TKWNT+5
=v
#1
:n

:s
b
:c
Spring-Slider Example 3.8
#3
:n
b
:v
.304799999999988
:s
i
:u
m
:d
ft
:c
Free spring length
#4
:n
h
:v
.13761899126871
:s
o
:u
m
:d
ft
:c
Vertical displacement of spring
#5
:n
L
:v
.3344279096573878
:s
o
:u
m
:d
ft
:c
Stretched spring length
#7
:n
k
:v
4378.150000000001
:s
i
:u
N/m
:d
lb/ft
:c
Spring stiffness
#9
:n

:s
b
:c
System forces
#10
:n
F_S
:v
129.715432666545
:s
o
:u
N
:d
lb
:c
Total spring force
#11
:n
F_Sx
:v
118.2235774438389
:s
o
:u
N
:d
lb
:c
x-spring force
#12
:n
F_Sy
:v
53.37864
:s
o
:u
N
:d
lb
:c
y-spring force
#13
:n
N
:v
118.2235774438389
:s
o
:u
N
:d
lb
:c
Normal force from bar
#14
:n
W
:v
53.37864
:s
i
:u
N
:d
lb
:c
Weight of slider
#16
:n

:s
b
:c
Related items
#17
:n
Potential
:v
1.921598560107461
:s
o
:u
N-m
:d
ft-lb
:c
Internal strain energy
#18
:n
Work
:v
7.345914592095617
:s
o
:u
N-m
:d
ft-lb
:c
External mechanical work
#19
:n
Total
:v
-5.424316031988155
:s
o
:u
N-m
:d
ft-lb
:c
Total Potential Energy
=u
#1
:c
Unit Master Sheet by R.L. Norton,
#2
:c
appended by J.E. Akin
#4
:c
length
#5
:f
cm
:m
10
:t
mm
#6
:f
m
:m
100
:t
cm
#7
:f
mm
:m
1000
:t
um
#8
:f
in
:m
2.5399999999999
:t
cm
#9
:f
ft
:m
12
:t
in
#10
:f
mile
:m
5280
:t
ft
#11
:f
in
:m
1000000
:t
uin
#12
:f
1/mm
:m
25.4
:t
1/in
#13
:f
1/cm
:m
2.54
:t
1/in
#14
:f
1/m
:m
.254
:t
1/in
#15
:c
area
#16
:f
in^2
:m
645.1626
:t
mm^2
#17
:f
m^2
:m
1000000
:t
mm^2
#18
:f
cm^2
:m
100
:t
mm^2
#19
:f
ft^2
:m
144
:t
in^2
#20
:c
volume
#21
:f
in^3
:m
16387.1623
:t
mm^3
#22
:f
ft^3
:m
1728
:t
in^3
#23
:f
m^3
:m
1E9
:t
mm^3
#24
:f
cm^3
:m
1000
:t
mm^3
#25
:f
cm^3
:t
cc
#26
:c
force
#27
:f
lb
:m
4.44822
:t
N
#28
:f
N
:m
100000
:t
dyne
#29
:f
ton
:m
2000
:t
lb
#30
:f
kips
:m
1000
:t
lb
#31
:f
lb
:t
lbf
#32
:f
lb
:t
lbm
#33
:c
moments and energy
#34
:f
in-lb
:m
.1138
:t
N-m
#35
:f
ft-lb
:m
12
:t
in-lb
#36
:f
N-m
:m
100
:t
N-cm
#37
:f
N-m
:m
1000
:t
N-mm
#38
:f
N-m
:m
8.850744000000001
:t
in-lb
#39
:f
N-m
:m
.7375620000000001
:t
ft-lb
#40
:f
lb-in
:t
in-lb
#41
:f
N-m
:t
m-N
#42
:f
N-cm
:t
cm-N
#43
:f
N-m
:t
joule
#44
:f
joules
:t
joule
#45
:f
joule
:t
J
#46
:c
pressure and stress
#47
:f
psi
:m
6894.757
:t
Pa
#48
:f
MPa
:m
1000000
:t
Pa
#49
:f
MPa
:t
Mpa
#50
:f
GPa
:m
1000
:t
MPa
#51
:f
GPa
:t
Gpa
#52
:f
Pa
:t
pa
#53
:f
N/m^2
:t
Pa
#54
:f
N/mm^2
:t
MPa
#55
:f
N/mm^2
:m
1000000
:t
N/m^2
#56
:f
N/cm^2
:m
10000
:t
N/m^2
#57
:f
kpsi
:m
1000
:t
psi
#58
:f
psi
:m
144
:t
psf
#59
:f
kpsi
:t
ksi
#60
:f
psig
:t
psi
:a
14.7
#61
:c
acceleration
#62
:f
in/sec^2
:m
2.5399999999999
:t
cm/sec^2
#63
:f
m/sec^2
:m
100
:t
cm/sec^2
#64
:f
m/sec^2
:m
1000
:t
mm/sec^2
#65
:f
m/s^2
:t
m/sec^2
#66
:f
ft/sec^2
:m
12
:t
in/sec^2
#67
:f
ft/s^2
:t
ft/sec^2
#68
:f
G
:m
32.17
:t
ft/sec^2
#69
:c
velocity
#70
:f
in/sec
:m
2.5399999999999
:t
cm/sec
#71
:f
m/sec
:m
100
:t
cm/sec
#72
:f
m/sec
:m
1000
:t
mm/sec
#73
:f
m/s
:t
m/sec
#74
:f
ft/sec
:m
12
:t
in/sec
#75
:f
ft/s
:t
ft/sec
#76
:f
in/s
:t
in/sec
#77
:f
rad/sec
:m
9.549296584
:t
rpm
#78
:f
mph
:m
1.466666666666667
:t
ft/sec
#79
:c
mass
#80
:f
blob
:m
386
:t
lb
#81
:f
slug
:m
32.17
:t
lb
#82
:f
kg
:m
2.204623
:t
lb
#83
:f
kg
:m
1000
:t
g
#84
:f
kg
:m
9.806649999999999
:t
N
#85
:c
mass mom of inertia
#86
:f
lb-in-sec^2
:m
.1138
:t
N-m-sec^2
#87
:f
N-m-sec^2
:t
kg-m^2
#88
:f
lb-in-sec^2
:t
lb-in-s^2
#89
:f
blob-in^2
:t
lb-in-s^2
#90
:f
N-m-sec^2
:t
N-m-s^2
#91
:c
area moment of inertia
#92
:f
in^4
:m
416231.4256
:t
mm^4
#93
:f
m^4
:m
1E12
:t
mm^4
#94
:f
m^4
:m
1E8
:t
cm^4
#95
:f
ft^4
:m
20736
:t
in^4
#96
:f
in^4
:m
.0000004162314256
:t
m^4
#97
:c
density
#98
:f
lb/in^3
:m
27.6805
:t
g/cc
#99
:f
g/cc
:m
.001
:t
g/mm^3
#100
:f
lb/ft^3
:m
1728
:t
lb/in^3
#101
:f
kg/m^3
:m
.000001
:t
g/mm^3
#102
:f
lb/in^3
:m
.002590673575129534
:t
blob/in^3
#103
:f
blob/in^3
:m
.08333333333333333
:t
slug/in^3
#104
:f
slug/ft^3
:m
1728
:t
slug/in^3
#105
:f
kg/mm^3
:m
1000
:t
g/mm^3
#106
:f
SG
:t
g/cc
#107
:c
spring rate
#108
:f
lb/in
:m
175.126
:t
N/m
#109
:f
N/mm
:m
1000
:t
N/m
#110
:f
lb/ft
:m
.08333333333333333
:t
lb/in
#111
:c
angles
#112
:f
radians
:m
57.29577951308232
:t
degrees
:c
 
#113
:f
rad
:m
57.2957795129
:t
deg
#114
:f
rev
:m
360
:t
deg
#115
:f
rad
:t
radian
#116
:c
temperature
#117
:f
C
:m
1.8
:t
F
:a
32
#118
:f
F
:t
R
:a
459.69
#119
:f
C
:t
K
:a
273.16
#120
:c
power
#121
:f
HP
:m
550
:t
ft-lb/sec
#122
:f
ft-lb/sec
:m
60
:t
ft-lb/min
#123
:f
ft-lb/sec
:m
12
:t
in-lb/sec
#124
:f
HP
:m
745.699
:t
watts
#125
:f
kw
:m
1000
:t
watts
#126
:f
HP
:t
hp
#127
:f
N-m/sec
:m
8.850756136188998
:t
in-lb/sec
#128
:f
N-m/sec
:t
watts
#129
:f
watt
:t
watts
#130
:c
flow
#131
:f
cfm
:m
1728
:t
cim
#132
:c
percent
#133
:f
dec%
:m
100
:t
%
#135
:c
fracture mechanics
#136
:f
MPa-m^.5
:m
.909
:t
ksi-in^.5
:c
stress intensity
#137
:f
MPa-m^.5
:m
1000000
:t
Pa-m^.5
:c
stress intensity
#138
:f
ksi-in^.5
:m
1000
:t
psi-in^.5
:c
stress intensity
#139
:f
kpsi-in^.5
:m
1000
:t
psi-in^.5
:c
stress intensity
#141
:c
frequency
#142
:f
1/sec
:m
60
:t
1/min
#143
:f
Hz
:t
1/sec
#144
:f
Hz
:t
hz
#145
:c
time
#146
:f
min
:m
60
:t
sec
#147
:f
hr
:m
60
:t
min
#148
:f
day
:m
24
:t
hr
#149
:f
week
:m
7
:t
day
#150
:f
year
:m
52
:t
week
#151
:f
year
:m
12
:t
month
#152
:c
viscosity
#153
:f
reyn
:t
lb-sec/in^2
:c
     absolute
#154
:f
reyn
:m
6894.696003767111
:t
Pa-s
#155
:f
reyn
:m
1000000
:t
ureyn
#156
:f
Pa-s
:m
1000
:t
mPa-s
#157
:f
cP
:t
mPa-s
#158
:c
   kinematic
#159
:f
m^2/sec
:m
10000
:t
cm^2/sec
#160
:f
cm^2/sec
:t
stoke
#161
:f
stoke
:m
100
:t
cS
#162
:f
m^2/sec
:m
1549.996853506387
:t
in^2/sec
#163
:c
stress intensity
#164
:f
psi-in^.5
:m
1098.843447385385
:t
Pa-m^.5
#165
:f
ksi-in^.5
:m
1000
:t
psi-in^.5
#166
:f
MPa-m^.5
:m
1000000
:t
Pa-m^.5
=l
=f
=r
#1
:r
;Bedford-Fowler Ex 3.8 3-rd Ed
:s
C
#2
:r
; Initial unloaded horizontal spring
:s
C
#4
:r
L^2 = h^2 + b^2     ; right triangle
#6
:r
F_S = k * (L - b)      ; linear spring force
#7
:r
F_Sx = F_S * b / L  ; similar triangles
#8
:r
F_Sy = F_S * h / L  ; similar triangles
#10
:r
; Equilibrium of concurrent forces
:s
C
#11
:r
N -  F_Sx = 0           ; ÓF_x = 0
#12
:r
F_Sy - W = 0           ; ÓF_y = 0
#14
:r
;Potential energy and work terms
:s
C
#15
:r
Potential = 0.5 * k * (L - b)^2  ; strain energy
#16
:r
Work = W * h                          ; external work
#17
:r
Total = Potential - Work         ; total energy
=p
=t
=n
=c
=g
#1
:c
.000001
:i
100
:t
1
:y
Yes
=d
:c
E
:f
0


:v
E
:g
0.000001
:i
1000
:t
100
:p
0.000001
:r
5.00
:e
0
:d
1
:s
0
:n
0
:a
0
=s
:r
0
:v
%Tv,f,3,0,0,1,0
%Or,f,20,1,0,1,0
%Xl,f,0,0,0,2,0,88,88,634,478,320,805,-1,-1,0,0,4,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,4,10,21,31,98
%Xp,f,0,0,0,2,0,110,110,656,500,0,781,-1,-1,0,0,5,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,3,13,25,99
%Xt,f,0,0,0,2,0,132,132,678,522,160,781,-1,-1,0,0,6,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,2,15,100
%Xn,f,0,0,0,2,0,154,154,700,544,320,781,-1,-1,0,0,7,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,2,15,100
%Xc,f,0,0,0,2,0,176,176,722,566,0,757,-1,-1,0,0,8,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,3,15,22,99
%Xf,f,0,0,0,2,0,0,0,993,664,0,805,0,0,0,0,2,-1,0,0,2,-21,700,34,0,0,0,161,Arial,4,16,26,38,98
%Xm,f,0,0,0,0,0,154,203,1147,867,160,757,0,0,0,0,9,-1,0,0,2,0,0,0,0,0,0,0,,0
%Xu,f,29,2,0,2,0,22,29,1015,693,160,805,-4,-23,0,0,3,-1,0,0,2,-21,700,34,0,0,0,161,Arial,5,10,20,34,48,96
%Xv,f,3,0,0,2,0,0,458,1213,922,480,815,-4,-23,0,0,0,-1,0,0,2,-21,700,34,0,0,0,161,Arial,6,6,14,22,30,40,91
%Xr,f,20,1,0,2,0,6,3,851,464,-1,-1,-4,-23,2,0,1,-1,0,0,3,-21,700,34,0,0,0,161,Arial,2,9,103
\G,0,960,1344,1,-1,-1
\G,0,1920,1344,1,-1,-1
\C,0,1920,0,0,3