FE mechanical practice exam [2017 ed.] 9781932613858, 1932613854

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11.; ~af ~n~e~ g

engineers and surveyors

mechanical practice exam

mechanical practice exam

Copyright ©2017 by NCEES®. All rights reserved. All NCEES sample questions and solutions are copyrighted under the laws of the United States. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without the prior written permission of NCEES. Requests for permissions should be addressed in writing to [email protected] or to NCEES Exam Publications, PO Box 1686, Clemson, SC 29633. ISBN 978-1-932613-85-8

Printed in the United States of America 1st printing March 2017

CONTENTS Introduction to NCEES Exams ................................................................ 1 About NCEES Exam Format Examinee Guide Scoring and reporting Updates on exam content and procedures

Exam Specifications .......................................................................... 3 Practice Exam .................................................................................... 9 Solutions ...........................................................................................79

iii

About NCEES NCEES is a nonprofit organization made up of the U.S. engineering and surveying licensing boards in all 50 states, U.S. territories, and the District of Columbia. We develop and score the exams used for engineering and surveying licensure in the United States. NCEES also promotes professional mobility through its services for licensees and its member boards.

Engineering licensure in the United States is regulated by licensing boards in each state and territory. These boards set and maintain the standards that protect the public they serve. As a result, licensing requirements and procedures vary by jurisdiction, so stay in touch with your board (ncees.org/licensingboards). Exam Format The FE exam contains 110 questions and is administered year-round via computer at approved Pearson VUE test centers. A 6-hour appointment time includes a tutorial, the exam, and a break. You'll have 5 hours and 20 minutes to complete the actual exam.

Beginning July 1, 2017, in addition to traditional multiple-choice questions with one correct answer, the FE exam will use common alternative item types such as • • • •

Multiple correct options-allows multiple choices to be correct Point and click-requires examinees to click on part of a graphic to answer Drag and drop-requires examinees to click on and drag items to match, sort, rank, or label Fill in the blank-provides a space for examinees to enter a response to the question

To familiarize yourself with the fonnat, style, and navigation of a computer-based exam, view the demo on ncees.org/ExamPrep. Examinee Guide The NCEES Examinee Guide is the official guide to policies and procedures for all NCEES exams. During exam registration and again on exam day, examinees must agree to abide by the conditions in the Examinee Guide, which includes the CBT Examinee Rules and Agreement. You can download the Examinee Guide at ncees.org/exams. It is your responsibility to make sure you have the current version. Scoring and reporting Exam results for computer-based exams are typically available 7-10 days after you take the exam. You will receive an email notification from NCEES with instructions to view your results in your MyNCEES account. All results are reported as pass or fail. Updates on exam content and procedures Visit us at ncees.org/exams for updates on everything exam-related, including specifications, exam-day policies, scoring, and corrections to published exam preparation materials. This is also where you will register for the exam and find additional steps you should follow in your state to be approved for the exam.

1

EXAM SPECIFICATIONS

3

Fundamentals of Engineering (FE) MECHANICAL CBT Exam Specifications Effective Beginning with the January 2014 Examinations •

The FE exam is a computer-based test (CBT). It is closed book with an electronic reference.

•

Examinees have 6 hours to complete the exam, which contains 110 multiple-choice questions. The 6-hour time also includes a tutorial and an optional scheduled break.

•

The FE exam uses both the International System of Units (SI) and the U.S. Customary System (USCS).

Number of Questions

Knowledge 1.

Mathematics A. Analytic geometry B. Calculus C. Linear algebra D. Vector analysis E. Differential equations F. Nwnerical methods

6-9

2.

Probability and Statistics A. Probability distributions B. Regression and curve fitting

4-6

3.

Computational Tools A. Spreadsheets B. Flow charts

3-5

4.

Ethics and Professional Practice A. Codes of ethics B. Agreements and contracts C. Ethical and legal considerations D. Professional liability E. Public health, safety, and welfare

3-5

5.

Engineering Economics A. Time value of money B. Cost, including incremental, average, sunk, and estimating C. Economic analyses D. Depreciation

3-5

4

3-5

6.

Electricity and Magnetism A. Charge, current, voltage, power, and energy B. Current and voltage laws (Kirchhoff, Ohm) C. Equivalent circuits (series, parallel) D. AC circuits E. Motors and generators

7.

Statics A. Resultants of force systems B. Concurrent force systems C. Equilibrium of rigid bodies D. Frames and trusses E. Centroids F. Moments of inertia G. Static friction

8-12

8.

Dynamics, Kinematics, and Vibrations A. Kinematics of particles B. Kinetic friction C. Newton's second law for particles D. Work-energy of particles E. Impulse-momentum of particles F. Kinematics of rigid bodies G. Kinematics of mechanisms H. Newton's second law for rigid bodies I. Work-energy of rigid bodies J. Impulse-momentum of rigid bodies K. Free and forced vibrations

9-14

9.

Mechanics of Materials A. Shear and moment diagrams B. Stress types (axial, bending, torsion, shear) C. Stress transfonnations D. Mohr's circle E. Stress and strain caused by axial loads F. Stress and strain caused by bending loads G. Stress and strain caused by torsion H. Stress and strain caused by shear I. Combined loading J. Defonnations K. Columns

8-12

5

10. Material Properties and Processing A. Properties, including chemical, electrical, mechanical, physical, and thermal B. Stress-strain diagrams C. Engineered materials D. Ferrous metals E. Nonferrous metals F. Manufacturing processes G. Phase diagrams H. Phase transformation, equilibrium, and heat treating I. Materials selection J. Surface conditions K. Corrosion mechanisms and control L. Thermal failure M. Ductile or brittle behavior N. Fatigue 0. Crack propagation

8-12

11. Fluid Mechanics A. Fluid properties B. Fluid statics C. Energy, impulse, and momentum D. Internal flow E. External flow F. Incompressible flow G. Compressible flow H. Power and efficiency I. Performance curves J. Scaling laws for fans, pumps, and compressors

9-14

12.

Thermodynamics A. Properties of ideal gases and pure substances B. Energy transfers C. Laws of thermodynamics D. Processes E. Performance of components F. Power cycles, thermal efficiency, and enhancements G. Refrigeration and heat pump cycles and coefficients of performance H. Nonreacting mixtures of gases I. Psychrometrics J. Heating, ventilating, and air-conditioning (HVAC) processes K. Combustion and combustion products

6

13-20

9-14

13. Heat Transfer A. Conduction B. Convection C. Radiation D. Thermal resistance E. Transient processes F. Heat exchangers G. Boiling and condensation

14. Measurements, Instrumentation, and Controls

5-8

A. Sensors

B. Block diagrams C. System response D. Measurement uncertainty

9-14

15. Mechanical Design and Analysis A. Stress analysis of machine elements B. Failure theories and analysis C. Deformation and stiffness D. Springs E. Pressure vessels F. Beams G. Piping H. Bearings I. Power screws J. Power transmission K. Joining methods L. Manufacturability M. Quality and reliability N. Hydraulic components 0. Pneumatic components P. Electromechanical components

7

PRACTICE EXAM

9

FE MECHANICAL PRACTICE EXAM The equation of a sphere with center at (0, 1, -2) and a radius of9 is:

1. 0

A.

0

B.

0

C.

0

D.

2.

x2 + (y- 1)2 + (z + 2)2 = 81 x2 + (y + 1)2 + (z - 2)2 = 81 (x + 1)2 + (y + 1)2 + (z + 2)2 = 81 (x)2 + (y-1)2 + (z+ 2)2 = 9

The area of the shaded portion of the figure shown below is most nearly: y

x=2 0 0 0 0

A.

18

B.

39

C. D.

117

Copyright © 2017

x=S

X

133

by NCEES

10

NEXT_.

FE MECHANICAL PRACTICE EXAM What is the area of the region in the first quadrant that is bounded by the line y curve x = y 12 , and the y-axis?

3.

o o o o

4.

A B.

2/5 3/5

C.

2/3

D.

1

= I,

the

Which of the following is a unit vector perpendicular to the plane determined by the vectors A = 2i + 4j and B = i + j - k?

-2i + j-k

0

A

0

B.

}s (i +

0

C.

1 - -(-2i + j- k)

0

D.

1 - -(-2i- j- k)

2j)

"6 "6

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11

NEXT-+

FE MECHANICAL PRACTICE EXAM Suppose/{t) = i2. The area under the curve for O:'.St :'.S 2, estimated by using the trapezoidal rule with M = 0.5, is most nearly:

5.

4.00-+-----~ 2.25 1.00 0.25

O A. 0 B.

o o

6.

C.

D.

4.00 2.75 2.67 1.33

A series of measurements gave values of 11, 11, 11, 11, 12, 13, 13, 14, for which the arithmetic mean is 12. The population standard deviation is most nearly:

0

o o o

A. B. C. D.

1.42 1.25 1.19 1.12

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12

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FE MECHANICAL PRACTICE EXAM Suppose the lengths of telephone calls form a normal distribution with a mean length of 8.0 min and a standard deviation of 2.5 min. The probability that a telephone call selected at random will last more than 15.5 min is most nearly:

7.

o o o o

A. B. C. D.

0.0013 0.0026 0.2600 0.9987

You wish to estimate the mean M of a population from a sample of size n drawn from the population. For the sample, the mean is x and the standard deviation is s. The probable accuracy of the estimate improves with an increase in:

8.

0

A.

B. 0 C. 0 D.

0

M n s

M+s

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13

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FE MECHANICAL PRACTICE EXAM 9.

Consider a set of three values: 4, 4, and 7. Match each of the statistical quantities with the correct value.

Statistical Quantities

Mean

10.

.l..

.1.

Variance

i

Median

.1-

A spreadsheet display shows the following values in Column A: A

1 2

-2 -1

3

0 1 2

4

5

B

Cell Bl contains the formula $Al"3 + A$1"2-3. The formula in Cell Bl is copied down in Column B with automatic cell referencing. The formula in Cell B5 will be:

0

A.

$A 1"3 + A$5"2 - 3

0

B.

A5"3 + B$1"2- 3

0

C.

$A5"3 + A$ I "2 - 3

0

D.

A5"3 + A5"2 - 3

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14

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FE MECHANICAL PRACTICE EXAM In a spreadsheet, the number in Cell A4 is set to 6. Then A5 is set to A4 + $A$4. This formula is copied into Cells A6 and A 7 with automatic cell referencing. The number shown in Cell A7 is most nearly:

11.

0

A.

o o o

B. C. D.

12.

12 24 36 216

The flowchart for a computer program contains the following segment:

[

VAR=O IF VAR< 5 THEN VAR= VAR+ 2 OTHERWISE EXIT LOOP LOOP

What is the value of VAR at the conclusion of this routine?

0

o o o

A. B.

0

C. D.

4 6

2

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15

NEXT-+

FE MECHANICAL PRACTICE EXAM 13.

The final value of Qin the following flowchart is most nearly:

START

Q=Q+2 K=KxQ

NO

END

0

o o o

A. B. C. D.

0 1

3 5

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16

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FE MECHANICAL PRACTICE EXAM 14.

According to the Model Rules, Section 240.15, Rules of Professional Conduct, licensed professional engineers are obligated to:

o

A.

ensure that design documents and surveys are reviewed by a panel of licensed engineers prior to affixing a seal of approval

o

B.

express public opinions under the direction of an employer or client regardless of knowledge of subject matter

o

C.

practice by performing services only in the areas of their competence and in accordance with the current standards of technical competence

o

D.

offer, give, or solicit services directly or indirectly in order to secure work or other valuable or political considerations

15.

As a professional engineer originally licensed 30 years ago, you are asked to evaluate a newly developed computerized control system for a public transportation system. The owner requires a currently licensed engineer to evaluate the system. You may accept this project if:

O A.

you are competent in the area of modem control systems

o

your professional engineering license has lapsed, but you have two FE interns working for you

B.

O C.

you took a transportation course in college

O D.

you have regularly attended meetings of a professional engineering society

Copyright © 2017 by NCEES

17

NEXT-+

FE MECHANICAL PRACTICE EXAM 16.

Which of the following is the general solution to the differential equation and boundary condition shown below?

!

17.

+Sy =O;y(O)= I

0

A.

es,

0

B.

0

C.

e-51 e.r-si

0

D.

se-51

A printer costs $900. Its salvage value after 5 years is $300. Annual maintenance is $50. If the interest rate is 8%, the equivalent uniform annual cost is _ _ _ __ Answer to the nearest integer.

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18

NEXT-+

FE MECHANICAL PRACTICE EXAM Economic analysis will be used to compute an equivalent value today for an estimated constant monthly expense that is projected to occur each month over the next three years.

18.

Mark the area of the single column of the factor table that contains the value that could be used for such an analysis. Factor Table -i = 2.00% n

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 40 50 60 100

PIF

PIA

PIG

FIP

0.9804 0.9612 0.9423 0.9238 0.9057 0.8880 0.8706 0.8535 0.8368 0.8203 0.8043 0.7885 0.7730 0.7579 0.7430 0.7284 0.7142 0.7002 0.6864 0.6730 0.6598 0.6468 0.6342 0.6217 0.6095 0.5521 0.4529 0.3715 0.3048 0.1380

0.9804 1.9416 2.8839 3.8077 4.7135 5.6014 6.4720 7.3255 8.1622 8.9826 9.7868 10.5753 11.3484 12.1062 12.8493 13.5777 14.2919 14.9920 15.6785 16.3514 17.0112 17.6580 18.2922 18.9139 19.5235 22.3965 27.3555 31.4236 34.7609 43.0984

0.0000 0.9612 2.8458 5.6173 9.2403 13.6801 18.9035 24.8779 31.5720 38.9551 46.9977 55.6712 64.9475 74.7999 85.2021 96.1288 107.5554 119.4581 131.8139 144.6003 157.7959 171.3795 185.3309 199.6305 214.2592 291.7164 461.9931 642.3606 823.6975 1,464.7527

1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 1.1487 1.1717 1.1951 1.2190 1.2434 1.2682 1.2936 1.3195 1.3459 1.3728 1.4002 1.4282 1.4568 1.4859 1.5157 1.5460 1.5769 1.6084 1.6406 1.8114 2.2080 2.6916 3.2810 7.2446

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FIA

19

1.0000 2.0200 3.0604 4.1216 5.2040 6.3081 7.4343 8.5830 9.7546 10.9497 12.1687 13.4121 14.6803 15.9739 17.2934 18.6393 20.0121 21.4123 22.8406 24.2974 25.7833 27.2990 28.8450 30.4219 32.0303 40.5681 60.4020 84.5794 114.0515 312.2323

AIP 1.0200 0.5150 0.3468 0.2626 0.2122 0.1785 0.1545 0.1365 0.1225 0.1113 0.1022 0.0946 0.0881 0.0826 0.0778 0.0737 0.0700 0.0677 0.0638 0.0612 0.0588 0.0566 0.0547 0.0529 0.0512 0.0446 0.0366 0.0318 0.0288 0.0232

AIF 1.0000 0.4950 0.3268 0.2426 0.1922 0.1585 0.1345 0.1165 0.1025 0.0913 0.0822 0.0746 0.0681 0.0626 0.0578 0.0537 0.0500 0.0467 0.0438 0.0412 0.0388 0.0366 0.0347 0.0329 0.0312 0.0246 0.0166 0.0118 0.0088 0.0032

AIG 0.0000 0.4950 0.9868 1.4752 1.9604 2.4423 2.9208 3.3961 3.8681 4.3367 4.8021 5.2642 5.7231 6. 1786 6.6309 7.0799 7.5256 7.9681 8.4073 8.8433 9.2760 9.7055 10.1317 10.5547 10.9745 13.0251 16.8885 20.4420 23.6961 33.9863

NEXT-.

FE MECHANICAL PRACTICE EXAM 19.

The power (W) dissipated in the 90-n resistor of the circuit shown below is most nearly: 90n

830 n

lSOQ

100V

0

A.

8 18

o B. o C.

40

O D.

71

In the resistor circuit shown below, the equivalent resistance Req (0) at Terminals a-b is most nearly:

20.

2Q

3Q

a

r O A.

o o

o

B.

3Q

b

22 20

C.

4

D.

2

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20

NEXT-.

FE MECHANICAL PRACTICE EXAM A 1,000-n resistor is in series with a 2-mH inductor. An ac voltage source operating at a frequency of 100,000 rad/s is attached as shown in the figure. The impedance (0) of the RL combination is most nearly:

21.

1,000 n

2mH

0

A.

0

B.

0

C.

0

D.

200 + jl,000 1,000 + )200 38.4 + /192 1,000-1200

An ammeter, a voltmeter, and a wattmeter were installed in an ac circuit and read 15 Arms, 115 Vrms, and 1,500 W, respectively. The power factor of the circuit is most nearly:

22.

0

A.

O B. C.

o o

D.

-0.87 -0.5 0.5 0.87

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21

NEXT-+

FE MECHANICAL PRACTICE EXAM Beam AB has a distributed load as shown and supports at A and B. If the weight of the beam is negligible, the force RB (kN) is most nearly:

23.

8kN/m

A i-----------------1. B

O A.

o o o

B.

24 12

C.

10

D.

8

Three forces act as shown below. The magnitude (N) of the resultant of the three forces is most nearly:

24.

y

4

-----------------------·x

J

SON

0 0 0

0

A. B. C. D.

140 191 370 396

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22

NEXT-+

FE MECHANICAL PRACTICE EXAM 25.

The moment of force F (N•m) shown below with respect to Point Pis most nearly: ~F=SOON

p~-----Drmm ,.....-1----- 300 mm ----•-1

0

A.

B. 0 C. 0 0

26.

D.

31.7 ccw 31.7 cw 43.3 cw 43.3 ccw

In the figure below, the force (kN) in Member BC is most nearly: A

B

D

C

E

F

3 kN

3kN

0 0 0 0

A.

B. C. D.

3kN

6 9

15 18

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23

NEXT-+,

FE MECHANICAL PRACTICE EXAM 27.

Mark all of the zero-force members of the simple truss below. D

I

{ I

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24

NEXT-+

FE MECHANICAL PRACTICE EXAM 28.

Consider the following graph: y

Which of the following expressions gives the distance from the y-axis to the centroid of the shaded area?

0

A.

J303!x3dx J:( x+jx2}1x

J:( -jx3 )dx J:( x-jx2)dx J:( x-jx2)dx J:( x-jx2)dx x2

O B.

o

C.

o D.

J:G x2+jx3)dx J:( x-jx2)dx

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25

NEXT~

FE MECHANICAL PRACTICE EXAM A pulley is driven by a belt as shown in the figure below. Neglecting centrifugal effects, the minimum coefficient of friction that will prevent slipping between the belt and the pulley is most nearly:

29.

300-mm-DIAMETER PULLEY

450N 3,000 N

O A.

o B. o C. o D.

0.60 0.56 0.31 0.20

In the figure below, the coefficient of static friction between the block and the inclined plane is 0.25. The block is in equilibrium. As the inclined plane is raised, the block will begin to slide when:

30.

(

f

o o o o

B.

sin = 1.0 cos = 1.0

C. D.

cos = 0.25 tan q> = 0.25

A.

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26

NEXT-.

FE MECHANICAL PRACTICE EXAM Two blocks, A and B, are arranged so that A rests on top of B and is attached to a vertical wall by an inextensible string. A force of 30 N is applied to Block B, which is sufficient to make it slide to the left. If µK = 0.2 between A and B, and if µK = 0.4 between Band the bottom surface, the acceleration of B (m/s 2) is most nearly:

31.

BLOCK A (2 kg)1---_IN_E_X_T_E_N_SI_B_LE_S_T_RI_N_G--v F=30N ~----iBLOCK B (2 kg)

() () () ()

32.

A. 13. C. D.

5.2 7.2 9.1 15.0

A 2-kg block slides along a rough horizontal surface and slows to 10 mis after traveling 20 m. If the kinetic coefficient of friction between the block and surface is 0.2, the initial speed (mis) of the block was most nearly: () A.

() B. () C. () D.

10.0 10.4 13.4 20.0

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27

NEXT-+

FE MECHANICAL PRACTICE EXAM 33.

The 2-kg block shown in the figure is accelerated from rest by force F along the smooth incline for 5 m until it clears the top of the ramp at a speed of 8 mis. The value ofF (N) is most nearly:

o o o o

A. B. C. D.

11.8

19.6 24.6 69.4

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28

NEXT-+

FE MECHANICAL PRACTICE EXAM 34.

The piston and cylinder of an internal combustion engine are shown in the following figure. If ro = 377 rad/s, the piston speed (mm/s) when 0 = 90° is most nearly:

' ' ...

0 A. O B.

o C. o D.

/ ,;

/

0 10,500 18,850 24,300

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29

NEXT-.

FE MECHANICAL PRACTICE EXAM The figure shows a four-bar linkage. If Link 3 rotates in the counterclockwise direction, the angle at Point P, measured in the global X-Y coordinate frame, is most nearly:

35.

X

Oz

LINK LENGTHS

LINKANGLES

L 1 = 400mm

02 = 60°

L2 = 158 mm

93 = 15°

L 3 = 216.97 mm

04 =120°

L4

=

222.84 mm

04

Op = 30°

LAP= 187mm

0

o o o

A. B. C.

D.

225° 135° 45° -45°

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30

NEXT-.

FE MECHANICAL PRACTICE EXAM 36.

An object with a mass m of 1.50 kg moves without friction in a circular path as shown below. Attached to the object is a spring with a spring constant k of 400 Nim. The spring is undefonned when the object is at Point P, and the speed of the object at Point Q is 2.00 mis.

k=400N/m

NOTTO SCALE The translational kinetic energy (J) of the object at Point Q is most nearly:

0

A.

o o o

B. C. D.

1.50 3.00 6.00 29.40

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31

NEXT-.

FE MECHANICAL PRACTICE EXAM 37.

If a pendulum is released from rest at Position 1, the velocity (mis) of the mass at Position 2 is most nearly:

I

~60°

m= 1 kg POSITION 1 ...... J ..... I

\

I

I

I \

'

,I ,'

POSITION 2 () /\..

5.0

() B. () C. () D.

7.0 9.8 12.7

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32

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FE MECHANICAL PRACTICE EXAM 38.

In the figure below, Block Bis initially at rest and is attached to an unstretched spring. Block A travels to the right and hits Block B. Immediately after impact, the velocity of Block B is 6 mis to the right. The maximum acceleration (m/s 2) of Block B after impact is most nearly:

0

o o o

39.

A. B.

C. D.

1.5 2.25 6.0

9.0

The shear diagram for a particular beam is shown below. All lines in the diagram are straight. The bending moment at each end of the beam is zero, and there are no concentrated couples along the beam. The maximum magnitude of the bending moment (kN·m) in the beam is most nearly:

,~:,.

tom

6

l 4ml 4

SHEAR (kN)

0

4

12

A. B. o C. O D. 0 0

8 16

18 26

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fr\.

I

\

h

'

,a

14

33

NEXT-+

FE MECHANICAL PRACTICE EXAM A 0.25-m steel rod with a cross-sectional area of 1,250 mm2 and a modulus of elasticity E of 200 GPa is subjected to a 5,000-N force as shown below. The elongation of the rod (µm) is most nearly:

40.

s,ooo N~
-=tan=µ cos cl>

tan

=0.25

THE CORRECT ANSWER IS: D

96

FE MECHANICAL SOLUTIONS 31.

Refer to the Friction section in the Dynamics chapter of the FE Reference Handbook. The upper frictional force due to Block A on Block Bis

__A_t___2_g____.I- Fu

Fu =0.2 mAg

=0.2(2)(9.81) =3.924 N

~t

Fu 2g

The lower frictional force on Block B at the bottom surface is FL= 0.4(mA +m8 )g

= 0.4(2+2)9.81 = 15.696 N

Then from the Kinetics section, ~F=ma F-FL -Fu =ma

30-15.696-3.924 = 2a a= 5.19 ~ 5.2 m/s 2

THE CORRECT ANSWER IS: A

32.

Refer to the Work and Energy section in the Dynamics chapter of the FE Reference Handbook.

I

•

X, V

Wi-..+2 =-Fx

1

2

1

2

-mv2 =-mv1 -µkmgx 2 2

m

Cancel m to obtain~.!_ (10)2 = .!_ v{- 0.2 (9.81)(20) 2 2 v1 =13.4m/s

THE CORRECT ANSWER IS: C

97

........_-F

f

N

FE MECHANICAL SOLUTIONS 33.

+ W1~2 = T2 + U2 0 + 0 + Fs = 112 mv2 + mgh 5F= 112 (2)(8)2 + (2)(9.81)(3) F=24.6N

Ti +

U1

THE CORRECT ANSWER IS: C

34.

Refer to the section Plane Motion of a Rigid Body-Kinematics (Instantaneous Center of Rotation) in the Dynamics chapter of the FE Reference Handbook. The crank and rod are two rigid bodies. At the moment when speed). ve = 50 mm x 377 rad/s

e = 90°, vp

is desired (piston

= 18,850 mm/s

Both points are on the rod. By the method of instantaneous centers, the center of rotation is located where the line at P, J_ to vp, intersects the line at C, J_ to ve. ve is parallel to vp so these meet at infinity. Thus the rotation of rod PC is 0, or rope= 0.

Since there is no rotation at this instant, all points of the rod move with the same velocity and vp = vc = 18,850 mm/s because vP

=vc + ro Pc x ~,c

THE CORRECT ANSWER IS: C

35.

L.VpA = 93 + Op + 90° = 15° + 30° + 90° =135°

THE CORRECT ANSWER IS: B

36.

The kinetic energy, T, when the object is at Q, is: T = 112 mv 2 =I/ 2 (1.5 kg){2 m / s )2 = 3 J

THE CORRECT ANSWER IS: B

98

and ro Pc

=0 .

FE MECHANICAL SOLUTIONS 37.

Refer to Principle of Work and Energy in the Dynamics section of the FE Reference Handbook.

T2 + U2 = Ti + W1~2=0 T1 =O 1 2 T2 = -mv2 2 U1 =mgh1 U2=0

U1

+ W1~2

.!.mvi =mg(2.5) => v2 =.Jsg =.J5(9.81) =7m/s 2

h 1 = 5 sin 30° = 2.5

THE CORRECT ANSWER IS: B

99

FE MECHANICAL SOLUTIONS 38.

Refer to the Free Vibration section in the Dynamics chapter of the FE Reference Handbook.

mx+kx=O :. X

=C1 cos(ront) +C2 sin(ov)

where Oln

Jf

=

x(0)=0:.C1 =0,and x =

C2 sin(ront)

m

x = C2ron cos (©nf) x(O) = 6 = C2 ron, solving for C2

6

C2=ron

x =-C2ro~ sin(ront) x = -6ron sin(ront) X = -6~sin(ront)

x = -9 m/s 2 sin(ront) 2 .. .·.xmax = 9 mls

THE CORRECT ANSWER IS: D

100

FE MECHANICAL SOLUTIONS 39.

10m X --=-lOkN 6kN

2

CD

x=6m

Area 1

= 13(2) = 26 kN·m

Area2

= 6 ( 6 ) = 18 kN·m

Area3

= 4(4) = 16 kN·m

X

12

14

SHEAR DIAGRAM

v=====

2

~ -16

-8

-26 MOMENT DIAGRAM

Maximum magnitude of the bending moment is 26 kN· m. THE CORRECT ANSWER IS: D

40.

From Uniaxial Loading and Deformation in the Mechanics of Materials section of the FE Reference Handbook, the uniaxial deformation is: .

PL

(5,000)(0.25)

6

Deformation = 6 = - = = 5.0 x 10- m = 5.0 µm AE (1, 250 x 10-6 )( 200 x 109 )

THE CORRECT ANSWER IS: C

41.

rF =PA= ( 1.4 x 106 )

(

it(O~S)2) = Frod

F'rod = 275 kN = o'A = 68 x 10

6

A

A= 40.4 x 10-4 m2

P=l.4MPa ~ m

THE CORRECT ANSWER IS: A

101

FE MECHANICAL SOLUTIONS 42.

Refer to the Torsion section in the Mechanics of Materials chapter of the FE Reference Handbook. where T = Torque at section of interest (N · mm) Tr t=J

r = radius

to point of interest {mm), 'outside for maximum shear

J = section (polar) moment of inertia {mm 4 )

For Section BC T = 1,000N •m

75 r=-mm 2 J=

1t{75

4

-

504 ) mm4

32

Hence the maximum torsional shear stress is given by

= 15 MPa

THE CORRECT ANSWER IS: A

43.

Td Tr 2 16T t=-=--=J 7[(/4 1Ui3 32 T

= 7td 3-r:

1t{0.2)3{840 x 103 )

16 T = 1,319N·m

16

THE CORRECT ANSWER IS: C

102

FE MECHANICAL SOLUTIONS 44.

Refer to Mohr's Circle in the Mechanics of Material section of the FE Reference Handbook. From a constructed Mohr's Circle, the maximum inplane shear stress is

R =

R

= (

40;20J +I0

2

R = .J200

R = 14.1 ksi

THE CORRECT ANSWER IS: B

103

tmax = R.

FE MECHANICAL SOLUTIONS 45.

The stress at Point O may be represented as

aav

--

~

H

where

Load

O'=--

Area

al =

' (100

a = v

av

10,000 N = -10 MPa mm )(10 mm)

5,000 N = 5 l\1Pa (100 mm){IO mm)

Since ah is compressive, a1

= 5 MPa, a2 = 0 MPa, 0'3 = -10 MPa,

Thus K~O

bi ~

=> K

0

$;

54

Hence, K max = 54

THE CORRECT ANSWER IS: D

125

FE MECHANICAL SOLUTIONS 91.

The equation of the system can be written as (

16 2

s s +0.8s+ 16

16

thus ro/

=16

and 2