do this, you will have to pick some arbitrary, large downwards acceleration to start out with, and some small constant upwards jerk (amount the acceleration shrinks by for each beat). But remember: jerk is a change in acceleration, not a change in velocity!
Show ALL work relating to your pattern.
ii. Draw both a position and a displacement diagram for your pattern.
iii. Using math, words, & diagrams (as necessary), explain why your pattern should produce a steady rhythm in the imaginary world where free-fall acceleration is downward but jerk is upward: i.e. justify your solution.