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48610 Introduction to Mechanical and Mechatronics
Engineering
Engineering Mechanics
Sample problems booklet (with solutions) The following set of problems is provided:
• To aid you in your learning of engineering mechanics; and, • As an example of the acceptable standard for setting out and presenting your work
The best way to make use of these example problems is to attempt them yourself before looking at the solutions. The majority of the problems have full handwritten solutions. Your solutions to quiz/assignment questions should be of similar quality in presentation and format. A soft copy of these sample problems is available on UTSOnline. All problems are from Hibbeler “Engineering Mechanics – Statics”, 3rd SI Ed., PrenticeHall except problems 2/19, 24, 30, 32, 41, 46, 3/6, 8 which are taken from Meriam and Kraige “Engineering Mechanics – Statics”, 3rd SI Ed., Wiley. Full handwritten solutions by Terry Brown, Faculty of Engineering, UTS
48610 Introduction to Mechanical and Mechatronics Engineering Sample problems booklet
Problem Set 1 2-2. Determine the magnitude of the resultant force if: (a) ; (b) 21 FFFR += 21 FFFR −=′
Prob. 2-2
Prob. 2-11
Prob. 2-3
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48610 Introduction to Mechanical and Mechatronics Engineering Sample problems booklet
Prob. 2-34
Prob. 2-31
Prob. 2-2
Prob. 2-39/40
Prob. 2-51
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Problem Set 2
Prob. 3-2
Prob. 3-1
Prob. 3-15
Prob. 3-7
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Prob. 3-35
Prob. 3-24
Problem Set 3
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48610 Introduction to Mechanical and Mechatronics Engineering Sample problems booklet
Prob. 4-30
Prob. 4-20
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48610 Introduction to Mechanical and Mechatronics Engineering Sample problems booklet
Prob. 4-76
Prob. 4-77
Prob. 4-114
Prob. 4-118/119
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48610 Introduction to Mechanical and Mechatronics Engineering Sample problems booklet
Problem Set 4
Prob. 5-3
Prob. 5-4
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Prob. 5-22 Prob. 5-2/12
Prob. 5-29
Prob. 5-26
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Rigid body equilibrium problem 1 The beam ABC is loaded via a 500 N.m couple and a 600 N force as shown. The beam
is connected to the rest of the system by a pin joint at B and a roller support at C. Determine the magnitude of the reaction forces on the beam at the supports.
400
500 N.m A
B
C
600 N 30
500300
Dimensions in mm
Rigid body equilibrium problem 2
The beam ABC is loaded via a 500 N.m couple and a 600 N force as shown. The beam is connected to the rest of the system by a pin joint at B and a roller support at C. Determine the magnitude of the reaction forces on the beam at the supports.
Dimensions in mm
400 500 N.m A
B
C
600 N
20
500 300
8a
48610 Introduction to Mechanical and Mechatronics Engineering Sample problems booklet
Prob. 5-46
Prob. 5-47
Prob. 5-51
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jRiR yxˆˆ +=R
ji ˆ245ˆ8.88 +=R
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Prob 4-30
Prob 4-77
Prob 4-76
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Prob 5-3
Prob 5-4
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Prob 5-2/12
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Prob 5-22
Prob 5-26
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Prob 5-29
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Rigid body equilibrium problem 1 The beam ABC is loaded via a 500 N.m couple and a 600 N force as shown. The beam
is connected to the rest of the system by a pin joint at B and a roller support at C. Determine the magnitude of the reaction forces on the beam at the supports.
400
500 N.m A
B
C
600 N 30
500300
Dimensions in mm
Solution:
400
500 N.m A
B C
300 500 60RBy
RBx RC
600 N
+ 0BM
08.060cos3.0600500 CR
170060cos8.0
3.0600500
CR N
+ 0yF
060060cos yBC RR
25060cos1700600 yBR N
+ 0xF
060sin xBC RR
147260sin1700 xBR N
14932501472 2222 yx BBB RRR N
Final answers: RB = 1.49 kN , RC = 1.70 kN Check: + 0CM
05005.06008.0 yBR
2508.0
5005.0600
yBR N OK
34b
Rigid body equilibrium problem 2
The beam ABC is loaded via a 500 N.m couple and a 600 N force as shown. The beam is connected to the rest of the system by a pin joint at B and a roller support at C. Determine the magnitude of the reaction forces on the beam at the supports.
Dimensions in mm
400 500 N.m A
B
C
600 N
20
500 300
Solution:
400 500 N.m A
B
C RC
RBy
RBx
20
500 300
600 N
+ 0BM
04.03.0600500 CR
17004.0
3.0600500
CR N
+ 0yF
060020sin yBC RR
118120sin1700600 yBR N
+ 0xF
020cos xBC RR
159720cos1700 xBR N
198611811597 2222 yx BBB RRR N
Final answers: RB = 1.99 kN , RC = 1.70 kN Check: + 0AM
05005.06008.0)20sin8.04.0( yBC RR
substitute 1181yBR N
169920sin8.04.0
5005.06008.01181
CR N OK
34c
Prob 5-46
Prob 5-47
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Prob 5-51
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