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Conceptual Questions

Exercise $$\PageIndex{1}$$

Models are particularly useful in relativity and quantum mechanics, where conditions are outside those normally encountered by humans. What is a model?

Exercise $$\PageIndex{2}$$

How does a model differ from a theory?

Exercise $$\PageIndex{3}$$

If two different theories describe experimental observations equally well, can one be said to be more valid than the other (assuming both use accepted rules of logic)?

Exercise $$\PageIndex{4}$$

What determines the validity of a theory?Add text here. For the automatic number to work, you need to add the "AutoNum" template (preferably at the end) to the page.

Exercise $$PageIndex{5}$$

Certain criteria must be satisfied if a measurement or observation is to be believed. Will the criteria necessarily be as strict for an expected result as for an unexpected result?

Exercise $$\PageIndex{6}$$

Can the validity of a model be limited, or must it be universally valid? How does this compare to the required validity of a theory or a law?

Exercise $$\PageIndex{7}$$

Classical physics is a good approximation to modern physics under certain circumstances. What are they?

Exercise $$\PageIndex{8}$$

When is it necessary to use relativistic quantum mechanics?

Exercise $$\PageIndex{9}$$

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Conceptual Questions

What is the relationship between the accuracy and uncertainty of a measurement?

Prescriptions for vision correction are given in units called diopters (D). Determine the meaning of that unit. Obtain information (perhaps by calling an optometrist or performing an internet search) on the minimum uncertainty with which corrections in diopters are determined and the accuracy with which corrective lenses can be produced. Discuss the sources of uncertainties in both the prescription and accuracy in the manufacture of lenses.

Problems & Exercises

Express your answers to problems in this section to the correct number of significant figures and proper units.

Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?

2 kg

A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?

(a) A car speedometer has a 5.0% uncertainty. What is the range of possible speeds when it reads 90 km/h? (b) Convert this range to miles per hour. (1 km=0.6214 mi)

1. 85.5to 94.5 km/h
2. 53.1to 58.7 mi/h

An infant’s pulse rate is measured to be 130±5 beats/min. What is the percent uncertainty in this measurement?

(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?

(a) 7.6×107 beats

(b) 7.57×107 beats

(c) 7.57×107 beats

A can contains 375 mL of soda. How much is left after 308 mL is removed?

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) (1.60×1019)(3712).

1. 3
2. 3
3. 3

(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?

(a) If your speedometer has an uncertainty of 2.0km/h at a speed of 90 km/h, what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h, what is the range of speeds you could be going?

a) 2.2%

(b) 59 to 61 km/h

(a) A person’s blood pressure is measured to be 120±2mm 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?

A person measures his or her heart rate by counting the number of beats in 30 s. If 40±1 beats are counted in 30.0±0.5s, what is the heart rate and its uncertainty in beats per minute?

80±3beats/min

What is the area of a circle 3.102cm in diameter?

If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon?

A marathon runner completes a 42.188-km course in 2h, 30 min, and 12 s. There is an uncertainty of 25 m 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?

The sides of a small rectangular box are measured to be 1.80±0.01cm2.05±0.02cm, and 3.1±0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where1lbm=0.4539kg. (a) If there is an uncertainty of 0.0001kg in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

The length and width of a rectangular room are measured to be 3.955±0.005m and 3.050±0.005m. Calculate the area of the room and its uncertainty in square meters.

A car engine moves a piston with a circular cross section of 7.500±0.002cm diameter a distance of 3.250±0.001cmto compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.

Conceptual Questions

Identify some advantages of metric units.

Problems & Exercises

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?

$$27.8 m/s$$

$$62.1 mph$$

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/hspeed limit?

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.

$$\frac{1.0m}{s}$$=$$\frac{1.0m}{s}$$* $$\frac{3600s}{1hr}$$*$$\frac{1km}{1000m}$$= $$3.6 km/h$$

4. American football is played on a $$100$$-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals $$3.281$$ feet.)

5. 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.)

length: 377 ft4.53×103 in. width: 280 ft3.3×103 in.

6. 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.)

7. Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)

8.847 km

8. The speed of sound is measured to be 342 m/s on a certain day. What is this in km/h?

9. 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?

(a) 1.3×10−9 m

(b) 40 km/My

10. (a) Refer to Table to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?