AP Physics 1 Question 127: Answer and Explanation
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A force probe is used to stretch a spring by 20 cm. The graph of the force as a function of distance shown in the preceding figure is produced and used to determine the amount of work done in stretching the spring 20 cm. The experimenter reports the result as 3,000 N·cm. Which of the following is a reasonable estimate of the experimental uncertainty on this measurement?
- A. 3,000 ± 3 N.cm
- B. 3,000 ± 30 N.cm
- C. 3,000 ± 300 N.cm
- D. 3,000 ± 3,000 N.cm
Correct Answer: C
C-The work done by the spring is the area under a force-distance graph because work = force times distance. Using the best-fit line drawn as the top of a triangle, the area is (1/2) × (300 N)(20 cm) = 3,000 N.cm.* Now, put your ruler along the data points. Try to draw another line that's still a reasonable best fit, but is a bit shallower. Where does that line intersect the 20-cm position? It intersects at a point probably not much below 280 N, maybe even 290 N. The smallest possible work done, given this data, would be area = (1/2)(280 N)(20 cm) = 2,800 N.cm, which is 200 N.cm short of the 3,000 N.cm original estimate. That's closest to Choice C. If you've done a lot of in-class lab work, you might have noticed that your data often look about as scattered as shown in the graph; and that anything you calculate is never much closer to a known value or to your classmates' calculations than 5 or 10 percent. Here, Choice B works out to an uncertainty of 1 percent; Choice D is 100 percent. So C is the reasonable choice.