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 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum Oct 29th 2016, 02:22 AM #1 Junior Member   Join Date: Oct 2016 Posts: 5 I need someone hel pto clarify my problem Question: A student used a digital stopwatch three time 10 oscillations of a pendulum. The timings were 13.52s, 13.64s and 13.58s a) Calculate i the average time for 10 oscillations, ii the time period of the oscillations. b) Estimate the accuracy of the timings, giving a reason for your estimate. The problem i have is with part b. In maths to estimate is round up ideally to 2 sf.(my answer is 1.4 to s.f) if i give my estimate my answer how do i give a reason. I feel to give my estimate to 2 sf because it seems to be the standard in physics (i could be wrong) but also knowing that gate timers and other forms of measuring time make be more effective than a stopwatch am i suppose to estimate the time on those and give it as my answer since it will be more accurate? I just a bit confused and need a second opinion   Oct 29th 2016, 06:58 AM #2 Physics Team   Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,347 You are estimating the accuracy of the timing using the stop watch. it doesn't matter that there may be more accurate ways to measure it - the data you were given is from the stop watch. As for an estimate of accuracy - the max deviation of any one measurement from the mean is 0.06s. So +/- 0.06s is one estimate of accuracy. However, given that there are only 3 data points it's quite possible that if a 4th measurement was taken it could very well lie outside the +/- 0.06s "window" about the mean value. So you could argue that the accuracy is a little worse than +/- 0.06s; perhaps +/- 0.1s. topsquark and alisdfd like this.   Oct 29th 2016, 09:40 AM   #3
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 Originally Posted by alisdfd Question: A student used a digital stopwatch three time 10 oscillations of a pendulum. The timings were 13.52s, 13.64s and 13.58s a) Calculate i the average time for 10 oscillations, ii the time period of the oscillations. b) Estimate the accuracy of the timings, giving a reason for your estimate. The problem i have is with part b. In maths to estimate is round up ideally to 2 sf.(my answer is 1.4 to s.f)
Who told you this? In physics or engineering (there is no reason to "round" in maths) the rule is that a measurement is accurate to 1/2 the most significant figure. If we are measuring a length with a meter stick, for example, we look at the end of the object being measured. If it lies between two marks, we take the one it is closest to so that our accuracy is 1/2 the distance between marks. That is, "13.52 s" could be anywhere from 13.515 to 13.525. Those figures are given to four significant figures and the accuracy is 0.005 s.

 if i give my estimate my answer how do i give a reason. I feel to give my estimate to 2 sf because it seems to be the standard in physics (i could be wrong) but also knowing that gate timers and other forms of measuring time make be more effective than a stopwatch am i suppose to estimate the time on those and give it as my answer since it will be more accurate? I just a bit confused and need a second opinion
The accuracy of a measurement depends upon the instrument used to measure so it makes no sense to base the accuracy on "more accurate" instruments you did not use!

Last edited by HallsofIvy; Oct 29th 2016 at 09:43 AM.   Oct 30th 2016, 10:24 AM   #4
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 You are estimating the accuracy of the timing using the stop watch. it doesn't matter that there may be more accurate ways to measure it - the data you were given is from the stop watch. As for an estimate of accuracy - the max deviation of any one measurement from the mean is 0.06s. So +/- 0.06s is one estimate of accuracy. However, given that there are only 3 data points it's quite possible that if a 4th measurement was taken it could very well lie outside the +/- 0.06s "window" about the mean value. So you could argue that the accuracy is a little worse than +/- 0.06s; perhaps +/- 0.1s.
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