2007 Engi.pps

ENGI 1313 Mechanics I

Lecture 31:

Mid-Term Review

Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland [email protected]

Overall Mid-Term Results 

Class Statistics (259) 

Average

• 67% 

Standard deviation

• 17% 

Standard deviation between sections

• 3% 

2

Solution Posted

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31

Term A/B Exam (Mon. Oct 22) 

Results are not Back 

Student Numbers

• 200600816 • 200641421 • 200641728 • 200643385 • 200714459 • 200737914 • 200749075 3

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31

No Record of Mid-Term Exam 

Contact Me Immediately to Resolve 

Student Numbers

• 200643849 • 200626752 • 200402782 • 200565687 • 200672285

4

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31

Problem 1 

Determine the components of the F force acting along the u and v axes. 

Given:

• 1 = 70 • 2 = 45 • 3 = 60 • F = 250N 5

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31

Problem 1 (cont.) 

Problem Characteristics 

Force vectors • No right rectangular

• 

Solution Method 

6

coordinate system Forces on specified axes

Parallelogram or triangle construction • Law of sines

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31

Problem 1 (cont.) 

Force Triangle   180   70   45   65  Fu 250 N Fv   sin 45  sin 65  sin70 

Fu  320N

Fv  332N

7

© 2007 S. Kenny, Ph.D., P.Eng.



Fv

F = 250 N

1 = 70 2 = 45

Fu

ENGI 1313 Statics I – Lecture 31

Problem 2 

The three cables are used to support the lamp of weight W. Determine the force developed in each cable for equilibrium. 

8

Given: • a=4m • b=4m • c=2m • W = 600 N © 2007 S. Kenny, Ph.D., P.Eng.

4m 2m 4m

W = 600 N ENGI 1313 Statics I – Lecture 31

Problem 2 (cont.) 

Problem Characteristics 

Particle Equilibrium

• Scalar or vector

4m

approach 

Solution Method 

2m 4m

Summation of Forces W = 600 N

9

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31

Problem 2 (cont.) 

FBD and Unit Vectors





  2 ˆi  4 ˆj  4 kˆ m 1 2 2 u AD    ˆi  ˆj  kˆ 3 3 3 22  42  42 4m  uAC  ˆi  u AB  ˆj  uW  kˆ

FAD

2m 4m FAC

FAB

W = 600 N 10

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31

Problem 2 (cont.) 

Equilibrium Equation      F   Fx ˆi   Fy ˆj   Fzkˆ  0

   FAB uˆ AB  FAC uˆ AC  FAD uˆ AD  W uˆ w  0 4 m



Three Equations  3 FAD  W  900 N 2  1  FAC  FAD  300 N 3  2  FAB  FAD  600N 3

11

FAD

© 2007 S. Kenny, Ph.D., P.Eng.

2m 4m FAC

FAB

W = 600 N ENGI 1313 Statics I – Lecture 31

Problem 3 

Force F is applied to the handle of the wrench. Determine the angle  between the tail of the force F and the handle AB. 

12

Given: • a = 0.30 m • b = 0.50 m • F = 80 N • 1 = 30 • 2 = 45 © 2007 S. Kenny, Ph.D., P.Eng.

F = 80N 

1 2

0.3 m 0.5 m

ENGI 1313 Statics I – Lecture 31

Problem 3 (cont.) 

Problem Characteristics 



F = 80N

Vector projection



Solution Method 

2

Dot product 0.3 m 0.5 m

13

© 2007 S. Kenny, Ph.D., P.Eng.

1

ENGI 1313 Statics I – Lecture 31

Problem 3 (cont.) 

Unit Vectors

 

 



 uF   cos 30  sin 45  ˆi  cos 30  cos 45  ˆj  sin 30  kˆ  u AB   ˆj





F = 80N

30 45



Dot Product    u 1 F  u AB    cos     uF u AB

   

0.3 m 0.5 m

 0.6124  0   0.6124  1  0.5  0      cos   1 . 0 1 . 0   1

14

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31

Problem 4 

The hood of the automobile is supported by the strut AB, which exerts a force F on the hood. Determine the moment of this force about the hinged axis y. 

15

Given: • a = 0.60 m • b = 1.50 m • c = 0.25 m • d = 1.00 m • F = 100 N © 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31

Problem 4 (cont.) 

Problem Characteristics 



Solution Method 

16

Moment about a specified axis Triple scalar product

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31

Problem 4 (cont.) 

Unit Vector





  1.25 ˆi  0.6 ˆj  1kˆ uF  1.25 2  0.6 2  12  uF   0.731 ˆi  0.3509 ˆj  1kˆ







Moment about Y-axis 0 1 0 uˆ y   uF  1.50 0 0 rOA  87.7 N  m   73.1 35.09 58.48 F

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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 31