Instruction3. The Counter Factual NOTE: In the counter-factual problems, we will sometimes provide you with scenarios in which there is data that is not in line with reality. As in this week’s problems, we may then ask you to draw conclusions from these data. As good scientists, your job is to draw conclusions from the data, not from what you assume to be the case. If it makes things clearer, imagine that these kinds of questions are taking place in an alternate reality. ALSO NOTE: sometimes you have to think hard & do a bunch of work to answer the counter-factual. Don’t cut corners! 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, 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 an interval 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.