© Pearson Education South Asia Pte Ltd 2014. 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.

1–1. Round off the following numbers to three significant

figures: (a) 4.65735 m, (b) 55.578 s, (c) 4555 N, and
(d) 2768 kg.

1
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–2.

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).

SOLUTION
(103) N (109) N
a) kN>ms = = = GN>s Ans.
(10-6) s s

(106) g (109) g
b) Mg>mN = = = Gg>N Ans.
(10-3) N N

(106) N (109) N
c) MN>(kg # ms) = = GN>(kg # s)
kg # s
=
kg # (10 ) s
-3
Ans.

2
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–3.

Represent each of the following combinations of units in

the correct SI form using an appropriate prefix: (a) m>ms,
(b) mkm, (c) ks>mg, and (d) km # mN.

SOLUTION
m 11023 m
a) m>ms = ¢ ≤ = ¢ ≤ = km>s Ans.
1102-3 s s

b) mkm = 1102-611023 m = 1102-3 m = mm Ans.

1102 s 3
1102 s
9
c) ks>mg = -6
= = Gs>kg Ans.
1102 kg kg

d) km # mN = 10 3
m 10 -6
N = 10 -3
m # N = mm # N Ans.

3
 © Pearson Education South Asia Pte Ltd 2014. 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.

1-4 .

A concrete column has diameter d and length L. If the density (mass/volume) of concrete is U,
determine the weight of the column in newtons.

Units Used:
3
Mg 10 kg

3
kip 10 lb

Given:

d 350 mm

L 2m
Mg
U 2.45
3
m

Solution:
2
S §¨
d· 3
V ¸ L V 0.19242 m
© 2¹
W 1U V 2 g W 0.471 (103) (9.81) 4.62 (103) N
4.62 kN Ans.

4
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–5. Represent each of the following combinations of

units in the correct SI form: (a) Mg>ms, (b) N>mm, and
(c) mN>(kg # ms).

5
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–6. Represent each of the following combinations of

units in the correct SI form using an appropriate prefix:
(a) kN> ms,(b) Mg> kN, and (c) kN>(kg # ms).

a) kN / ms =
(10 ) N = (10 ) N = MN / s
3 6

Ans.
(10 ) s s
−3

b) Mg / kN =
(10 ) g = (10 ) g = kg / N
6 3

Ans.
(10 ) N N
3

c) kN / (kg ⋅ ms) =
(10 ) N = (10 ) N = GN / (kg ⋅ s)
3 9

Ans.
kg ⋅ (10 ) s
−6 kg ⋅ s

6
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–7.

A rocket has a mass of 3.529 (106) kg on earth. Specify

(a) its mass in SI units and (b) its weight in SI units. If the
rocket is on the moon, where the acceleration due to gravity
is gm = 1.61 m>s 2, determine to three significant figures
(c) its weight in SI units and (d) its mass in SI units.

SOLUTION

( )
a) 3.529 106 kg = 3.53Gg Ans.

( ) (
b) We = mg = ⎡⎢3.529 106 kg ⎤⎥ 9.81 m / s 2
⎣ ⎦ )
( ) 6
= 34.619 10 kg ⋅ m / s 2

= 34.6 MN Ans.

( ) (
c) Wm = mgm = ⎡⎢3.529 106 kg ⎤⎥ 1.61 m / s 2
⎣ ⎦ )
( )
= 5.682 106 N = 5.68 MN Ans.
Or
⎛g ⎞ ⎛ 1.61 m / s2 ⎞
Wm = We ⎜ m ⎟ = (34.619 MN) ⎜ = 5.68 MN
⎜ 9.81 m / s2 ⎟⎟
⎝ g ⎠ ⎝ ⎠
d) Since the mass is independent of tis location, then
mm = me = 3.53Gg Ans.

7
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–8.

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, (b) (35 mm)2(48 kg)3.

SOLUTION
0.631 A 106 B m 8532 m
a) (0.631 Mm)>(8.60 kg)2 = a b =
(8.60)2 kg2 kg2

= 8.53 A 103 B m>kg2 = 8.53 km>kg2 Ans.

b) (35 mm)2(48 kg)3 = C 35 A 10 - 3 B m D 2 (48 kg)3 = 135 m2 # kg3 Ans.

8
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–9. Determine the mass in kilograms of an object that

has a weight of (a) 50 mN, (b) 250 kN, and (c) 80 MN.
Express the answer to three significant figures.

Applying Eq. 1 – 3, we have

a) m =
(−3
)
W 50 10 kg ⋅ m / s
=
2

= 5.10 g Ans.
g 9.81 m / s 2

b) m = =
3
( )
W 250 10 kg ⋅ m / s
2

= 25.5 Mg Ans.
g 9.81 m / s 2

c) m = =
( )
6
W 80 10 kg ⋅ m / s
2

= 8.15 Gg Ans.
g 9.81 m / s2

9
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–10. 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.

10
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–11.

Evaluate each of the following and express with an

appropriate prefix: (a) 1430 kg22, (b) 10.002 mg22, and
(c) 1230 m23.

SOLUTION
a) 1430 kg22 = 0.18511062 kg2 = 0.185 Mg2 Ans.

b) 10.002 mg22 = 32110-62 g42 = 4 mg2 Ans.

c) 230 m 3
= 0.23 103 m 3
= 0.0122 km3 Ans.

11
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–12.

Determine the mass 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.

SOLUTION
Applying Eq. 1–3, we have

W 20 A 10 - 3 B kg # m>s2
a) m = = = 2.04 g Ans.
g 9.81 m>s2

W 150 A 103 B kg # m>s2

b) m = = = 15.3 Mg Ans.
g 9.81 m>s2

W 60 A 106 B kg # m>s2
c) m = = = 6.12 Gg Ans.
g 9.81 m>s2

12
 © Pearson Education South Asia Pte Ltd 2014. 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.

1-13.

Represent each of the following with SI units having an appropriate prefix: (a) S1, (b) S2, (c) S3.

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 Ans.

( b) S2 8.368 kN Ans.

( c) S3 893 g Ans.

13
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–14. Evaluate (204 mm)(0.00457 kg)> (34.6 N) to three

significant figures and express the answer in SI units using
an appropriate prefix.

14
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–15.

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.

SOLUTION
m1 m2
F = G
r2
Where G = 66.73 A 10-12 B m3>(kg # s2)

8(12)
F = 66.73 A 10 - 12 B B R = 10.0 A 10 - 9 B N = 10.0 nN Ans.
(0.8)2

W1 = 8(9.81) = 78.5 N Ans.

W2 = 12(9.81) = 118 N Ans.

15
 © Pearson Education South Asia Pte Ltd 2014. 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.

1–16.

If a man weighs 690 newtons on earth, specify (a) his mass

in kilograms. If the man is on the moon, where the
acceleration due to gravity is gm = 1.61 m>s 2, determine
(b) his weight in newtons and (c) his mass in kilograms.

SOLUTION
690
a) m = = 70.3 kg Ans.
9.81

1.61
b) W = 690c d = 113 N Ans.
9.81

690
c) m = = 70.3 kg Ans.
9.81

16