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(II) 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 $$ (a) 5 s,(b) 50 s,(c) 5 \min ? $$

A) percent uncertainty is 4$\%$B) percent uncertainty is 0.4$\%$C) percent uncertainty is 0.07$\%$

Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

Jevie F.

September 5, 2020

Cornell University

University of Winnipeg

McMaster University

Lectures

04:16

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(II) Time intervals measur…

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our question asked that Oh our states that the time interval measured with the stopwatch typically has an uncertainty of about 0.2 seconds. Duty, human reaction time with starting stop moments. What is the percent uncertainty of the ham time measurement if a the measurements done for five seconds, be for 50 seconds and see for five minutes. So I went ahead and wrote, We have given here, which is the percent uncertain or I'm sorry, which is the uncertainty of the stop watch, which is 0.2 seconds. I wrote uncertainty as thie symbol Sigma. So then the question is, what is the percent uncertainty or percent Sigma? If both of situation a five seconds B 50 seconds or C five minutes are carried out for the amount of time measured with the stopwatch, so let's go ahead and do a first. So for a we're going to use the formula for percent uncertainty here, which states that the percent uncertainty is equal to the uncertainty which 0.2 seconds divided by the time of measurement, which for party is five seconds and then that ratio needs to be multiplied by 100% to convert it into units of percent. That gives us 4% for pardon. Let's go ahead and box that in as her solution hoops. Come on to that box Cox that in a solution. Hey, for part B, we want to calculate the percent uncertainty. Four a timing of 50 seconds with the stopwatch. So again, our uncertainty a 0.2 seconds. But this time we're going to divide it by our measurement, which is 50 seconds. We need to multiply that by 100 once again to convert that into units of percent. That gives a 0.4% for a solution to party. Go ahead, Paxton in crews. Yeah, for part. See, we were told that the timing is done for five minutes, but since our uncertainty is given in seconds, we need to convert that in two seconds. So five minutes converted into seconds. It was done by taking five minutes and multiplying it by the ratio, which is 60 seconds for every one minute. That gives us 300 seconds in five minutes. So now that we have it in seconds, we go, we can go ahead and once again calculate R percent uncertainty which is our uncertainty divided by our time. So 0.2 seconds invited by 300 seconds that racial multiplied by 100% to put it in units of percent. And that comes out to be 0.7 seconds. I'm sorry. 0.7% as our solution to part, see?

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