A person measures his or her heart rate by counting the number of beats in 30s30s . If 40±140±1 beats are counted in 30.0±0.5s30.0±0.5s , what is the heart rate and its uncertainty in beats per minute?
Question
A person measures his or her heart rate by counting the number of beats in 30s30s . If 40±140±1 beats are counted in 30.0±0.5s30.0±0.5s , what is the heart rate and its uncertainty in beats per minute?
Solution
To calculate the heart rate in beats per minute, we first need to double the number of beats counted in 30 seconds. This is because there are 60 seconds in a minute, and we have the count for 30 seconds. So, 40 beats in 30 seconds would be 40 * 2 = 80 beats per minute.
Next, we calculate the uncertainty. The rule for multiplication and division is to add the relative uncertainties. The relative uncertainty in the count is 1/40 = 0.025 or 2.5%, and the relative uncertainty in the time is 0.5/30 = 0.0167 or 1.67%. Adding these gives a total relative uncertainty of 4.17%.
To find the absolute uncertainty in the heart rate, we multiply the heart rate by the relative uncertainty: 80 beats per minute * 4.17/100 = 3.34 beats per minute.
So, the heart rate is 80 ± 3.34 beats per minute.
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