Engineering Mechanics - Statics Chapter 1 Problem 1-1 Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) m/ms (b) μkm (c) ks/mg (d) km⋅μN Units Used: − 6 μN = 10 N − 6 μkm = 10 km 9 Gs = 10 s 3 ks = 10 s − 3 mN = 10 N − 3 ms = 10 s Solution: (a) m 3 m = 1 × 10 ms s m km = 1 ms s − 3 (b) μkm = 1 × 10 m μkm = 1mm (c) ks 9 s = 1 × 10 mg kg ks Gs = 1 mg kg − 3 (d) km⋅μN = 1 × 10 m N km⋅μN = 1mm⋅N 1 © 2007 .R C . iH eb el r . ilbuP she d yb eP arsno Ecud atino , nI c ,. pU per Saeld iR ev r , .JN lA rights reserev .d hT is am teria l is prto ecte d nu ed r a l cpo ry ight al sw as the y cru rent yl eix st . oN pro tino fo this am teria l am y eb reprcudo e ,d in an y rof m ro yb an y em ans , iw thtuo perim ssino in rw iting rf mo the pilbu sher. Engineering Mechanics - Statics Chapter 1 Problem 1-2 Wood has a density d. What is its density expressed in SI units? Units Used: Mg = 1000 kg Given: slug d = 4.70 3 ft Solution: 1slug = 14.594 kg Mg d = 2.42 3 m Problem 1-3 Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) Mg/mm (b) mN/μs (c) μm⋅Mg Solution: 3 6 Mg 10 kg 10 kg Gg (a) = = = mm − 3 m m 10 m Mg Gg = mm m − 3 3 mN 10 N 10 N kN (b) = = = μs − 6 s s 10 s mN kN = μs s − 6 3 − 3 (c) μm⋅Mg = (10 m)(10 kg) = 10 m⋅kg μm⋅Mg = mm⋅kg 2 © 2007 .R C . iH eb el r . ilbuP she d yb eP arsno Ecud atino , nI c ,. pU per Saeld iR ev r , .JN lA rights reserev .d hT is am teria l is prto ecte d nu ed r a l cpo ry ight al sw as the y cru rent yl eix st . oN pro tino fo this am teria l am y eb reprcudo e ,d in an y rof m ro yb an y em ans , iw thtuo perim ssino in rw iting rf mo the pilbu sher. Engineering Mechanics - Statics Chapter 1 Problem 1-4 Represent each of the following combinations of units in the correct SI form: (a) Mg/ms, (b) N/mm, (c) mN/( kg⋅μs). Solution: 3 6 Mg 10 kg 10 kg Gg (a) = = = ms − 3 s s 10 s Mg Gg = ms s N 1 N 3 N kN (b) = = 10 = mm − 3 m m 10 m N kN = mm m − 3 mN 10 N kN (c) = = kg⋅μs − 6 kg⋅s 10 kg⋅s mN kN = kg⋅μs kg⋅s Problem 1-5 Represent each of the following with SI units having an appropriate prefix: (a) S , (b) S , (c) S . 1 2 3 Units Used: − 3 3 kg = 1000 g ms = 10 s kN = 10 N Given: S = 8653 ms 1 S = 8368 N 2 S = 0.893 kg 3 Solution: (a) S = 8.653 s 1 3 © 2007 .R C . iH eb el r . ilbuP she d yb eP arsno Ecud atino , nI c ,. pU per Saeld iR ev r , .JN lA rights reserev .d hT is am teria l is prto ecte d nu ed r a l cpo ry ight al sw as the y cru rent yl eix st . oN pro tino fo this am teria l am y eb reprcudo e ,d in an y rof m ro yb an y em ans , iw thtuo perim ssino in rw iting rf mo the pilbu sher. Engineering Mechanics - Statics Chapter 1 (b) S2 = 8.368 kN (c) S3 = 893 g Problem 1-6 Represent each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) x, (b) y, and (c) z. Units Used: 6 MN = 10 N − 6 μg = 1 × 10 gm 3 kN = 10 N Given: x = 45320 kN 5 y = (568 × 10 ) mm z = 0.00563 mg Solution: (a) x = 45.3 MN (b) y = 56.8 km (c) z = 5.63 μg Problem 1-7 Evaluate ( a⋅b)/c to three significant figures and express the answer in SI units using an appropriate prefix. Units Used: − 6 μm = 10 m Given: a = (204 mm) 4 © 2007 .R C . iH eb el r . ilbuP she d yb eP arsno Ecud atino , nI c ,. pU per Saeld iR ev r , .JN lA rights reserev .d hT is am teria l is prto ecte d nu ed r a l cpo ry ight al sw as the y cru rent yl eix st . oN pro tino fo this am teria l am y eb reprcudo e ,d in an y rof m ro yb an y em ans , iw thtuo perim ssino in rw iting rf mo the pilbu sher. Engineering Mechanics - Statics Chapter 1 b = (0.00457 kg) c = (34.6 N) Solution: a b μm⋅kg l = l = 26.945 c N Problem 1-8 If a car is traveling at speed v, determine its speed in kilometers per hour and meters per second. Given: mi v = 55 hr Solution: km v = 88.514 hr m v = 24.6 s Problem 1-9 3 Convert: (a) S to N⋅m , (b) S to kN/m , (c) S to mm/s. Express the result to three 1 2 3 significant figures. Use an appropriate prefix. Units Used: 3 kN = 10 N Given: S = 200g lb⋅ ft 1 lb S = 350g 2 3 ft ft S = 8 3 hr 5 © 2007 .R C . iH eb el r . ilbuP she d yb eP arsno Ecud atino , nI c ,. pU per Saeld iR ev r , .JN lA rights reserev .d hT is am teria l is prto ecte d nu ed r a l cpo ry ight al sw as the y cru rent yl eix st . oN pro tino fo this am teria l am y eb reprcudo e ,d in an y rof m ro yb an y em ans , iw thtuo perim ssino in rw iting rf mo the pilbu sher. Engineering Mechanics - Statics Chapter 1 Solution: (a) S = 271 N⋅m 1 kN (b) S = 55.0 2 3 m mm (c) S = 0.677 3 s Problem 1-10 What is the weight in newtons of an object that has a mass of: (a) m , (b) m , (c) m ? Express 1 2 3 the result to three significant figures. Use an appropriate prefix. Units Used: 3 Mg = 10 kg − 3 mN = 10 N 3 kN = 10 N Given: m = 10 kg 1 m = 0.5 gm 2 m = 4.50 Mg 3 Solution: (a) W = m g 1 W = 98.1 N (b) W = m g 2 W = 4.90 mN (c) W = m g 3 W = 44.1 kN 6 © 2007 .R C . iH eb el r . ilbuP she d yb eP arsno Ecud atino , nI c ,. pU per Saeld iR ev r , .JN lA rights reserev .d hT is am teria l is prto ecte d nu ed r a l cpo ry ight al sw as the y cru rent yl eix st . oN pro tino fo this am teria l am y eb reprcudo e ,d in an y rof m ro yb an y em ans , iw thtuo perim ssino in rw iting rf mo the pilbu sher. Engineering Mechanics - Statics Chapter 1 Problem 1-11 If an object has mass m, determine its mass in kilograms. Given: m = 40 slug Solution: m = 584 kg Problem 1-12 The specific weight (wt./vol.) of brass is ρ. Determine its density (mass/vol.) in SI units. Use an appropriate prefix. Units Used: 3 Mg = 10 kg Given: lb ρ = 520 3 ft Solution: Mg ρ = 8.33 3 m Problem 1-13 A concrete column has diameter d and length L. If the density (mass/volume) of concrete is ρ, determine the weight of the column in pounds. Units Used: 3 Mg = 10 kg 3 kip = 10 lb Given: d = 350 mm L = 2 m 7 © 2007 .R C . iH eb el r . ilbuP she d yb eP arsno Ecud atino , nI c ,. pU per Saeld iR ev r , .JN lA rights reserev .d hT is am teria l is prto ecte d nu ed r a l cpo ry ight al sw as the y cru rent yl eix st . oN pro tino fo this am teria l am y eb reprcudo e ,d in an y rof m ro yb an y em ans , iw thtuo perim ssino in rw iting rf mo the pilbu sher. Engineering Mechanics - Statics Chapter 1 Mg ρ = 2.45 3 m Solution: 2 ⎛ d⎞ V = π ⎜ ⎟ L V = 192.423 L ⎝ 2⎠ W = ρ V W = 1.04 kip Problem 1-14 The density (mass/volume) of aluminum is ρ. Determine its density in SI units. Use an appropriate prefix. Units Used: Mg = 1000 kg Given: slug ρ = 5.26 3 ft Solution: Mg ρ = 2.17 3 m Problem 1-15 Determine your own mass in kilograms, your weight in newtons, and your height in meters. Solution: Example W = 150 lb m = W m = 68.039 kg W g = 667.233 N h = 72 in h = 1.829 m 8 © 2007 .R C . iH eb el r . ilbuP she d yb eP arsno Ecud atino , nI c ,. pU per Saeld iR ev r , .JN lA rights reserev .d hT is am teria l is prto ecte d nu ed r a l cpo ry ight al sw as the y cru rent yl eix st . oN pro tino fo this am teria l am y eb reprcudo e ,d in an y rof m ro yb an y em ans , iw thtuo perim ssino in rw iting rf mo the pilbu sher. Engineering Mechanics - Statics Chapter 1 Problem 1-16 Two particles have masses m and m , respectively. If they are a distance d apart, determine 1 2 the force of gravity acting between them. Compare this result with the weight of each particle. Units Used: 3 − 12 m G = 66.73 × 10 2 kg⋅s − 9 nN = 10 N Given: m = 8 kg 1 m = 12 kg 2 d = 800 mm Solution: G m m 1 2 F = 2 d F = 10.0 nN W 1 9 W = m g W = 78.5 N = 7.85 × 10 1 1 1 F W 2 10 W = m g W = 118 N = 1.18 × 10 2 2 2 F Problem 1-17 2 Using the base units of the SI system, show that F = G(m m )/r is a dimensionally 1 2 homogeneous equation which gives F in newtons. Compute the gravitational force acting between two identical spheres that are touching each other. The mass of each sphere is m , and 1 the radius is r. Units Used: 3 − 6 − 12 m μN = 10 N G = 66.73 10 2 kg⋅s 9 © 2007 .R C . iH eb el r . ilbuP she d yb eP arsno Ecud atino , nI c ,. pU per Saeld iR ev r , .JN lA rights reserev .d hT is am teria l is prto ecte d nu ed r a l cpo ry ight al sw as the y cru rent yl eix st . oN pro tino fo this am teria l am y eb reprcudo e ,d in an y rof m ro yb an y em ans , iw thtuo perim ssino in rw iting rf mo the pilbu sher. Engineering Mechanics - Statics Chapter 1 Given: m = 150 kg 1 r = 275 mm Solution: 2 G m 1 F = 2 (2r) F = 4.96 μN Since the force F is measured in Newtons, then the equation is dimensionally homogeneous. Problem 1-18 Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) x, (b) y, (c) z. Units Used: 6 MN = 10 N 3 kN = 10 N − 6 μm = 10 m Given: 2 x = (200 kN) 2 y = (0.005 mm) 3 z = (400 m) Solution: 2 (a) x = 0.040 MN 2 (b) y = 25.0 μm 3 (c) z = 0.0640 km 10 © 2007 .R C . iH eb el r . ilbuP she d yb eP arsno Ecud atino , nI c ,. pU per Saeld iR ev r , .JN lA rights reserev .d hT is am teria l is prto ecte d nu ed r a l cpo ry ight al sw as the y cru rent yl eix st . oN pro tino fo this am teria l am y eb reprcudo e ,d in an y rof m ro yb an y em ans , iw thtuo perim ssino in rw iting rf mo the pilbu sher.