Table Of Content

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 mN km⋅μN = 1mm⋅N 1 © 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 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. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 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: S1 = 8653 ms S2 = 8368 N S3 = 0.893 kg Solution: (a) S1 = 8.653 s 3 © 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Engineering Mechanics - Statics Chapter 1 (b) S2 = 8.368kN (c) S3 = 893g 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 = 45.3MN (b) y = 56.8km (c) z = 5.63μg 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. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Engineering Mechanics - Statics Chapter 1 b = (0.00457 kg) c = (34.6 N) Solution: ab 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 Convert: (a) S to N⋅m , (b) S to kN/m3, (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: S1 = 200g lb⋅ft lb S2 = 350g 3 ft ft S3 = 8 hr 5 © 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Engineering Mechanics - Statics Chapter 1 Solution: (a) S1 = 271N⋅m kN (b) S2 = 55.0 3 m mm (c) S3 = 0.677 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: m1 = 10 kg m2 = 0.5 gm m3 = 4.50 Mg Solution: (a) W = m1g W = 98.1 N (b) W = m2g W = 4.90mN (c) W = m3g W = 44.1 kN 6 © 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 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. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Engineering Mechanics - Statics Chapter 1 Mg ρ = 2.45 3 m Solution: 2 ⎛d⎞ V = π⎜ ⎟ L V = 192.423 L ⎝2⎠ W = ρV 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 Wg = 667.233 N h = 72 in h = 1.829 m 8 © 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 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: m1 = 8 kg m2 = 12 kg d = 800 mm Solution: G m1 m2 F = 2 d F = 10.0 nN W1 9 W1 = m1 g W1 = 78.5 N = 7.85× 10 F W2 10 W2 = m2 g W2 = 118 N = 1.18× 10 F Problem 1-17 Using the base units of the SI system, show that F = G(m m )/r2 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. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Engineering Mechanics - Statics Chapter 1 Given: m1 = 150 kg r = 275 mm Solution: 2 G m1 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 = 0.040MN 2 (b) y = 25.0μm 3 (c) z = 0.0640km 10 © 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.