CE399 Diagnostic Test
Transcript of CE399 Diagnostic Test
CE399 Diagnostic Test
General
The following multiple-choice questions are indicative of the scope and difficulty of the problems that
will be covered in the CE399 Bridge Program during the Summer 2013 quarter. The questions are
intended to be similar in scope and difficulty to those contained in the morning session of the current
Fundamentals of Engineering (FE) exam.
The questions are organized into the following categories:
Math (18 questions)
Chemistry (12 questions)
Engineering Physics (Statics/Dynamics/Strength of Materials) (19 questions)
General Physics (12 questions)
This time limit for the diagnostic exam is 122 minutes. The time limit is not enforced, but should be
considered when evaluating your performance.
Supplied Reference Handbook When taking the following diagnostic test, you should use the NCEES Fundamentals of Engineering Supplied Reference Handbook. No other notes will be allowed during the actual bridge program, nor during the FE exam. You may download a PDF copy of the Supplied Reference Handbook at the following website: http://ncees.org/exams/study-materials/download-fe-supplied-reference-handbook/
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Diagnostic Criteria/Evaluation To be prepared for the upper-division Civil/Environmental Engineering program at PSU, it is important to have a firm grasp of the fundamental principles that underlie the concepts covered in the junior and senior-level classes. This diagnostic test is intended to gauge your understanding of these fundamental principles. Although there is not a firm “passing” criteria for the diagnostic test, the guidelines below may help you decide whether or not to register for the summer bridge program (CE399):
Number of Correct Answers (out of 61)
Recommendation
< 31 Take CE399
31-45 Consider taking CE399
(may want to discuss situation with instructor)
> 45 CE399 not suggested
Solutions There is an answer key PDF on the Bridge Program website (http://www.pdx.edu/cee/SummerBridge). The answer key includes worked-out solutions and references the portion of the Supplied Reference Handbook (if any) required to solve the problem.
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Mathematics
Math-001
Question
What is the general form of the equation for a line whose x-intercept is 8 and y-intercept is -6?
(A) 036123 =y+x
(B) 02443 =yx
(C) 036412 =+yx
(D) 02434 =x+y
Solution The answer is (B)
Determine slope of the line.
12
12
xx
yy=m
80
06
=m
4/3=m
Once the slope and y-intercept are known, the slope intercept form is applied.
Slope intercept: b+mx=y
0=b+ymx
064
3=yx
02443 =yx
Reference Equations for straight lines are on page 21 of the Supplied Reference Handbook.
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Math-002
Question
What is the length of the line with slope 5/2 from the point (8,3) to the y-axis?
(A) 11.5
(B) 17
(C) 33
(D) 21.5
Solution The answer is (D)
The point slope equation form: b+mx=y
2
5=m and known point is )(=yx, 8,3
b+= 82
53
82
53
=b
17=b
The complete equation is
172
5x=y
2
12
2
12 xx+yy=d
2208173 +=d
21.5=d
Reference Equations of straight lines are on page 21 of the Supplied Reference Handbook.
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Math-003
Question
A line goes through the point 56, and is perpendicular to the line 83x +=y . What is the equation of
the line?
(A) 104
1+x=y
(B) 73
1+x=y
(C) 53
26y x=
(D) 93
23y +x=
Solution The answer is (B)
The slopes of two lines that are perpendicular are related by
2
1
1
m=m
The slope of the line perpendicular to the line with slope 31 =m is
3
11
1
2
=m
=m
The equation for the line is given in the form
b+mx=y
3/1=m and a known point is 6,5=yx,
7
63
15
63
15
=b
=b
b+=
73
1+x=y
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Reference Equations for straight lines are on page 21 of the Supplied Reference Handbook.
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Math-004
Question
What is the equation of the circle passing through the (x, y) points (0,0), (6,0), and (0,-6)?
(A) 96322
=+y++x
(B) 156922
=+y++x
(C) 186622
=+y+x
(D) 183322
=+y+x
Solution The answer is (D)
The center radius form of the equation of a circle is
222r=ky+hx
Substitute the first two points, (0,0) and (6,0) .
222
222
06
00
r=k+h
r=k+h
Since both equations are equal to r2, set the left hand sides equal. Simplify and solve for h
3
6
6
22
2222
=h
h=h
h+k=k+h
Substitute the third point, (0,-6), into the center radius form.
22260 r=k+h
Set this third equation equal to the first equation. Simplify and solve for k.
3
6
6
22
2222
=k
k=k
k+h=k+h
Now that h and k are known substitute into the first equation to determine r2.
183322
222
=+
r=k+h
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Substitute the known values of h, k, and r2 into the center-radius form.
183322
=+y+x
Reference The equation for standard form of a circle is on page 22 of the Supplied Reference Handbook.
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Math-005
Question
For the three vectors u, v, and w, what is the product uvw ?
(A) 25
(B) 34
(C) 57
(D) 215
Solution The answer is (C)
Find the cross product v x u:
312
524
kji=uv
kj+i=
k+j+i=uv
8211
44101256
Now calculate the dot product.
57
=
++=uvw 1882311
Reference The vector identities are on page 24 of the Supplied Reference Handbook.
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Math-006
Question A surveyor is trying to determine the height of a column CD. The angle from horizontal to the top of the
column is observed to be 50°31' at point A. The surveyor walks 12 m directly away from point A to point
B and finds the angle from the horizontal to the top of the column is 36°12'. What is the approximate
height of column CD?
(A) m22
(B) m50
(C) m210
(D) m63
Solution The answer is (A)
12 m
36°12’ 50°31’
A
B
C
D
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Work with triangle ADC.
'°=θ
θ'+°+°=°
2139
315090180
Work with triangle BDC.
'°=φ
°=φ'+°°+''+°
2714
1802139901236
Work with triangle BAC. Use the law of sines to find side b.
m=b
b
'°=
m
'°
28.4
12sin36
12
27sin14
Work with triangle ADC. The pipeline length is
mm=
'°m=L
2221.9
31sin5028.4
Reference The trigonometric identities are on page 22 of the Supplied Reference Handbook.
12 m
36°12’ 50°31’
A
B
C
D
L
b
φ
Θ
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Math-007
Question
Which of the following numbers is equal to 35log6 ?
(A) 3.68
(B) 1.98
(C) 2.3
(D) 0.778
Solution The answer is (B)
Using the logarithmic identity : b
x=x
a
ab
log
loglog
6log35log35log 10610 =
1.98
6log
35log35log
10
106
=
=
Reference The logarithmic identities are on page 22 of the Supplied Reference Handbook.
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Math-008
Question What is the complete solution to the following differential equation?
40
105y
=y
=y'+
(A) 165x +e
(B) 125 5x +e
(C) 615 2x +e
(D) 22 5x +e
Solution The answer is (D)
Find the homogeneous solution. The characteristic equation is:
05 =+r
The root is r = -5. The homogeneous solution is
5x
1
1
eC=
eC=y ax
h
Find a particular solution. The forcing function is a constant. The particular solution is constant.
0
2
=y'
C=y
p
p
Substitute the particular solution into the original equation.
2
10
5C05y
2
2
=C
=
+=y'+
The solution is
25x +Ce=y+y=xy ph
Use the initial condition to determine the coefficient C1.
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2
42
420
1
1
05
1
=C
=+C
=+eC=y
The complete solution is
22 5x +e=xy
Reference The differential equation definitions are on page 30 of the Supplied Reference Handbook.
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Math-009
Question
Evaluate y
v
for the following expression.
zx+
zx
y=v 22 cos
ln3xy4x
(A) z+2cos3y4x
(B) zx ln
13x
(C)
y+xx
y sinln
13xy4x 22
(D) zx+ 22 sin6y4x
Solution The answer is (B)
To evaluate partial derivatives, all variables are taken as constants except the variable that the
function's derivative is taken with respect to.
zx=
+zx
=
zx+zx
y
y
ln
13x
0ln
13x0
cosln
3xy4x 22
Reference The differential calculus definitions are on page 25 of the Supplied Reference Handbook.
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Math-010
Question Solve the following set of simultaneous linear equations for U, V, and W.
215w12v
38w4v2u
53w6v3u
=+u
=+
=+
(A) 24,3,
(B) 2.347,5.8,
(C) 11.56.1,4.3,
(D) 1.32.5,2,
Solution The answer is (D)
Use Cramer's rule to solve the simultaneous linear equations.
The coefficient matrix is
5121
842
363=D
The determinate is
204
124813630296203
84
361
512
362
512
843
=
++=
++=D
The determinate of the substitutional matrices are
394
51221
843
365 ==A
1
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504
5211
832
353
==A2
274
21121
342
563
==A3
2204
394
==U
2.5204
504==V
1.3204
274==W
Reference The matrix identities are on page 23 of the Supplied Reference Handbook.
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Math-011
Question Evaluate the following limit.
3
9lim
2
x
x
(A) 5
(B) 3
(C)
(D) 6
Solution The answer is (D)
Use L'Hopital's rule because the expression approaches 0/0 at the limit
0
0
33
933
=
The L'Hopital's rule states that the limit of the expression is the same as the limit of the derivatives of
the numerator and denominator.
6
1
32
1
2xlim
3
9lim
2
===x
x
Reference The trigonometric identities are on page 26 of the Supplied Reference Handbook.
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Math-012
Question Evaluate the following integral.
dxe2x6
(A) 2xe
(B) 2x12 e
(C) 2x3 e
(D) 0.812
Solution The answer is (C)
The solution for the indefinite integral
axax ea=dxe /1
2x
2x2x
3
62/16
e=
e=dxe
Reference The table of indefinite integrals is on page 27 of the Supplied Reference Handbook.
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Math-013
Question What is the approximate area under the curve y=1/x between y=3 and y=7?
(A) 0.84
(B) 0.12
(C) 2.3
(D) 0.65
Solution The answer is (D)
Since the function's independent variable is x, convert the limits of integration to x. The function in
terms of y is x=1/y. The x limits are 1/3 and 1/7.
The integral of f(x) represents the area under the curve f(x) between the limits of integration.
0.650.648
7
1ln
3
1ln
ln
1
3/1
7/1
=
=
x=
dxx
=
dxxf=A
Reference The integral calculus definitions are on page 26 of the Supplied Reference Handbook.
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Math-014
Question Determine the intersection points of the two equations given.
28 x=y and 34x 2 +=y
(A) 2
1
2
1,
(B) 11 ,
(C) 69 ,
(D) 52,
Solution The answer is (B)
Find the intersection points by setting the two equations equal:
34x8 22 +=x
25x5=
1±=x
Reference The mathematic identities are on page 21 of the Supplied Reference Handbook.
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Math-015
Question
Determine the maximum value of the following function on the interval 0x .
103x4x 23 +x=y
(A) 15
(B) 6
(C) 9
(D) 8
Solution The answer is (D)
The critical point is located where dy/dx=0.
38x3x 2 +=dx
dy
0313x
038x3x 2
=+x
=+
3
1=x or 3=x
A critical point is a maximum if d2y/dx2 < 0
86x2
2
+=dx
yd
At x=1/3, the second derivative is
1083
16 =+
At x= -3, the second derivative is
10836 =+
Therefore, x= -3, is a maximum, and x=1/3, is a minimum.
The maximum value is
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8103334323
=+
Reference The differential calculus identities are on page 25 of the Supplied Reference Handbook.
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Math-016
Question What type of differential equation is shown?
'''e= 11y6y3y 7x
(A) linear, third order, non-homogenous
(B) linear, second order, non-homogenous
(C) non-linear, second order, homogenous
(D) linear, first order, homogenous
Solution The answer is (B)
Rearrange the terms into the general form of a differential equation.
7x3y6y11y e='+'+'
This is a linear, second order, non-homogenous differential equation.
Reference The differential equation identities are on page 31 of the Supplied Reference Handbook.
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Math-017
Question Determine the sum of the vector A + B.
kji
kji
+=B
+=A
ˆˆˆ
ˆˆˆ
653
532
(A) kji
+= ˆˆˆ 623
(B) kji
++= ˆˆˆ 221
(C) kji
+= ˆˆˆ 1125
(D) kji
+= ˆˆˆ 121
Solution The answer is (D)
The operation for vector addition is
kb+a+jb+a+ib+a=B+A zzyyxxˆˆˆ
For the given vectors
k+j++i=B+A ˆ65ˆ53ˆ32
kji+= ˆˆˆ 121
Reference The vector identities are on page 27 of the Supplied Reference Handbook.
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Math-018
Question Determine the angle between vectors A and B.
kji
kji
+=B
+=A
ˆˆˆ
ˆˆˆ
653
532
(A) °172.01
(B) °35.26
(C) °73.42
(D) °165.31
Solution The answer is (A)
There are two ways to apply the dot product of vectors. Apply both methods and set their results equal
to one another.
θBA=BA cos
θ=
θ++++=
cos8.366.16
cos653532222222
51
655332
=
++=
ba+ba+ba=BA zzyyxx
°=
=θ
=θ
=θ
172.01
0.9903cos
0.9903cos
51cos8.366.16
1
Reference The vector identities are on page 24 of the Supplied Reference Handbook.
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Chemistry
Chemistry-001
Question Balance the following reaction.
_C4H10 + _O2 _CO2 + _H2O
(A) C4H10 + 2O2 CO2 + 5H2O
(B) 2C4H10 + 13O2 8CO2 + 10H2O
(C) C4H10 + 4O2 4CO2 + 5H2O
(D) 2C4H10 + 8O2 2CO2 + 10H2O
Solution The answer is (B)
_C4H10 + _O2 4CO2 + 5H2O
O2 in reactants is not able to be balanced by odd moles of H2O in products. H2O moles must be even.
2C4H10 + _O2 4CO2 + 10H2O
Carbon and hydrogen are balanced in reactants and products, but oxygen is not. Balance the oxygen.
2C4H10 + 13O2 8CO2 + 10H2O
Reactants and products each have 8 carbon atoms, 20 hydrogen atoms, and 26 oxygen atoms.
Reference No references for stoichiometry.
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Chemistry-002
Question A radioactive material sample has 60% of the original substance remaining after 20 years. What
percentage of the substance will remain after an additional 60 years?
(A) 13.0%
(B) 0.0%
(C) 12.1%
(D) 30.0%
Solution The answer is (A)
Solve for the half-life, τ, with the given information.
.
( )( )
Use calculated half-life value to find surviving percentage of substance after 80 years.
( )( )( )
Reference The half-life equation is on page 106 of the Supplied Reference Handbook.
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Chemistry-003
Question What is the name of the group of metals that includes rubidium, potassium, cesium, sodium, and
lithium?
(A) halogens
(B) alkaline earth metals
(C) rare earth group
(D) alkali metals
Solution The answer is (D)
The first column of the periodic table contains rubidium, potassium, cesium, sodium, and lithium, which
is known as Group IA or the alkali metals.
Reference A periodic table of the elements is located on page 101 of the Supplied Reference Handbook.
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Chemistry-004
Question Which of the following chemical formulas is incorrect?
(A) CaCl
(B) KOH
(C) Ca(OH)2
(D) Na2CO3
Solution The answer is (A)
Find the oxidation numbers of each molecular element and check for neutrality.
Combining Ca2+ and Cl- creates a positively charged molecule.
Combining K+ and OH- creates a neutral molecule.
Combining Ca2+ and (OH-)2 creates a neutral molecule.
Combining (Na1+)2 and CO32- creates a neutral molecule.
Therefore, the incorrectly written chemical formula is CaCl.
Reference A periodic table of the elements is located on page 101 of the Supplied Reference Handbook.
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Chemistry-005
Question A small gaseous mixture consists of 4 grams of xenon, 5 grams of oxygen, and 3 grams of nitrogen. What
is the mole fraction of the oxygen gas?
(A) 0.42
(B) 0.71
(C) 0.53
(D) 0.40
Solution The answer is (C)
Using molecular weights of Xe=131.3g/mol, O2=32g/mol, and N2=28g/mol, calculate the number of
moles of each gas.
Xe:
O2:
N2:
Mole fraction of oxygen
Reference A periodic table of the elements is located on page 101 of the Supplied Reference Handbook.
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Chemistry-006
Question What is the mass of 0.0072 m3 of hydrogen at STP (1 atm and 0o C)?
(A) 1.23x10-3 g
(B) 1.13x10-3 g
(C) 0.72 g
(D) 0.65 g
Solution The answer is (D)
Since at STP (standard temperature and pressure), P=1atm and T=0o C=273K, and assuming hydrogen
behaves as an ideal gas, the ideal gas law can be used to solve for the moles of hydrogen and molecular
weight can be used to obtain the mass of hydrogen.
, ,
,
( )( )
(
) ( )
MW of H2 ( ) (
)
( ) ( ) (
)
Reference A periodic table of the elements is located on page 101 and the ideal gas law can be found on page 73 of
the Supplied Reference Handbook.
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Chemistry-007
Question In the gaseous state reaction shown below, equilibrium concentrations for A, B, and C are 6.72x10-2
mol/L, 2.55x10-2 mol/L, and 4.27x10-2 mol/L, respectively. For this reaction, what is the equilibrium
constant?
2A B + 2C
(A) 6.92x10-3 mol/L
(B) 0.835 mol/L
(C) 0.865 mol/L
(D) 6.92x10-2 mol/L
Solution The answer is (A)
Since there are 2 moles of substance A and 2 moles of substance C, a and c are both equal to 2.
( ) ( )
( )
Reference The equation for equilibrium constants is located on page 100 of the Supplied Reference Handbook.
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Chemistry-008
Question To make a 0.07 molar solution, how much water must be added to 200 mL of a 0.5 molar solution of
KCl?
(A) 1.23 L
(B) 4.84 L
(C) 2.52x102 mL
(D) 2.65x102 mL
Solution The answer is (A)
Find the number of moles of solute present.
(
) ( )
Find volume required for a 0.07 molar solution.
The amount of water that must be added to solution is
Reference No reference for dimensional analysis.
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Chemistry-009
Question A batch of zinc ore contains 0.450 kg of zinc sulfide (ZnS). The ZnS is roasted in excess air to form sulfur
dioxide (SO2) and zinc oxide (ZnO). If 7% of the zinc is lost in the roasting process, how many grams of
zinc can be subsequently recovered?
(A) 419 g
(B) 280 g
(C) 2.5x103 g
(D) 21.8 g
Solution The answer is (B)
Find the fraction of zinc in zinc sulfide:
The mass of zinc that can be recovered is:
( )( )( )
Reference A periodic table of the elements is located on page 101 of the Supplied Reference Handbook.
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Chemistry-010
Question 4.00 g of a substance was dissolved in 250 g of water and produced a boiling point elevation of 0.070oC.
What was the molecular weight of the substance?
(A) 5.02 g/mol/kg
(B) 10.2 g/mol/kg
(C) 117 g/mol/kg
(D) 246 g/mol/kg
Solution The answer is (C)
Rearrange the boiling point elevation equation to solve for molecular weight:
( )
( )(
)
( )( )(
)
Reference A periodic table of the elements is located on page 101 of the Supplied Reference Handbook. No
reference for the boiling point elevation equation is available.
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Chemistry-011
Question A gaseous compound has a mass of 0.644 g and occupies 0.2 L at STP conditions (0oC and 1 atm). Which
of the following is most likely the compound’s formula?
(A) CH4
(B) C2H6
(C) C5H12
(D) C3H8
Solution The answer is (C)
Avogadro’s hypothesis states that 1 gram-mole of any gas occupies 22.4 L of space.
Find mass of 1 gram-mole of the compound:
(
) ( )
MW of C5H12 is (5)(12.011g/mol)+(12)(1.0079g/mol)=72.15 g/mol
Reference Avogadro’s hypothesis is located on page 100 and the ideal gas law is located on page 73 of the Supplied
Reference Handbook.
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Chemistry-012
Question For the reaction below, a mixture originally contains 22.50 g of Fe2O3 and 14.81 g of CO. Once the
mixture has reacted completely, what is the mass of the excess reactant remaining?
Fe2O3 (s) + 3CO (g) 2Fe (s) + 3CO2 (g)
(A) 7.98 g
(B) 87 g
(C) 2x10-3 kg
(D) 2.98 g
Solution The answer is (D)
(
)(
)(
)
(
) (
) (
)
Since the given mass of Fe2O3 (in comparison to CO) produced the least amount of Fe in products, Fe2O3
is the limiting reactant.
Now calculate how much of the non-limiting reactant actually reacted with the limiting reactant.
(
)(
)(
)
14.81 g CO (original amount) – 11.83 g CO (amount reacted) = 2.98 g CO
Reference A periodic table of the elements is located on page 101.
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Strength of Materials
Strength of Materials-001
Question Stress has units of:
(A) force per unit length
(B) force per unit area
(C) force-area
(D) area per unit force
Solution The answer is (B)
Reference The stress strain relationships are on page 33 of the Supplied Reference Handbook.
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Strength of Materials-002
Question Consider the stress strain diagram below. What is the slope of the initial linear portion of the curve
called?
(A) percent elongation
(B) plastic deformation
(C) yielding strength
(D) modulus of elasticity
Solution The answer is (D)
The slope of the linear portion of the curve is the modulus of elasticity, with units of stress over strain.
Reference The stress-strain definitions are on page 33of the Supplied Reference Handbook.
0
10000
20000
30000
40000
50000
0 0.001 0.002 0.003 0.004 0.005 0.006
Stre
ss [
psi
]
Strain [in/in]
Stress Strain Curve for Mild Steel
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Strength of Materials-003
Question Consider the cantilever beam and loading shown below. Which of the following diagrams correctly
represents the shape of the shear diagram?
(A)
(B)
(C)
(D)
Solution The answer is (C)
The load varies linearly between A and B and the shear force will vary quadratically between these two
points. In addition, since the load is increasing, the shear diagram when drawn will be convex between
these two points.
Reference The mechanics of materials relationships are on page 33 of the Supplied Reference Handbook.
A B
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Strength of Materials-004
Question A 0.6 ft. diameter steel rod is loaded axially in tension as shown. Steel has a modulus of elasticity of
30,000 ksi and Poisson’s ration of 0.30. What is the change in the diameter of the rod due to the applied
load?
(A)
(B)
(C)
(D)
Solution The answer is (B)
The decrease in the diameter of the rod is
( )( )
( )
( )( )
( )
(
)( )
3 ft
x
y
z
120 K 120 K
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Reference The mechanics of materials are on page 33 of the Supplied Reference Handbook.
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Strength of Materials-005
Question A 0.6 ft. diameter steel rod is loaded axially in tension as shown. Steel has a modulus of elasticity of
30,000 ksi.
If the rod decreases in diameter by while the length increases, what is the percent change
in volume of the rod?
(A)
(B)
(C)
(D)
Solution The answer is (B)
The change in length of the rod is
( )( )( )
( ) ( )
The change in the diameter of the rod was given.
The percent change in volume of the rod is
120 K 120 K
y
z
3 ft
x
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( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( ) ( )
Reference The mechanics of materials definitions are on page 33 of the Supplied Reference Handbook.
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Strength of Materials-006
Question With respect to positive sign convention, identity the stress components shown on the 2D element.
(A) Negative normal stress; positive shear stress
(B) Negative normal stress; negative shear stress
(C) Positive normal stress, positive shear stress
(D) Positive normal stress, negative shear stress
Solution The answer is (A)
The positive sign convention is shown on the 2D element.
Reference The mechanics of materials definitions are on page 33 of the Supplied Reference Handbook.
σx σx
τxy
τxy
σy
σy
x
y
τxy
σx x
y
σx
τxy
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Strength of Materials-007
Question The shear diagram for a simply supported beam is as shown. What is the maximum moment in the
beam?
(A)
(B)
(C)
(D)
Solution The answer is (A)
The maximum moment occurs at point B where the shear is zero. The relationship between shear and
moment is
( ) ( )
Integrating,
∫ ( )
MA= 0 since the beam is simply supported.
The integral is equal to the area under the shear force diagram between the two points.
( )( ) (
) ( )( ) (
) ( )( )
3.2 ft 2.6 ft 2.6 ft 3.2 ft
7.5K
3 K
A B C
7.5K
3 K
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Reference The trigonometric identities are on page 5 of the Supplied Reference Handbook.
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Statics/Dynamics
Statics/Dynamics-001
Question A uniform beam with a length L and a mass of 175kg is resting on a pin support located 0.65L from the
left end of the beam. The beam is inclined 35o from the horizontal. A construction worker with a mass of
75kg walks along the beam from the left to right until the beam is balanced horizontally. How far from
the left end of the beam is the construction worker when the beam is balanced horizontally?
(A) 0.80L
(B) 1.00L
(C) 0.45L
(D) 0.65L
Solution The answer is (B)
Sum the moments about the pin support, then set them equal to zero to solve for the construction
worker’s location when the beam is in equilibrium.
∑ ( ) ( )
( )( ) ( )( )
( )( )
Reference Moments are explained on page 49 of the Supplied Reference Handbook.
175kg
0.35L
75kg 0.65L
0.15L
0.65L
0.35L
m=175kg
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Statics/Dynamics-002
Question Find an expression for the reaction at point B for the statically determinant beam shown below.
(A) woL2/6
(B) woL2/2
(C) woL/2
(D) woL/6
Solution The answer is (D)
∑ ( ) (
) (
) (
)
(
) (
)
Reference Moments are explained on page 49 of the Supplied Reference Handbook.
wo
F=woL/6
B A
2L
L
RA
A
woL/2
L/3
L
RB
F=woL/6
B
2L
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Statics/Dynamics-003
Question Find the (x, y) coordinates of the centroid of the area.
(A) (3.50cm, 4.33cm)
(B) (3.50cm, 4.00cm)
(C) (3.50cm , 4.23cm)
(D) (4.23cm, 3.60cm)
Solution The answer is (C)
AHCBA = (3cm)(4cm) = 12cm2
AFEDG = (7cm)(3cm) = 21cm2
ATOTAL = 12cm2 + 21cm2 = 33cm2
∑
( )( ) ( )( )
∑
( )( ) ( )( )
Reference Centroids of shapes are shown in page 51 of the Supplied Reference Handbook.
G
A
C
B
3 cm x
4 cm
D
3 cm
E 7 cm y
F
H
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Statics/Dynamics-004
Question What is the force in member DE?
(A) 6502 N
(B) 7027 N
(C) 4090 N
(D) 12,568 N
Solution The answer is (B)
∑ ( )( ) ( )
(Upward Direction)
∑
( )(
)
√( ) ( ) (Tension)
Reference Requirements for a body in static equilibrium are found on page 49 of the Supplied Reference
Handbook.
G
B D F
A
8 m
E C
8 m 8 m
20,000 N
12 m
B
A
RAy
C
D
FDE
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Statics/Dynamics-005
Question An 80 kg block is at rest on a frictionless incline. Given the forces shown that are applied to the block,
calculate the minimum force, P, such that no downward motion occurs.
(A) 392 N
(B) 623 N
(C) 400 N
(D) 40 N
Solution The answer is (A)
∑ ( )
( ) ( ) (
) ( )
Reference Requirements for a body in static equilibrium are found on page 49 of the Supplied Reference
Handbook.
9 N 1
P 30o
80 kg
2
P
mg N
9 N
x
y
30o
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Statics/Dynamics-006
Question Resolve the 200 N force into components along the line P and along the line Q (F, P, and Q are coplanar).
(A) FQ=101 N, FP=145 N
(B) FQ=90 N, FP=110 N
(C) FQ=0 N, FP=200 N
(D) FQ=105 N, FP=141 N
Solution The answer is (D)
∑ ( ) ( ) ( )
( ) ( ( )
( ))
∑ ( ) ( ) ( )
( ) ( ) ( ) ( )
Reference Requirements for a body in static equilibrium are found on page 49 of the Supplied Reference
Handbook.
30o
Q
P
F=200 N 42o
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Statics/Dynamics-007
Question A 20-gram projectile is shot directly upward with an initial velocity of 900 m/s from ground level. What
will be the velocity of the projectile when it impacts the ground? Neglect air resistance.
(A) 900 m/s
(B) -900 m/s
(C) 1800 m/s
(D) -1800 m/s
Solution The answer is (B)
Since energy is conserved,
( ) (
)
Reference Conservation of energy can be found on pages 56 and 57 of the Supplied Reference Handbook.
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Statics/Dynamics-008
Question A wheel with a radius of 0.180 m rolls along a flat surface with a velocity of 5 m/s. What is the velocity of
point A when point B contacts the ground?
(A) 23 m/s
(B) 10 m/s
(C) 5 m/s
(D) 7 m/s
Solution The answer is (D)
( ) ( )
√( ) ( ) 25.5 cm
The triangle created between the center of the wheel and points A and B is proportional to the triangle
created by the VA (resultant velocity of point A) and 5 m/s vectors.
Reference Plane circular motion is located on page 54 of the Supplied Reference Handbook.
B
5 m/s
A
0.18 m
A 18 cm 5 m/s
VA B
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Statics/Dynamics-009
Question A particle’s position is defined by the equation below. What is the magnitude of the particle’s velocity at
t=3.5rad?
( ) ( ) ( ) [t is in radians]
(A) 3.02
(B) 2.57
(C) 4.73
(D) 6.70
Solution The answer is (C)
( ) ( )
( ) ( )
| ( )| √ ( ) ( )
Reference Vector operations can be found on page 24, and planar motion components can be found on page 54 or
the Supplied Reference Handbook.
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Statics/Dynamics-010
Question 6000-kg truck is pulling a 150-kg trailer at 80 km/h. What is the total momentum of the truck-trailer
combination?
(A) 129 kN·s
(B) 147 kN·s
(C) 137 kN·s
(D) 119 kN·s
Solution The answer is (C)
( ) (
) ( )
Reference Equations for momentum can be found on page 56 of the Supplied Reference Handbook.
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Statics/Dynamics-011
Question A person keeps a toy airplane attached to a string flying horizontally in a circle. The mass of the plane is
2 kg and the string is 1 m long. Assume that the string is weightless and is always in the plane of the
circular flight path. If the plane flies at 12m/s, what is the tension in the string?
(A) 300 N
(B) 288 N
(C) 24 N
(D) 144 N
Solution The answer is (B)
The normal acceleration of the airplane is
(
)
The tension in the string is equal to the centripetal force exerted on the plane by the string.
(
)
Reference Normal kinetics for planar problems can be found on page 56 of the Supplied Reference Handbook.
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Statics/Dynamics-012
Question A truck travels around an unbanked curve with a radius of 60 m. If the truck does not skid and the
coefficient of friction between the road and the tires is 0.4, what is the truck’s maximum speed?
(A) 15.34 m/s
(B) 11.89 m/s
(C) 10.35 m/s
(D) 17.32 m/s
Solution The answer is (A)
The centrifugal force is resisted by friction between the tires and the road.
√ √( ) (
) ( )
Reference Friction relationships can be found on page 57, and plane circular motion can be found on page 54 of
the Supplied Reference Handbook
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General Physics
General Physics-001
Question What is the magnitude of the electric field 4.2 cm away from the center of a thin metal plate with
dimensions of 45cm x 45cm that carries a total charge of 21μC?
(A) 4.23x106 N/C
(B) 2.64x106 N/C
(C) 2.10x106 N/C
(D) 5.50x106 N/C
Solution The answer is (B)
Since the separation distance is much smaller than the plate dimensions, consider the plate to be
infinite in size. Find the density of the sheet charge.
( )
( )( )
Reference Sheet charge electric field relationships can be found on page 193 of the Supplied Reference Handbook
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General Physics -002
Question Find the total capacitance between terminals A and B.
(A) 6.5 pF
(B) 6.0 μF
(C) 26 μF
(D) 6.0 mF
Solution The answer is (A)
Solve for capacitance by combining capacitors in series like resistors in parallel.
( )
Reference Resistors in series and parallel can be found on page 194 of the Supplied Reference Handbook.
A
B 13pF
13μF
13μF
13pF
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General Physics -003
Question A 20oC room is heated from a standard 120 V rms, 60 Hz power supply to replace a heat loss of 4 kW.
What must the heating element’s resistance be to maintain a constant room temperature of 20oC?
(A) 3.4
(B) 2.5
(C) 4.4
(D) 3.6
Solution The answer is (D)
( )
Reference See section for power absorbed by a resistive element on page 194 of the Supplied Reference
Handbook.
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General Physics -004
Question What is the current, I, in the following diagram?
(A) 5A
(B) 10A
(C) -10A
(D) -5A
Solution The answer is (C)
Use Kirchhoff’s law of currents to find I.
∑
∑
∑ ∑
Reference Kirchhoff’s laws are located on page 194 of the Supplied Reference Handbook.
I
6A
9A
5A
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General Physics -005
Question A 25 V source is connected across terminals A and B, and a current through resistor R1 is measured to be
12 A. Find the current that would flow through R1 if the 25 V source was replaced with a 30 V source.
(A) 17.0 A
(B) 13.5 A
(C) 10.0 A
(D) 14.4 A
Solution The answer is (D)
Using Ohm’s law,
( ) ( )
Reference Ohm’s law can be found on page 194 of the Supplied Reference Handbook.
A
B
R1
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General Physics -006
Question A copper power line with a diameter of 2.5 cm has a resistivity of 1.25 x 10-6 Ω·cm. Find the resistance of
6 km of power line.
(A) 0.15
(B) 0.125
(C) 6.536
(D) 0.655
Solution The answer is (A)
Using the relationship between resistance, electrical resistivity, conductor length, and cross-sectional
area,
( )
(
)
Reference Equations for resistivity can be found on page 194 of the Supplied Reference Handbook.
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General Physics -007
Question What is the average power dissipated by an electric heater with a resistance of 60 Ω if the heater draws
a current of 30sin(15t) A?
(A) 30 kW
(B) 27 kW
(C) 2 kW
(D) 2700 W
Solution The answer is (B)
Calculate the average power by rms values to maximum values, as Imax is given above.
The form of the sine wave is ( ) ( )
( ) ( )
Reference Relationships between power, current, and resistance are located on page 194 of the Supplied
Reference Handbook.
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General Physics -008
Question Find the resonant frequency for the circuit shown below.
(A) 224 rad/s
(B) 215 rad/s
(C) 0.417 rad/s
(D) 3.75 rad/s
Solution The answer is (A)
To compute the radian resonant frequency, use the following relationship:
√
√( )( )
(
)
Reference Resonance relationships are located on page 196 of the Supplied Reference Handbook.
4 H 3 Ω 5 μF
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General Physics -009
Question A DC generator with a magnetic flux of 0.05 Wb is operating at 1000 rpm and has a constant of Ka=1.5
V/rpm·Wb. What is the output voltage of the generator?
(A) 25 V
(B) 50 V
(C) 75 V
(D) 125 V
Solution The answer is (C)
To find output voltage, use the relationship between the DC machine constant, armature speed, and
magnetic flux:
(
)(
) ( )
Reference DC machine equations are located on page 198 of the Supplied Reference Handbook.
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General Physics -010
Question What is the equivalent capacitance of the battery in the circuit shown below?
(A) 125
(B) 112
(C) 75.5
(D) 62.5
Solution The answer is (D)
Use series and parallel capacitor relationships to find equivalent capacitance:
( )( )
Reference Capacitors in parallel and series are located on page 195 of the Supplied Reference Handbook.
+ 30 μF 15 μF 10 μF
15 μF
15 μF
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General Physics -011
Question A DC generator produces 400 V at 2150 rpm. Ignoring armature resistance, what is the new operating
voltage if the speed is reduced to 1500 rpm?
(A) 260 V
(B) 573 V
(C) 279 V
(D) 529 V
Solution The answer is (C)
If armature resistance is ignored, the speed is approximately proportional to the output voltage.
(
)
(
) ( )
Reference The turns ratio relationship is located on page 198 of the Supplied Reference Handbook.
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General Physics -012
Question After being open for a long time, the switch in the circuit shown below is closed at t=0. Just prior to the
switch being closed, what is the energy stored in the two inductors?
(A) 3.7 kJ
(B) 4.0 kJ
(C) 27.5 J
(D) 190 J
Solution The answer is (A)
Find the equivalent inductance:
Since the current through the resister is 15 A, the energy stored in the inductors is
( )( )
( )
Reference Equivalent inductance and energy stored in inductors are located on page 195 of the Supplied Reference
Handbook.
t=0
18 H
1.5 kΩ
15 H
15 A