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 handtimed measurement of (a) 5 s, (b) 50 s, (c) 5 min?
Hint: This seems like a trick question ;)
Percent uncertainty is usually just the uncertainty times by 100!
a) 4%
b) 0.4%
c) 0.07%
To calculate the percent uncertainty, we need to divide the uncertainty by the measured value and multiply by 100.
a) For a 5 second measurement:
Uncertainty = 0.2 s
Measured value = 5 s
Percent uncertainty = (0.2 s / 5 s) * 100 = 4%
b) For a 50 second measurement:
Uncertainty = 0.2 s
Measured value = 50 s
Percent uncertainty = (0.2 s / 50 s) * 100 = 0.4%
c) For a 5-minute measurement:
Uncertainty = 0.2 s
Measured value = 5 minutes = 300 seconds
Percent uncertainty = (0.2 s / 300 s) * 100 = 0.067% (rounded to 3 decimal places)
To determine the percent uncertainty, we need to calculate the relative uncertainty, which is the value of the uncertainty divided by the measured value.
(a) For a measurement of 5 seconds:
The uncertainty is 0.2 seconds.
Relative uncertainty = (0.2 s / 5 s) * 100% = 4%
(b) For a measurement of 50 seconds:
The uncertainty is still 0.2 seconds.
Relative uncertainty = (0.2 s / 50 s) * 100% = 0.4%
(c) For a measurement of 5 minutes:
We need to convert minutes to seconds by multiplying by 60.
5 minutes = 5 * 60 = 300 seconds.
The uncertainty is still 0.2 seconds.
Relative uncertainty = (0.2 s / 300 s) * 100% = 0.067%
So, the percent uncertainties for the measurements are:
(a) 4%
(b) 0.4%
(c) 0.067%