24

CHAPTER 2

The sta ndard second is based o n the rate of vibration of the cesiu m ato m . The vibratio n is produced by radio waves, and it is not affected by such external infl uences as temperature and g ravity. The rate of vibratio n can be tuned precisely to the rad io waves that are producing it. The definition adopted in 1967 is 1 second (s) :;: 9 192 631 770 vibrations of cesium·133 atoms Figure 2·5. A decimal ciock. This watch was made in anticipation of the adoption of decimal days. which never took place .

When the metric syste m was first proposed , an effort was made to redefine other time intervals as we ll. One proposal ca lled for a mo nth of three ten-day weeks. In this system , the day was divid ed into ten hours, the ho ur into 100 minutes, and each minute into 100 seconds. A d ecimal wa tch of this kind is shown in Figure 2·5. However, d ecimal days were never officially ado pted in any country. Thus, the numbers on our clocks a nd cale ndars remain conspicuo us exce ptions to the me tric sys tem .

Q UESTIONS : GRO UP A

PROBLEMS: GROUP A

1. (a) What is the mathematica l basis fo r the me tric system ? (b) What is its o ffi· cial na me? (c) Why is it th e syste m used in scie nce? 2. What is the most recent definition of the standa rd meter? 3. What is the o nly funda me ntal quantity meas ured by comparison with a physi· cal object? Why? 4. A box of crackers a t the grocery store is labeled " 1 pound (454 g)." What is wrong with this label?

1. Conve rt each o f the following to the units shown: = _ mL (a) 2 dm' =_ L (b) 350 em' (e) 16 g =I'g = _ mm (d) 0.75 km (e) 675 mg =- g = _ dm' (f) 0.596 m' =_ L (g) 75 m 2 = _ Col ! (h ) 2 h 10 min = _ s (i) 462 ILm = _ em (j) 35 kmlh = _ mls 2. From the data in Fig ure 2·1, d ete rmine how many ki lometers there are in a mile by making a ratio of a d ista nce measured in mil es to the correspond· ing one in kilo me te rs . 3. (a) Calcul ate the cross·sectiona l a rea of one of the sta ndard kilogram cylinde rs shown in Fig ure 2-4. (b) What is the volume? (The data fo r the heig ht and diameter of the cylind ers are in the caption .) 4. How many two-liter bottles of carbon· a ted wa ter would it take to fill a jug that holds 5 dm)?

GROUP B 5. (a) What was the origin al standard for a second? (b) Wha l is it now? (c) Why was it changed? 6. Id entify the follow ing units as fund ame nta l or derived. In w hich branch of physics is each used ? (a) newton, (b) li ter/mole, (c) cand ela , (d) ki logram, (c) ampere. 7. A box of cookies is labeled , " 0.5 kg (4.9 N)." Wou ld th e labe l be correct if you took the cookies to the moon , where the fo rce of gravity is less?

25

MEASUREMENT AND PROBLEM SOLVING

CROUP B

grams of the soda, if it is mostly wa ter? (c) What is its weight in newtons? 7. How m uch fo rce will it take in ord er for you to lift this book, which has a mass of 1350 g? 8. How ma ny fo ur-liter buckets of wa ter d o you need to fill your bath tub, which is 123 em long, 57.2 em deep, and 33.0 em wide?

5. A cra ne mu st lift a crate w ith a mass of 3.5 x 1IY kg. (a) How much force wiU be required? (b) On the moon, do you think it would ta ke more or less fo rce to lift the cra te? Explain . 6. (a) When you bu y a two-lite r bottle of soda pop, how many dOl 3 have you purchased? How many cm3 ? How ma ny mL? (b) What is the mass in

MAKIJ\IC Ai\,D RECORDINC MEASUREMENTS 2.6 Accuracy The measurement of a physical quantity is always subject to some degree of uncertainty. There a re several reasons for this: the limitations inherent in the construction of the measurin g instrument or device, the conditions und er which the measurement is made, and the different ways in w hich the person uses or reads the instrument, as you ca n see in Figure 2-6. Consequ ently, in reporting the measurements made during a scientific expe ri ment, it is necessary to ind icate the degree of uncertainty so far as it is known . One way to express the uncertainty of a measurement is in terms of acclIracy . Accuracy refers to the closelless of a mea-

surement to the accepted value for a specific physical qllmllity. It is expressed as eithe r an absolute or a relative error. Absolute error is the actual differe nce between the measured va lu e

Figure 2-6. The accuracy of measurement depends upon the instrument used and the care with which the reading is made.

and the accepted value. The eq uation for absolute error is E. = IO - AI

w here Ea is the absolute error, 0 is the observed (measured) va lue, and A is the acce pted va lu e. (The vertica l lines mea n the absolu te va lu e is used, rega rdless of sign.) Relative error is expressed as a percentage and is ofte n called the percentage e rro r. It is calcula ted as follows:

E.

Er = A

Accuracy is expressed as absolute error or re/alive error.

x 1OO %

whe re E, is the relati ve e rror, Ea the absolute error, a nd A the acce pted va lue. 2.7 Precision In common usage, accuracy and precisioll are often used synonymously. But in science it is im portan t to make a distinction between them . You should lea rn

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