1.E: The Nature of Science and Physics (Exercises)
- Page ID
- 126704
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1.2: Physical Quantities and Units
1. The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?
2. A car is traveling at a speed of \(33 m/s\)
(a) What is its speed in kilometers per hour?
(b) Is it exceeding the \(90 km/h\)
3. Show that \(1.0 m/s=3.6 km/h\)
[Hint: Show the explicit steps involved in converting \(1.0 m/s=3.6 km/h\)].
4. Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)
5. What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)
6. The speed of sound is measured to be 342 m/s on a certain day. What is this in km/h?7. Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year.
(a) What distance does it move in 1 s at this speed?
(b) What is its speed in kilometers per million years?
1.3: Accuracy, Precision, and Significant Figures
8. Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?
9. A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?
10. (a) A car speedometer has a \(5.0%\) uncertainty. What is the range of possible speeds when it reads \(90km/h\)?
(b) Convert this range to miles per hour. (\(1 km=0.6214 mi\))
11. An infant’s pulse rate is measured to be \(130±5\) beats/min. What is the percent uncertainty in this measurement?
12. (a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y?
(b) In 2.00 y?
(c) In 2.000 y?
13. State how many significant figures are proper in the results of the following calculations:
(a) \((106.7)(98.2)/(46.210)(1.01)\)
(b) \((18.7)^2\)
(c) \((1.60×10^{−19})(3712)\)
14. (a) How many significant figures are in the numbers 99 and 100?
(b) If the uncertainty in each number is 1, what is the percent uncertainty in each?
(c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?
15. (a) A person’s blood pressure is measured to be \(120±2\) mm Hg. What is its percent uncertainty?(b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of \(80\) mm Hg?
16. A person measures his or her heart rate by counting the number of beats in \(30s\). If \(40±1\) beats are counted in \(30.0±0.5s\) , what is the heart rate and its uncertainty in beats per minute?
17. A marathon runner completes a \(42.188-km\) course in \(2h\), 30 min, and \(12s\). There is an uncertainty of \(25m\) in the distance traveled and an uncertainty of 1 s in the elapsed time.
(a) Calculate the percent uncertainty in the distance.
(b) Calculate the uncertainty in the elapsed time.
(c) What is the average speed in meters per second?
(d) What is the uncertainty in the average speed?
18. The sides of a small rectangular box are measured to be \(1.80±0.01cm, 2.05±0.02cm,\) and \(3.1±0.1 cm\) long. Calculate its volume and uncertainty in cubic centimeters.
1.4: Approximation
19. How many heartbeats are there in a lifetime?
Solution
Sample answer: \(2×10^9\) heartbeats
20. A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD? (Hint: You must use an approximation for the length of a lifetime).
21. Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of \(10^{−27} kg\) and the mass of a bacterium is on the order of \(10^{−15} kg\).)
This color-enhanced photo shows Salmonella typhimurium (red) attacking human cells. These bacteria are commonly known for causing foodborne illness. Can you estimate the number of atoms in each bacterium? (credit: Rocky Mountain Laboratories, NIAID, NIH)
22. Approximately how many atoms being placed next to each other can become as thich as a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?
23. Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?
Contributors and Attributions
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).