, Chapter 1 - Section A - Mathcad Solutions
1.4 The equation that relates deg F to deg C is: t(F) = 1.8 t(C) + 32. Solve this
equation by setting t(F) = t(C).
Guess solution: t 0
Given t = 1.8t 32 Find(t) 40 Ans.
F
1.5 By definition: P= F = massg Note: Pressures are in
A gauge pressure.
2
P 3000bar D 4mm A D A 12.566 mm
2
4
m F
F PA g 9.807 mass mass 384.4 kg Ans.
2 g
s
F
1.6 By definition: P= F = massg
A
2
P 3000atm D 0.17in A D 2
4
ft F
F PA g 32.174 mass mass 1000.7 lbm Ans.
2 g
sec
1.7 Pabs = gh Patm
gm m
13.535 g 9.832 h 56.38cm
3
cm s2
Patm 101.78kPa Pabs gh Patm Pabs 176.808 kPa Ans.
gm ft
1.8 13.535 g 32.243 h 25.62in
3 2
cm s
Patm 29.86in_Hg Pabs gh Patm Pabs 27.22 psia Ans.
1
, gm m
1.10 Assume the following: 13.5 g 9.8
3 2
cm s
P
P 400bar h h 302.3 m Ans.
g
1.11 The force on a spring is described by: F = Ks x where Ks is the spring
constant. First calculate K based on the earth measurement then gMars
based on spring measurement on Mars.
On Earth:
m
F = massg = Kx mass 0.40kg g 9.81 x 1.08cm
2
s
F N
F massg F 3.924 N Ks Ks 363.333
x m
On Mars:
3
x 0.40cm FMars Kx FMars 4 10 mK
FMars
mK
gMars gMars 0.01 Ans.
mass kg
d MP d MP
1.12 Given: P = g and: = Substituting: P= g
dz RT dz RT
P z
Denver 1 Denver Mg
Separating variables and integrating: dP = dz
P
P 0 RT
sea
PDenver Mg zDenver
After integrating: ln =
Psea RT
Taking the exponential of both sides Mg z
Denver
and rearranging: PDenver = Psea e RT
gm m
Psea 1atm M 29 g 9.8
mol 2
s
2
, 3
cm atm
R 82.06 T (10 273.15)K zDenver 1mi
molK
Mg
zDenver 0.194
RT
Mg z
Denver
PDenver Psea e
RT PDenver 0.823 atm Ans.
PDenver 0.834 bar Ans.
1.13 The same proportionality applies as in Pb. 1.11.
ft ft
gearth 32.186 gmoon 5.32 lmoon 18.76
2 2
s s
gearth
learth lmoon learth 113.498
gmoon
M learthlbm M 113.498 lbm Ans.
wmoon Mgmoon wmoon 18.767 lbf Ans.
5.00dollars hr 0.1dollars hr
1.14 costbulb 10 costelec 10 70W
1000hr day kWhr day
dollars dollars
costbulb 18.262 costelec 25.567
yr yr
dollars
costtotal costbulb costelec costtotal 43.829
yr Ans.
ft
1.15 D 1.25ft mass 250lbm g 32.169
2
s
3
1.4 The equation that relates deg F to deg C is: t(F) = 1.8 t(C) + 32. Solve this
equation by setting t(F) = t(C).
Guess solution: t 0
Given t = 1.8t 32 Find(t) 40 Ans.
F
1.5 By definition: P= F = massg Note: Pressures are in
A gauge pressure.
2
P 3000bar D 4mm A D A 12.566 mm
2
4
m F
F PA g 9.807 mass mass 384.4 kg Ans.
2 g
s
F
1.6 By definition: P= F = massg
A
2
P 3000atm D 0.17in A D 2
4
ft F
F PA g 32.174 mass mass 1000.7 lbm Ans.
2 g
sec
1.7 Pabs = gh Patm
gm m
13.535 g 9.832 h 56.38cm
3
cm s2
Patm 101.78kPa Pabs gh Patm Pabs 176.808 kPa Ans.
gm ft
1.8 13.535 g 32.243 h 25.62in
3 2
cm s
Patm 29.86in_Hg Pabs gh Patm Pabs 27.22 psia Ans.
1
, gm m
1.10 Assume the following: 13.5 g 9.8
3 2
cm s
P
P 400bar h h 302.3 m Ans.
g
1.11 The force on a spring is described by: F = Ks x where Ks is the spring
constant. First calculate K based on the earth measurement then gMars
based on spring measurement on Mars.
On Earth:
m
F = massg = Kx mass 0.40kg g 9.81 x 1.08cm
2
s
F N
F massg F 3.924 N Ks Ks 363.333
x m
On Mars:
3
x 0.40cm FMars Kx FMars 4 10 mK
FMars
mK
gMars gMars 0.01 Ans.
mass kg
d MP d MP
1.12 Given: P = g and: = Substituting: P= g
dz RT dz RT
P z
Denver 1 Denver Mg
Separating variables and integrating: dP = dz
P
P 0 RT
sea
PDenver Mg zDenver
After integrating: ln =
Psea RT
Taking the exponential of both sides Mg z
Denver
and rearranging: PDenver = Psea e RT
gm m
Psea 1atm M 29 g 9.8
mol 2
s
2
, 3
cm atm
R 82.06 T (10 273.15)K zDenver 1mi
molK
Mg
zDenver 0.194
RT
Mg z
Denver
PDenver Psea e
RT PDenver 0.823 atm Ans.
PDenver 0.834 bar Ans.
1.13 The same proportionality applies as in Pb. 1.11.
ft ft
gearth 32.186 gmoon 5.32 lmoon 18.76
2 2
s s
gearth
learth lmoon learth 113.498
gmoon
M learthlbm M 113.498 lbm Ans.
wmoon Mgmoon wmoon 18.767 lbf Ans.
5.00dollars hr 0.1dollars hr
1.14 costbulb 10 costelec 10 70W
1000hr day kWhr day
dollars dollars
costbulb 18.262 costelec 25.567
yr yr
dollars
costtotal costbulb costelec costtotal 43.829
yr Ans.
ft
1.15 D 1.25ft mass 250lbm g 32.169
2
s
3