FIN-469 Investments Analysis
Professor Michel A. Robe
Practice Set #4 and Solutions.
What to do with this practice set?
To help students prepare for the assignment and the exams, practice sets with solutions will be
handed out. These sets contain worked-o
Problem 6.83 The pressure force exerted on the piston is 2 kN toward the left. Determine the couple M
necessary to keep the system in equilibrium.
B
300 mm
350 mm
45
A
C
M
400 mm
Solution: From the diagram, the coordinates of point B are (d, d)
where d =
Problem 6.94 A load W = 2 kN is supported by the
members ACG and the hydraulic actuator BC. Determine the reactions at A and the compressive axial force
in the actuator BC.
A
0.75 m
B
C
1m
G
0.5 m
W
1.5 m
Solution:
1.5 m
The sum of the moments about A is
Problem 6.59 Determine the forces on member BC
and the axial force in member AC.
0.3 m
0.5 m
800 N
B
0.4 m
C
A
Solution:
Element BC: The sum of the moments about B:
M = (0.3)800 + (0.8)C = 0,
300 m
from which C = 300 N . The sum of the forces
Fy = B 800 +
Problem 6.79 What are the magnitudes of the forces
exerted by the pliers on the bolt at A when 30-lb forces
are applied as shown? (B is a pinned connection.)
6 in
45
2
in
30 lb
B
A
30 lb
Solution:
Element AB: The sum of the moments about B:
MB = 2F (6)30
4.100 Separate streams of air and water flow through the compressor and heat exchanger
arrangement shown in Fig. P4.100. Steady-state operating data are provided on the figure. Heat
transfer with the surroundings can be neglected, as can all kinetic and p
PROBLEM. 5. a
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nub: 3h. that tug 1 um but irrewnrbh.
nnumvnc i sure b :
5mm. Mona:
(l) The $131. lung"! 53 R in 1N. Inca-upon M, 39".
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PROBLE n4 4.106
A simple gas turbine power cycle operating at steadv
state with air as the working substance is shown in Fig.14. IDG.
The cycle components include an air compressor mounted i
on the same shaft as the turbine. The air is heated in the'
high
PEoBlE M 5- 1'
5.9. Use the Kelvin~Planck statement of the second law to
show that the specied process is irreversible.
(a) As shown in Fig. P5911, a hot thermal reservoir is
separated from a cold thermal reservoir by a cylindrical rod
insulate/\on its la
W
5.3 Classify the following processcs of a. closed system as
passiblc. impossible. or mdererminate.
Entropy Entropy Entropy
Change Transfer Production
(2) >0 0
(b) <0 >0
(c) 0 >0
(d) >0 >0
(e) 0 <0
(0 >0 <0
(5) <0 <0
FIJI]. (a Medlyskh:
[Eu-um: _ E
Problem 6.31 For the truss in Problem 6.30, use the
method of sections to determine the axial forces in members BC, CF , and F G.
A
B
C
D
E
F
G
H
1m
Solution:
BC
C
J
D
100 kN
45
1m
CF
Solving BC = 300 kN (T )
CF = 141.4 kN (C)
J
F
FG
G
H
1m
F G = 200 kN (
Problem 7.39 Determine the x coordinate of the centroid of the Boeing 747s vertical stabilizer.
y
11 m
48
x
70
12.5 m
Solution: We can treat the stabilizer as a rectangular area (1) with
two triangular cutouts (2 and 3): The dimensions a and b are
y
a = 1
Problem 6.54 For the frame shown, determine the
reactions at the built-in support A and the force exerted
on member AB at B.
A
200 lb
B
6 ft
C
20
6 ft
Solution:
and
3 ft
3 ft
Element AB: The equilibrium equations are:
FX = AX + BX = 0,
A
200 lb
B
FY = AY
Portfolio Optimization Questions
Risk Management
Dr. Castro Fall 2002
1. Suppose that your wealth is $250,000. You buy a $200,000 house and invest the remainder in
a risk-free asset paying an annual interest rate of 6%. There is a probability of .001 that
Portfolio Optimization Questions
Risk Management
Dr. Castro Fall 2002
1. Suppose that your wealth is $250,000. You buy a $200,000 house and invest the remainder in
a risk-free asset paying an annual interest rate of 6%. There is a probability of .001 that
Portfolio Optimization Questions
Risk Management
Dr. Castro Fall 2002
1. Suppose that your wealth is $250,000. You buy a $200,000 house and invest the remainder in
a risk-free asset paying an annual interest rate of 6%. There is a probability of .001 that
Portfolio Optimization Questions
Risk Management
Dr. Castro Fall 2002
1. Suppose that your wealth is $250,000. You buy a $200,000 house and invest the remainder in
a risk-free asset paying an annual interest rate of 6%. There is a probability of .001 that
Problem 6.98 The Pratt bridge truss supports loads at
F , G, and H. Determine the axial forces in members
BC, BG, and F G.
Solution:
The angles of the cross-members are = 45 .
The complete structure as a free body:
B
C
D
4m
E
A
F
G
The sum of the moments
Problem 6.75 The pin support B will safely support a
force of 24-kN magnitude. Based on this criterion, what
is the largest mass m that the frame will safely support?
C
500 mm
100 mm
E
D
B
300 mm
m
A
300 mm
Solution: The weight is given by W = mg = 9.81 g
Problem 6.71 The man using the exercise machine
is holding the 80-lb weight stationary in the position
shown. What are the reactions at the built-in support E
and the pin support F ? (A and C are pinned connections.)
2 ft 2 in
1 ft 6 in
2 ft
D
B
C
A
9 in
Problem 7.16 Determine the coordinates of the centroid of the area.
y
(1, 1)
y = x 1/2
y = x2
Let dA be a vertical strip: The area dA =
Solution:
x1/2 x2 dx, so
1
5/2
4 1
x
x dA
x3/2 x3 dx
x4
5/2
0
x = A
= 01
=
1 = 0.45.
x3/2
x3
dA
x1/2 x2 dx
3/2
3
Problem 7.23 The Supermarine Spitre used by Great
Britain in World War II had a wing with an elliptical
prole. Determine the coordinates of its centroid.
y
y2 = 1
x2 +
a2
b2
x
2b
a
Solution:
y
x2 y2 =
+
y
a2
1
x2 +
y2 =
b2
a2
1
b2
b
x
b
x
2b
a
By symm
Problem 7.10 Determine the coordinates of the centroid of the metal plates cross-sectional area.
y
1
y = 4 x 2 ft
4
x
Let dA bea vertical strip:
The area dA = y dx = 4 14 x2 dx. The curve intersects the x
1 2
axis where 4 4 x = 0, or x = 4.
Therefore
4
Problem 7.4 The x coordinate of the centroid of the
area shown in Problem 7.3 is x = 2. What is the y
coordinate of the centroid?
From Problem 7.4, a = 2.5
2.5
2.5
1
1 6
y(y dx)
x dx
y dA
2
2
0
0
y =
=
= 2.5
2.5
dA
y dx
x3 dx
Solution:
0
2.5
2.5
4x3
Problem 6.103
Determine the forces on member
ABC, presenting your answers as shown in Fig. 6.35.
D
400 lb
2 ft
200 ft-lb
A
1 ft
B
C
100 lb
1 ft
E
2 ft
2 ft
Solution: The complete structure as a free body: The sum of the
moments:
MA = 100(1) 400(6) 200 + 4
m1
247.5 ft 3
ft 3
13.75
lb
= 18.0 lb
Solving for the final mass
m2 = 18.0 lb + 2.9 lb = 20.9 lb
The specific volume at the final state is
V
247.5 ft 3
v2
= 11.84 ft3/lb
m2
20.9 lb
The energy rate balance reduces to
dU cv
Qcv Wcv m i hi m ehe
dt
There