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/

http://ncees.org/exams/study-materials/download-fe-supplied-reference-handbook/

CE399 Diagnostic Test Summer 2013

2

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.

http://www.pdx.edu/cee/SummerBridge


3

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.


4

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.


5

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=


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


6

Reference Equations for straight lines are on page 21 of the Supplied Reference Handbook.


7

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


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


8

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.


9

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.


10

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


11

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


12

Math-007

Question

Which of the following numbers is equal to 35log6 ?

(A) 3.68

(B) 1.98

(C) 2.3

(D) 0.778


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.


13

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


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.


14

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.


15

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


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.


16

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,


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


17

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.


18

Math-011

Question Evaluate the following limit.

3

9lim

2

x

x

(A) 5

(B) 3

(C)

(D) 6


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



19

Math-012

Question Evaluate the following integral.

dxe2x6

(A) 2xe

(B) 2x12 e

(C) 2x3 e

(D) 0.812


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.


20

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


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.


21

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,


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.


22

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


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


23

8103334323

=+

Reference The differential calculus identities are on page 25 of the Supplied Reference Handbook.


24

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


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.


25

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


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



26

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


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



27

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


_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.


28

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%


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.


29

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


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.


30

Chemistry-004

Question Which of the following chemical formulas is incorrect?

(A) CaCl

(B) KOH

(C) Ca(OH)2

(D) Na2CO3


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.



31

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


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



32

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


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.


33

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


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.


34

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


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.


35

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


Find the fraction of zinc in zinc sulfide:

The mass of zinc that can be recovered is:

( )( )( )



36

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


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.


37

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


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.


38

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


(

)(

)(

)

(

) (

) (

)

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.


39

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


Reference The stress strain relationships are on page 33 of the Supplied Reference Handbook.


40


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


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


41


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)


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


42


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)


The decrease in the diameter of the rod is

( )( )

( )

( )( )

( )

(

)( )

3 ft

x

y

z

120 K 120 K


43

Reference The mechanics of materials are on page 33 of the Supplied Reference Handbook.


44


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)


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


45

( ) ( ) ( )

( ) ( )

( ) ( ) ( ) ( )

( ) ( )

Reference The mechanics of materials definitions are on page 33 of the Supplied Reference Handbook.


46


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


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


47


Question The shear diagram for a simply supported beam is as shown. What is the maximum moment in the

beam?

(A)

(B)

(C)

(D)


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


48



49

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


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


50


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


∑ ( ) (

) (

) (

)

(

) (

)

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


51


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)


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


52


Question What is the force in member DE?

(A) 6502 N

(B) 7027 N

(C) 4090 N

(D) 12,568 N


∑ ( )( ) ( )

(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


53


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


∑ ( )

( ) ( ) (

) ( )


Handbook.

9 N 1

P 30o

80 kg

2

P

mg N

9 N

x

y

30o


54


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


∑ ( ) ( ) ( )

( ) ( ( )

( ))

∑ ( ) ( ) ( )

( ) ( ) ( ) ( )


Handbook.

30o

Q

P

F=200 N 42o


55


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


Since energy is conserved,

( ) (

)

Reference Conservation of energy can be found on pages 56 and 57 of the Supplied Reference Handbook.


56


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


( ) ( )

√( ) ( ) 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


57


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


( ) ( )

( ) ( )

| ( )| √ ( ) ( )

Reference Vector operations can be found on page 24, and planar motion components can be found on page 54 or

the Supplied Reference Handbook.


58


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


( ) (

) ( )

Reference Equations for momentum can be found on page 56 of the Supplied Reference Handbook.


59


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


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.


60


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


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


61

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


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


62

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


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


63


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


( )

Reference See section for power absorbed by a resistive element on page 194 of the Supplied Reference

Handbook.


64


Question What is the current, I, in the following diagram?

(A) 5A

(B) 10A

(C) -10A

(D) -5A


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


65


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


Using Ohm’s law,

( ) ( )

Reference Ohm’s law can be found on page 194 of the Supplied Reference Handbook.

A

B

R1


66


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


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.


67


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


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.


68


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


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


69


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


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.


70


Question What is the equivalent capacitance of the battery in the circuit shown below?

(A) 125

(B) 112

(C) 75.5

(D) 62.5


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


71


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


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.


72


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


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

ce399 diagnostic test

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