Final answer:
When comparing sprinters' times with a stopwatch uncertainty of ±0.05 s, the times are too close to definitively conclude improved speed. Percent uncertainty calculations for a measuring tape and infant's pulse rate are provided as examples. The same percent uncertainty approach is applied to estimate blood pressure measurement uncertainty.
Step-by-step explanation:
Regarding the high school track stopwatch with an uncertainty of ±0.05 s, if the top sprinter's times were 12.04 s last week and 11.96 s this week, we cannot conclude definitively that this week's time was faster due to the uncertainty being greater than the difference in times. The difference in times (0.08 s) is within the range of uncertainty. Therefore, the times are not distinct enough to make a clear conclusion about improved speed.
For a percent uncertainty calculation, you can use the formula:
- Percent Uncertainty = (Uncertainty / Measurement) × 100%
Applying this to a good-quality measuring tape that can be off by 0.50 cm over a distance of 20 m (2000 cm), we get:
- Percent Uncertainty = (0.5 cm / 2000 cm) × 100% = 0.025%
And for the infant's pulse rate measured at 130 ± 5 beats/min, the percent uncertainty is:
- Percent Uncertainty = (5 beats/min / 130 beats/min) × 100% = 3.846%
In answering a similar question about uncertainty in blood pressure measurement: Assuming the same relative percent uncertainty applies, the uncertainty in a blood pressure measurement of 80 mm Hg would be the same percent as the pulse rate measurement. If the pulse rate measurement is 3.846%, then 3.846% of 80 mm Hg would be the blood pressure uncertainty. Calculating this gives:
- Uncertainty in blood pressure = (3.846% / 100%) × 80 mm Hg = 3.0768 mm Hg (approximately)