# Exam-2-Study-Guide by tangshuming

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```									ES226 Exam 2 Study Guide                                                                                            Page 1

ES226
Engineering Mechanics: Statics
Spring 2013
Lafayette College
Engineering Division

Exam 2 Study Guide
Exam 2: Wednesday, February 27, 2013, in class
Exam Format: 50 minute time limit. Closed book. Students are allowed to have a calculator, , pencils, etc. Students may
also bring a protractor and ruler, but this is not essential.

Exam Coverage: Lessons 7 through 12:
Lesson 7 Concurrent Systems in 3D
Lesson 9 Moments and the Principle of Moments
Lesson 10 Moments in 3D
Lesson 11 Moment Couples
Lesson 12 Simplification of Force/Couple Systems

Given Formulae (provided on the exam):

Sine Law:     A     B    C      [Cc, Bb, Aa]                          B
                                          c
sin a sin b sin c
A                    a

Cosine Law: C  A2  B 2  2 AB cosc      [SAS]      b           C

Sample Problems – Categorized by Lesson Objectives

Lesson 7 Concurrent Systems in 3D
Compute the unknowns (forces, angles, distances, spring extensions) for three-dimensional concurrent statics problems
Recommended Hibbeler Problems (12th Edition): 3-55, 3-59, 3-78
1. (35 points) Determine the magnitude of P and the tension in each cable. A cylinder of weight W=650N is
supported by two cables AC and BC, which are attached to the top of vertical posts. A horizontal force P,
perpendicular to the place containing the posts, holds the cylinder in the position shown.

2.   (35 points) Determine the magnitude of force acting along the axis of each of the three struts AB, AC, and AD and
specify whether this force is positive (tension) or negative (compression). Given: the chain supports a 500-kg
block. (Ans: FB=-19.2 kN, FC=10.4kN, FD=6.32kN)
ES226 Exam 2 Study Guide                                                                                            Page 2

3.   (45 points) Three cables are connected at A. If the tension in cable AD is 305N, determine P (Ans: 960N)

Lesson 8 Moments and the Principle of Moments
Compute the moment of a force about a point in a plane by breaking the force into its Cartesian components and/or moving
the vector to a more computationally-convenient position.
Recommended Hibbeler Problems (12th Edition): F4-5, 4-5, 4-7, 4-9, 4-23
4. (25 points) Determine the direction  (0° ≤  ≤ 180°) of the force F = 40 lb so that it produces a) the maximum
magnitude of moment about point A and b) the minimum moment magnitude about point A (hint: maximum
moment will occur if the perpendicular distance from the force to A is maximum).

Compute the resultant moment of a system of planar forces on a point.
5. (25 points) Determine the resultant moment of the three forces with respect to point A.
ES226 Exam 2 Study Guide                                                                                            Page 3

6.   (30 points) If is known that a moment of 960 N-m about D is required to straighten the fence post CD, determine the
tension that must be applied in the cable winch puller AB to create the required moment. Given: d = 2.80m.

7.   (10 points) Determine the moment of the 100-lb force about point A.
100-lb
45°

5 ft

A

5 ft

Specify the direction and sense of a moment using the right-hand rule.

Lesson 9 Moments in 3D
Compute the moment of a force about a point in space with and without the cross product.
Suggested Hibbeler 12th edition problems: F4-11, F4-12, 4.42, 4.43
8. (25 points) Determine the three Cartesian components of the moment of the 39-lb force about point A.
ES226 Exam 2 Study Guide                                                                                            Page 4

9.   (25 points) Determine the moment of the force about point O. Given: F = -50i. Note: Yes, the answer will be a
vector!

Compute the resultant moment from a system of forces in space with and without the cross product.
10. (25 points) Determine the resultant moment couple if d=0.4m.

Solution:

Lesson 11 Moment Couples
Show that a couple is a free vector.
Suggested Hibbeler 12th edition problems: F4.23, F4.24, 4.97, 4.101
11. (10 points). Show that the couple is a free vector.
100 lbs.

A                                      C                               E
B                                      D
10 ft.              10 ft.               10 ft.       10 ft.

100 lbs.

Compute the moment of a couple.
12. (20 points) Determine the magnitude of F so that the resultant couple moment is 450 lb-ft counterclockwise

13. (25 points) Determine the magnitude F of the vertical force applied to each wrench if the couple moment acting on
the pipe has a magnitude of 400 N-m (Ans: 992N)
ES226 Exam 2 Study Guide                                                                                                Page 5

Determine the resultant of moment couples and specify magnitude and direction angles.
14. (25 points). Specify the resultant moment couple in vector notation (ans: 52.0i +50j+30k)
Given: Applied moment couples M1 and M2, with orientations shown.

15. (25 points). Specify the resultant moment couple in vector notation.
Given: Four applied moment couples with orientations shown.

Lesson 12 Simplification of Force/Couple Systems
Replace a 2D or 3D system of forces and couples with an equivalent system, consisting of a single resultant force and
moment at a point
16. (30 points) Replace the system of forces and moments with a resultant force and moment acting at point O.
ES226 Exam 2 Study Guide                                                                                              Page 6

17. (20 points). Replace the system of forces with a resultant force and moment acting at point A.

18. (40 points) Replace the forces and couples that are applied to the pipe assembly with a single resultant force and
couple moment at point O, specifying the resultant force and moment as a Cartesian vector.

Replace a 2D system of forces and couples with an equivalent system, consisting of a single resultant force and specify the
location of the force.
19. (20 points) Replace the three forces acting on the shaft with a single equivalent resultant force, specifying where the
force acts, measured from end B.
ES226 Exam 2 Study Guide                                                                                            Page 7

20. (30 points) Replace the loading on the frame with a single force. Specify the angle this resultant force makes with
respect to the horizontal and determine where its line of action intersects member CD, measured from side C.

21. (30 points) Replace the loading on the frame with a single force. Specify the angle this resultant force makes with
respect to the horizontal and determine where its line of action intersects member AB, measured from side A.

1. FA=FB=575N; P=300N
2. FB = -19.2 kN, FC = 10.3 kN, FD = 6.34 kN
3. FB = 447N, FC = 342N, FD = 305N, P=960N
4. Moment is 0 at 166 degrees. Max Moment is 330 ft-lbs at 76 degrees
5. -2530 N-m
6. F=1225 N
7. M=0
8. <96,84,-180>
9. <0,-51.2,35.4>
10.
11. Moment about A is the same with the set of forces at C,D as when they are at B,C
12. F=139 lbs
ES226 Exam 2 Study Guide                                                                 Page 8

13. F=992 N
14. Resultant M = <51.96,50,30>
15. Resultant M = <85,40,0>
16. FR = <0 0 -500>, MR = <-650,462,28>
17. FR = <-40, -60, -80>, MR = <720, 0, 480>
18. FR = <141, 100, 159>, MR = <127, 0, -27>
19. FR = <-300, -740, 0> @ 6.57 feet
20. Resultant magnitude is 991 N at 117 degrees wrt to +x, at 2.8 meters from C.
21. Resultant magnitude is 922 lbs at 102.5 degrees wrt to +x, at 3.56 feet from A.

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