HW 3 Solutions - Solution for Long-answer Homework 3 Motion...

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Solution for Long-answer Homework 3 Motion problems Solution to Long-answer Homework Problem 3.1(Motion diagrams) Problem: Let’s think back to some of the data analysis we have done in lab. (a)Given the theoretical line below, sketch in how you would expect the data to look for 10 data points for systematic and random error. You don’t have to get too technical, but in a few words in the space below them, explain the difference in your drawings. random systematic (b)Why do we like to plot things in a straight line relationship and get our answer from the slope when we can? (c)Let’s say we knew what the theoretical y - intercept should be for our straight line. If we had a systematic error, would we want to include this as a data point? Why or why not? Solution to Part (a) A systematic error always affects the data the same way, like having a slightly chipped ruler, or having friction in the system. A random error can fluctuate, so sometimes you err a little high, and sometimes a little low, like running a timer, or using any other measuring device. Grading Key: Part (a) 11 Points 2 point(s) : A few words meaning: Systematic always same way 2 point(s) : A few words meaning: random fluctuates 1 point(s) : data points all either above or below on systematic 2 point(s) : the slope of the line you would draw through the data points on systematic is same as theoretical line 1 point(s) : data points scattered above and below on random 2 point(s) : the slope of the line you would draw through the data points on random is same as theoretical line 1 point(s) : used approximately 10 points as asked on each graph Solution to Part (b) It is a graphical way to use the brain to calculate the weighted error. Or, something about how the use of a straight line helps correct for random error. A point back towards points missed elsewhere if they discuss how the slope of a line is unaffected by systematic error. 1
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Grading Key: Part (b) 3 Points 3 point(s) : 3 if reasonable, 2 pts if sort of, 1 pt if anything salvageable Solution to Part (c) For a systematic error you do NOT want to force the y-intercept, since all your data is off in the same direction. Grading Key: Part (c) 4 Points 2 point(s) : No (unless they got random and systematic confused in a) 2 point(s) : Theoretical y-intercept does not have error, and since error all in same direction, would skew the slope. (Does not have to be exact, but clear they understand this. 1 pt if not really clear, but you can tell they sort of understood.) Total Points for Problem: 18 Points Solution to Long-answer Homework Problem 3.2(When And Where Do Two Objects Collide) Problem: Two cars are at rest. Car A is at x = 2500m , and car B is at x = - 1000m . At t = 5s car A instantly travels at a constant velocity of 25 m s in the positive x direction. At the same time car A takes off car B instantly travels at a constant velocity of 30 m s , also in the positive x direction.
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