2010Pearson
PearsonEducation,
Education,Inc.,
Inc.,Upper
UpperSaddle
SaddleRiver,
River,NJ.
NJ.All
Allrights
rightsreserved.
reserved.This
Thismaterial
materialisisprotected
protectedunder
underall
allcopyright
copyrightlaws
lawsas
asthey
theycurrently
currently
©©2011
exist.No
Noportion
portionofofthis
thismaterial
materialmay
maybe
bereproduced,
reproduced,ininany
anyform
formor
orby
byany
anymeans,
means,without
withoutpermission
permissionin
inwriting
writingfrom
fromthe
thepublisher.
publisher.
exist.
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.
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>ks2, and (d) kN>ms.
a)
mMN = 10–6(106) N = N
Ans
b)
N
N
=
= 106 N/m = MN/m
mm 10–6 m
Ans
c)
106 N
MN
=
= N/s2
2
(103)2 s2
ks
Ans
d)
N
kN 103 N
= 106
= MN/s
=
s
ms 10–3 s
Ans
1–3. Represent each of the following quantities in the
correct SI form using an appropriate prefix: (a) 0.000431 kg,
(b) 35.3(103) N, and (c) 0.00532 km.
a)
0.000431 kg = 0.000431(103) g = 0.431 g
Ans
b)
35.3(103) N = 35.3 kN
Ans
c)
0.00532 km = 0.00532(103) 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)
Mg 103 kg
=
= 106 kg/s = Gg/s
ms 10–3 s
Ans
b)
1N
N
=
= 103 N/m = kN/m
mm 10–3 m
Ans
c)
10–3 kg
mN
= –4
= kN/(kg · s)
(kg · ms) 10 kg · s
Ans
11
SM_CH01.indd
01 Ch01 1-6.indd1 1
2/15/11
6/12/09 9:30:50
8:02:52 AM
AM
2011
Pearson
Education,
Inc.,
Upper
Saddle
River,
All
rights
reserved.
This
material
is protected
under
copyright
laws
they
currently
©©
2010
Pearson
Education,
Inc.,
Upper
Saddle
River,
NJ.NJ.
All
rights
reserved.
This
material
is protected
under
allall
copyright
laws
as as
they
currently
exist.
portion
this
material
may
reproduced,
any
form
any
means,
without
permission
writing
from
publisher.
exist.
NoNo
portion
ofof
this
material
may
bebe
reproduced,
in in
any
form
oror
byby
any
means,
without
permission
in in
writing
from
thethe
publisher.
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)
3
(109) N
kN/ms = (10 ) N =
= GN/s
–6
s
(10 ) s
Ans
b)
6
(109) g
Mg/mN = (10 ) g =
= Gg/N
N
(10–3) N
Ans
c)
MN/(kg # ms) =
Ans
(109) N
(106) N
=
= GN/(kg # s)
–3
kg · s
kg · (10 ) s
1–6. Represent each of the following to three significant
figures and express each answer in SI units using an
appropriate prefix: (a) 45 320 kN, (b) 568(105) mm, and (c)
0.005 63 mg.
Ans
a)
45 320 kN = 45.3(104)N = 45.3 MN
b)
568(105) mm = 56.8(104)(10–3)m = 56.8 km Ans
c)
0.005 63 mg = 5.63(10–6) g = 5.63 mg
Ans
3 6
1–7.
) )slugs
1–7. A rocket
rocket has
has aa mass
mass ofof250(10
3.65(10
kg on earth.
Specify
its massininSI
SIunits.
units If
and
its weight
SImoon,
units.
Specify (a)
its weight
the(b)
rocket
is on in
the
If
the rocket
is on the moon,
the acceleration
where
the acceleration
due where
to gravity
is gm = 1.62due
m/sto2,
gravity
is gtom three
to weight
three in
significant
= 5.30significant
ft>s2, determine
determine
figures its
SI units
figures
itsinweight
in SI units and (d) its mass in SI units.
and its (c)
mass
SI units.
Applying Eq. 1–3, we have
a) We = mg = [3.65(106) kg] (9.81 m/s2)
= 35.81(106) kg · m/s2
= 35.8
Ans
⎛g ⎞
⎛ 1.62 m/s 2 ⎞
Wm = We ⎜ m ⎟ = (35.81 MN) ⎜
= 5.91
⎝g⎠
⎝ 9.81 m/s 2 ⎟⎠
d) Since the mass is independent of its location, then
mm = me = 3.65(106) kg = 3.65 Gg
Ans
*1–8.
, determine
itsits
speed
in
*1–8. If
If aacar
carisistraveling
travelingatat5588mi>h
km/h,
determine
speed
in meters per
kilometers
persecond.
hour and meters per second.
⎛
⎞⎛
⎞⎛
⎞
88.5 km/h = ⎜88.5 km⎟ ⎜1000 m⎟ ⎜ 1 h ⎟ = 24.6 m/s
⎝ 1 h ⎠ ⎝ 1 km ⎠ ⎝ 3600 s⎠
Ans
22
SM_CH01.indd
01
Ch01 1-6.indd2 2
2/15/11 8:02:54
9:30:51 AM
AM
6/12/09
2010Pearson
PearsonEducation,
Education,Inc.,
Inc.,Upper
UpperSaddle
SaddleRiver,
River,NJ.
NJ.All
Allrights
rightsreserved.
reserved.This
Thismaterial
materialisisprotected
protectedunder
underall
allcopyright
copyrightlaws
lawsas
asthey
theycurrently
currently
©©2011
exist.No
Noportion
portionofofthis
thismaterial
materialmay
maybe
bereproduced,
reproduced,ininany
anyform
formor
orby
byany
anymeans,
means,without
withoutpermission
permissionin
inwriting
writingfrom
fromthe
thepublisher.
publisher.
exist.
1–9. The
The pascal
pascal (Pa)
(Pa) is
is actually
actually a very small unit of
2
lb>ft2.
1 Pa
= 1 N>m2 to
pressure. Given
(1 Pathis,
= 1 N/m
), and
a atmospheric
pressure
To show
convert
2
2
at
sea level is 101.325
this?
Atmospheric
pressurekN/m
at sea. How
level many
is 14.7pascals
lb> in . is
How
many
pascals is this?
1 ATM = 101.325 kN/m2
= 101 kPa
Ans
1–10. 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/s2)(10 kg) = 98.1 N
Ans
b)
W = (9.81 m/s2)(0.5 g)(10–3 kg/g) = 4.90 mN
Ans
c)
W = (9.81 m/s2)(4.5 Mg)(103 kg/Mg) = 44.1 kN
Ans
1–11. 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) > (0.0356 kN),
(b) (0.004 53 Mg)(201 ms), and (c) 435 MN> 23.2 mm.
a)
–3
3
(354 mg)(45 km)/0.0356 kN = [354(10 ) g][45(10 ) m]
3
0.0356(10 ) N
0.447(103) g · m
N
= 0.447 kg · m/N
=
b)
c)
Ans
(0.00453 Mg)(201 ms) = [4.53(10–3)(103) kg][201(10–3) s]
= 0.911 kg · s
Ans
6
9
435 MN/23.2 mm = 435(10 ) N = 18.75(10 ) N = 18.8 GN/m Ans
23.2(10–3) m
m
*1–12. The specific weight (wt.
(wt./vol.)
> vol.) of brass is 85
520kN/m
lb>ft3.
Determine its density (mass
(mass/vol.)
> vol.) in
in SI units. Use an
appropriate prefix.
⎛ 85.000 N⎞
85 kN/m3 = ⎜
⎝ m 3 ⎟⎠
⎛ 1 kg ⎞
⎜⎝ 9.81 N ⎟
⎠
= 8.66 Mg/m3
33
SM_CH01.indd
01 Ch01 1-6.indd3 3
2/15/11
6/12/09 9:30:51
8:02:55 AM
AM
©©2010
Upper
Saddle
River,
NJ.
All
rights
reserved.
This
material
is protected
under
allall
copyright
laws
as as
they
currently
2011Pearson
PearsonEducation,
Education,Inc.,
Inc.,
Upper
Saddle
River,
NJ.
All
rights
reserved.
This
material
is protected
under
copyright
laws
they
currently
exist.
No
portion
ofof
this
material
may
bebe
reproduced,
inin
any
form
oror
byby
any
means,
without
permission
in in
writing
from
thethe
publisher.
exist.
No
portion
this
material
may
reproduced,
any
form
any
means,
without
permission
writing
from
publisher.
*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 1m 2
r2
Where G = 66.73(10–12) m3/(kg · s2)
F = 66.73(10–12)
8(12)
� (0.8) � = 10.0(10
2
–9
) N = 10.0 nN
Ans
W1 = 8(9.81) = 78.5 N
Ans
W2 = 12(9.81) = 118 N
Ans
44
SM_CH01.indd
01
Ch01 1-6.indd4 4
2/15/11
6/12/09 9:30:51
8:02:56 AM
AM
2010Pearson
PearsonEducation,
Education,Inc.,
Inc.,Upper
UpperSaddle
SaddleRiver,
River,NJ.
NJ.All
Allrights
rightsreserved.
reserved.This
Thismaterial
materialisisprotected
protectedunder
underall
allcopyright
copyrightlaws
lawsas
asthey
theycurrently
currently
©©2011
exist.No
Noportion
portionofofthis
thismaterial
materialmay
maybe
bereproduced,
reproduced,ininany
anyform
formor
orby
byany
anymeans,
means,without
withoutpermission
permissionin
inwriting
writingfrom
fromthe
thepublisher.
publisher.
exist.
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
a)
m=
W 20(10–3) kg · m/s2
=
= 2.04 g
9.81 m/s2
g
Ans
b)
m=
W 150(103) kg · m/s2
=
= 15.3 Mg
9.81 m/s2
g
Ans
c)
m=
W 60(106) kg · m/s2
=
= 6.12 Gg
9.81 m/s2
g
Ans
1–15. 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)2 = 40 000(106) N2 = 0.04(1012) N2 = 0.04 MN2
Ans
b)
(0.005 mm)2 = 25(10–12) m2 = 25 mm2
Ans
c)
(400 m)3 = 0.064(109) m3 = 0.064 km3
Ans
1–16. 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. 1–2.
F=G
m 1m 2
r2
m3 ⎞
N= ⎛
⎜⎝kg · s2⎟⎠
F=G
⎛ kg · kg⎞ = kg · m
⎜⎝ m2 ⎟⎠
s2
(Q.E.D.)
m 1m 2
r2
= 66.73(10–12)
�200(200)
0.6 �
2
= 7.41(10 ) N = 7.41 mN
–6
Ans
55
SM_CH01.indd
01 Ch01 1-6.indd5 5
2/15/11
6/12/09 9:30:51
8:02:57 AM
AM
2011Pearson
PearsonEducation,
Education,
Inc.,
Upper
Saddle
River,
NJ.
All
rights
reserved.
This
material
is protected
under
copyright
laws
they
currently
©©2010
Inc.,
Upper
Saddle
River,
NJ.
All
rights
reserved.
This
material
is protected
under
allall
copyright
laws
as as
they
currently
exist.
No
portion
this
material
may
reproduced,
any
form
any
means,
without
permission
writing
from
publisher.
exist.
No
portion
ofof
this
material
may
bebe
reproduced,
inin
any
form
oror
byby
any
means,
without
permission
in in
writing
from
thethe
publisher.
*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)
b)
6
⎛
⎞
8532 m
0.631 Mm/(8.60 kg)2 = ⎜0.631(10 ) m⎟ =
2
kg2
⎝ (8.60) kg2 ⎠
(35 mm)2(48 kg)3
= 8.53(103) m/kg2 = 8.53 km/kg2
Ans
= [35(10–3) m]2 (48 kg)3 = 135 m2kg3
Ans
1–18. Evaluate (204 mm)(0.00457 kg) (34.6 N) to three
significant figures and express the answer in SI units using
an appropriate prefix.
(204 mm)(0.004 57 kg)/(34.6N) =
=
⎛ [204(10–3) m][4.57(10–3) kg] ⎞
⎟⎠
⎜⎝
34.6 N
⎛ 26.9(10–6) m · kg ⎞
⎜⎝
⎟⎠
1N
= 26.9 mm · kg/N
Ans
66
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9:30:51 AM
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