Solved Problems from Cutnell & Johnson Ed 7

Basic Physics I – Selected Solved Problems from Cutnell & Johnson Textbook 7th Edition – Wiley Compiled by Associate Professor Dr. Jaafar Jantan aka Dr JJ Faculty of Applied Sciences, University Teknologi MARA, Shah Alam, Selangor, Malaysia http://drjj.uitm.edu.my HP: +60193551621; Email: jjnita@salam.uitm.edu.my

Introduction and Mathematical Concepts

2. Vesna Vulovic survived the longest fall on record without a parachute when her plane exploded and she fell 6 miles, 551 yards. What is this distance in meters? REASONING We use the facts that 1 mi = 5280 ft, 1 m = 3.281 ft, and 1 yd = 3 ft. With these facts we construct three conversion factors: (5280 ft)/(1 mi) = 1, (1 m)/(3.281 ft) = 1, and (3 ft)/(1 yd) = 1. SOLUTION By multiplying by the given distance d of the fall by the appropriate conversion factors we find that

5280 ft d 6 mi 1 mi

1 m 3.281 ft

3 ft 551 yd 1 yd

1 m 10 159 m 3.281 ft

3.

Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) on flat sections of the road. What is this speed in (a) kilometers per hour (km/h) and (b) meters per second (m/s)? REASONING a. To convert the speed from miles per hour (mi/h) to kilometers per hour (km/h), we need to convert miles to kilometers. This conversion is achieved by using the relation 1.609 km = 1 mi (see the page facing the inside of the front cover of the text). b. To convert the speed from miles per hour (mi/h) to meters per second (m/s), we must convert miles to meters and hours to seconds. This is accomplished by using the conversions 1 mi = 1609 m and 1 h = 3600. SOLUTION a. Multiplying the speed of 34.0 mi/h by a factor of unity, (1.609 km)/(1 mi) = 1, we find the speed of the bicyclists is

mi mi 1.609 km km Speed = 34.0 1 34.0 54.7 h h 1 mi h b. Multiplying the speed of 34.0 mi/h by two factors of unity, (1609 m)/(1 mi) = 1 and (1 h)/(3600 s) = 1, the speed of the bicyclists is

mi mi 1609 m 1 h m Speed = 34.0 11 34.0 15.2 h s h 1 mi 3600s ___________________________________________________________________________ 4. Azelastine hydrochloride is an antihistamine nasal spray. A standard size container holds one fluid ounce (oz) of the liquid. You are searching for this medication in a European drugstore and are asked how many milliliters (mL) there are in one fluid ounce. Using the following conversion factors, determine the number Compiled by A.P. Dr. Jaafar Jantan aka Dr. JJ, FSG, UiTM http://drjj.uitm.edu.my; email: jjnita@salam.uitm.edu.my Page | 1

PHY 406

Solved Problems from Cutnell & Johnson Ed 7

of

milliliters

in

a

volume

of , and

one

fluid

ounce: .

,

REASONING Multiplying an equation by a factor of 1 does not alter the equation; this is the basis of our solution. We will use factors of 1 in the following forms:

1 gal 1 , since 1 gal = 128 oz 128 oz

3.785 103 m3 1 , since 3.785 103 m3 = 1 gal 1 gal 1 mL 1 , since 1 mL = 106 m3 6 3 10 m

SOLUTION The starting point for our solution is the fact that Volume = 1 oz Multiplying this equation on the right by factors of 1 does not alter the equation, so it follows that 1 gal 3.785 103 m3 1 mL Volume 1 oz 111 1 oz 29.6 mL 128 oz 106 m3 1 gal

Note that all the units on the right, except one, are eliminated algebraically, leaving only the desired units of milliliters (mL).

5.

The mass of the parasitic wasp Caraphractus cintus can be as small as (a) grams (g), (b) milligrams (mg), and (c) micrograms (μg)? REASONING

. What is this mass in

When converting between units, we write down the units explicitly in the calculations and treat them like any algebraic quantity. We construct the appropriate conversion...