Mech Sample Probs(3)

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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48610 Introduction to Mechanical and Mechatronics Engineering Sample problems booklet

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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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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