1 1. Round off the following numbers to three significant figures: (a) m, (b) s, (c) 4555 N, and (d) 2768 kg.

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1 1 1. Round off the following numbers to three significant figures: (a) m, (b) s, (c) 4555 N, and (d) 2768 kg. a) 4.66 m b) 55.6 s c) 4.56 kn d) 2.77 Mg Ans 1 2. Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) mmn, (b) N>mm, (c) MN>ks 2, and (d) kn>ms. a) mmn 10 6 (10 6 ) N N Ans b) c) d) N N 10 6 N/m MN/m Ans mm 10 6 m MN ks 2 kn ms 10 6 N N/s 2 Ans (10 3 ) 2 s N N 10 3 s 106 s MN/s Ans 1 3. Represent each of the following quantities in the correct SI form using an appropriate prefix: (a) kg, (b) 35.3(10 3 ) N, and (c) km. a) kg (10 3 ) g g Ans b) 35.3(10 3 ) N 35.3 kn Ans c) km (10 3 ) m 5.32 m Ans *1 4. Represent each of the following combinations of units in the correct SI form: (a) Mg>ms, (b) N>mm, and (c) mn>(kg # ms). a) b) c) Mg 10 3 kg 10 6 kg/s Gg/s Ans ms 10 3 s N 1 N 10 3 N/m kn/m Ans mm 10 3 m mn (kg ms) 10 3 kg 10 kn/(kg s) Ans 4 kg s 1 1 SM_CH01.indd 1 2/15/11 9:30:50 AM

2 1 5. Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) kn>ms, (b) Mg>mN, and (c) MN>(kg # ms). a) kn/ms (10 3 ) N (10 ) N (10 6 ) s s GN/s Ans b) Mg/mN (10 6 ) g (10 ) g (10 3 ) N N Gg/N Ans (10 6 ) N kg (10 3 ) s (10 9 ) N kg s c) MN/(kg # ms) GN/(kg # s) Ans 1 6. Represent each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) kn, (b) 568(10 5 ) mm, and (c) mg. a) kn 45.3(10 4 )N 45.3 MN Ans b) 568(10 5 ) mm 56.8(10 4 )(10 3 )m 56.8 km Ans c) mg 5.63(10 6 ) g 5.63 mg Ans 1 7. A rocket has a mass of of 250( (10 3 ) 6 ) slugs kg on earth. Specify (a) its weight its mass in in SI SI units. If and the (b) rocket its weight is on in the SI moon, units. If where the rocket the acceleration is the moon, due where to gravity the acceleration is g m 1.62 due m/s to 2, gravity determine is gto m three 5.30significant ft>s 2, determine figures its to weight three in significant SI units figures and its (c) mass its in weight SI units. in SI units and (d) its mass in SI units. Applying Eq. 1 3, we have a) W e mg [3.65(10 6 ) kg] (9.81 m/s 2 ) 35.81(10 6 ) kg m/s Ans 2 g m 1.62 m/s W m W e (35.81 MN) g 9.81 m/s d) Since the mass is independent of its location, then m m m e 3.65(10 6 ) kg 3.65 Gg Ans *1 8. If a car is is traveling at at 5588 mi>h km/h,, determine its its speed speed in kilometers in per second. hour and meters per second km/h 88.5 km 1000 m 24.6 m/s Ans 1 h 1 h 1 km 3600 s 2 2 SM_CH01.indd 2

3 1 9. The pascal (Pa) is actually a very small unit of pressure. Given To show (1 Pa this, 1 N/m convert 2 ), and 1 Pa a atmospheric 1 N>m 2 to pressure lb>ft 2. at Atmospheric sea level is pressure kn/m at sea 2. How level many is 14.7 pascals lb> in 2. is How this? many pascals is this? 1 ATM kn/m kpa Ans What is the weight in newtons of an object that has a mass of: (a) 10 kg, (b) 0.5 g, and (c) 4.50 Mg? Express the result to three significant figures. Use an appropriate prefix. a) W (9.81 m/s 2 )(10 kg) 98.1 N Ans b) W (9.81 m/s 2 )(0.5 g)(10 3 kg/g) 4.90 mn Ans c) W (9.81 m/s 2 )(4.5 Mg)(10 3 kg/mg) 44.1 kn Ans Evaluate each of the following to three significant figures and express each answer in Sl units using an appropriate prefix: (a) 354 mg(45 km) > ( kn), (b) ( Mg)(201 ms), and (c) 435 MN> 23.2 mm. a) (354 mg)(45 km)/ kn [354(10 3 ) g][45(10 3 ) m] (10 3 ) N 0.447(10 3 ) g m N kg m/n Ans b) ( Mg)(201 ms) [4.53(10 3 )(10 3 ) kg][201(10 3 ) s] kg s Ans c) 435 MN/23.2 mm 435(10 6 ) N 18.75(10 9 ) N 18.8 GN/m Ans 23.2(10 3 ) m m *1 12. The specific weight (wt./vol.) > of brass is kn/m lb>ft 3. Determine its density (mass/vol.) > in SI units. Use an appropriate prefix N 85 kn/m 3 m Mg/m 3 1 kg 9.81 N 3 3 SM_CH01.indd 3

4 *1 13. Two particles have a mass of 8 kg and 12 kg, respectively. If they are 800 mm apart, determine the force of gravity acting between them. Compare this result with the weight of each particle. F G m 1 m 2 r 2 Where G 66.73(10 12 ) m 3 /(kg s 2 ) 8(12) F 66.73(10 12 ) 10.0(10 9 ) N 10.0 nn Ans (0.8) 2 W 1 8(9.81) 78.5 N W 2 12(9.81) 118 N Ans Ans 4 4 SM_CH01.indd 4

5 1 14. Determine the mass in kilograms of an object that has a weight of (a) 20 mn, (b) 150 kn, and (c) 60 MN. Express the answer to three significant figures. Applying Eq. 1 3, we have W 20(10 a) m 3 ) kg m/s g Ans g 9.81 m/s 2 W 150(10 b) m 3 ) kg m/s Mg Ans g 9.81 m/s 2 W 60(10 c) m 6 ) kg m/s Gg Ans g 9.81 m/s Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) (200 kn) 2, (b) (0.005 mm) 2, and (c) (400 m) 3. a) (200 kn) (10 6 ) N (10 12 ) N MN 2 Ans b) (0.005 mm) 2 25(10 12 ) m 2 25 mm 2 Ans c) (400 m) (10 9 ) m km 3 Ans Using the base units of the SI system, show that Eq. 1 2 is a dimensionally homogeneous equation which gives F in newtons. Determine to three significant figures the gravitational force acting between two spheres that are touching each other.the mass of each sphere is 200 kg and the radius is 300 mm. Using Eq F G m m 1 2 r 2 N m 3 kg kg kg m (Q.E.D.) kg s 2 m 2 s 2 F G m m 1 2 r (10 12 ) 200(200) (10 6 ) N 7.41 mn Ans 5 5 SM_CH01.indd 5

6 *1 17. Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) (0.631 Mm) (8.60 kg) 2, and (b) (35 mm) 2 (48 kg) 3. a) Mm/(8.60 kg) (10 6 ) m (8.60) 2 kg m kg (10 3 ) m/kg km/kg 2 Ans b) (35 mm) 2 (48 kg) 3 [35(10 3 ) m] 2 (48 kg) m 2 kg 3 Ans Evaluate (204 mm)( kg) (34.6 N) to three significant figures and express the answer in SI units using an appropriate prefix. (204 mm)( kg)/(34.6n) [204(10 3 ) m][4.57(10 3 ) kg] 34.6 N 26.9(10 6 ) m kg 1 N 26.9 mm kg/n Ans 6 6 SM_CH01.indd 6