Giancoli's Physics: Principles with Applications, 7th Edition

1

Introduction, Measurement, Estimating

Change chapter1-4: Measurement, Uncertainty, Significant Figures

1-5 and 1-6: Units, Standards, SI, Converting Units

1-7: Order-of-Magnitude Estimating

1-8: Dimensions

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.

Problem 6

Q

Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of

- 5.5 s,
- 55 s,
- 5.5 min?

A

a) $4 \%$

b) $0.4 \%$

c) $0.06 \%$

b) $0.4 \%$

c) $0.06 \%$

Error in the video: I mistakenly wrote fractional errors instead of percent errors. The answers written above are correct, not the answers in the video, although the working in the video is correct.

In order to watch this solution you need to have a subscription.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Percent uncertainty is calculated by dividing the absolute uncertainty which is the uncertainty in the same units as your measurement— 0.2 seconds in this case is the absolute uncertainty— divided by the measurement in part (a) of 5.5 seconds and 0.2 divided by 5.5 times a 100 to turn it into a percent is 0.04 percent uncertainty. In part (b), it's 0.2 seconds divided by 55 seconds and this same uncertainty of 0.2 seconds should matter less when you have such a long measurement of 55 seconds as compared to only 5.5 seconds and the percent uncertainty reflects that. So it's 0.004 percent uncertainty which is a much smaller percent uncertainty than you had in part (a). In part (c), we are dividing by 5 minutes; now we have to make the units the same so on the denominator we have 5 minutes times 60 seconds per minute and the minutes cancel giving us this many seconds and this percent uncertainty is 6.7 times 10 to the minus 4 percent uncertainty.

COMMENTS

By sondylevykh on Wed, 3/11/2015 - 1:42 AM

These answers are all miscalculated. i'm looking at the book now, it has different results.

By Mr. Dychko on Wed, 3/11/2015 - 4:30 AM

Hi sondylevykh, thanks for spotting the errors here. I was writing fractional error rather than percent error, so the answers are off by a factor of 100. I've flagged this video for a re-do, and I'll put a note above it.

All the best,

Mr. Dychko

Giancoli Answers, including solutions and videos, is copyright © 2009-2022 Shaun Dychko, Vancouver, BC, Canada. Giancoli Answers is not affiliated with the textbook publisher. Book covers, titles, and author names appear for reference purposes only and are the property of their respective owners. Giancoli Answers is your best source for the 7th and 6th edition Giancoli physics solutions.