ENGI 1313 Mechanics I
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1 ENGI 1313 Mechanics I Lectue 03: Foce Vectos and Paallelogam Law Shawn Kenny, Ph.D., P.Eng. Assistant Pofesso Faculty of Engineeing and Applied Science Memoial Univesity of Newfoundland spkenny@eng.mun.ca
2 Revised Couse Method of Evaluation 6 Tutoial Quizzes 15% Duing week 38, 39, 40, 43, 44, & 45 Best 5 out of 6 towad final Mid-Tem Exam 30% Oct. 18 Final Exam 55% Dec S. Kenny, Ph.D., P.Eng.
3 Tutoial Sessions Teaching Assistants Kenton Pike Nasse Daiyan YanZhen Ou Section Day Mon Thu Thu Thu Fi Fi Time 3 3:50 2 2:50 4 4: :50 3 3:50 4 4:50 Room EN1040 EN1040 EN1040 EN2007 EN1040 EN S. Kenny, Ph.D., P.Eng.
4 Chapte 2 Objectives to eview concepts fom linea algeba to sum foces, detemine foce esultants and esolve foce components fo 2D vectos using Paallelogam Law to expess foce and position in Catesian vecto fom to intoduce the concept of dot poduct S. Kenny, Ph.D., P.Eng.
5 Lectue 03 Objectives to eview concepts fom linea algeba to sum foce vectos, detemine foce esultants, and esolve foce components fo 2D vectos using Paallelogam Law S. Kenny, Ph.D., P.Eng.
6 Intoductoy Concepts Scala Magnitude (value) and sense (positive, negative) No diection Examples Mass Volume Length Tempeatue Speed C = A + B C = 10 kg + 12 kg = 22 kg S. Kenny, Ph.D., P.Eng.
7 Intoductoy Concepts Vecto Magnitude Sense (+, -) Diection o oientation Magnitude Convention Textbook is boldface, A PowePoint notation typically A Examples Foce Velocity Diection Sense S. Kenny, Ph.D., P.Eng.
8 Scala Multiplication and Division Change in Magnitude Change in Sense F = m a S. Kenny, Ph.D., P.Eng.
9 Vecto Opeations Engineeing Need Detemine esultant foce due to applied foces Resolve foce into components Method Paallelogam law F = F Tiangle constuction R F + F + F S. Kenny, Ph.D., P.Eng.
10 Vecto Addition Paallelogam Law Resultant Vecto (F R ) Gaphical constuction F = F + F R 1 2 Component Vectos (F 1, F 2 ) Vecto Tip F1 F R Resultant Vecto foms the Paallelogam Diagonal Vecto Tail F 2 Vecto Tip S. Kenny, Ph.D., P.Eng.
11 Vecto Addition Paallelogam Law Special case Collinea vectos Algebaic addition S. Kenny, Ph.D., P.Eng.
12 Vecto Addition Paallelogam Paallelogam Law Tip-to-Tail technique F = F + F R 1 2 Tiangle constuction F2 F1 F R S. Kenny, Ph.D., P.Eng.
13 Vecto Addition Paallelogam Paallelogam Law Tip-to-Tail technique F = F + F R 2 1 Tiangle constuction F R F 1 F S. Kenny, Ph.D., P.Eng.
14 Vecto Subtaction Paallelogam Law Tiangle Constuction Tip-to-Tail technique F 2 F = ( ) F F = F + F F R F S. Kenny, Ph.D., P.Eng.
15 Paallelogam Law Multiple Foce Vectos F + F 1 F2 2 F = = F 1 F R F + F F 2 + F3 ( F ) 1 + F2 + F3 F 1 F 2 F S. Kenny, Ph.D., P.Eng.
16 Vecto Summation Resultant Foce Magnitude Cosine law S. Kenny, Ph.D., P.Eng.
17 Vecto Summation Resultant Foce Diection o Magnitude of Component Foces Sine law a + b + c = 180 o S. Kenny, Ph.D., P.Eng.
18 Applications Lifting Devices S. Kenny, Ph.D., P.Eng.
19 Applications Guyed Towes S. Kenny, Ph.D., P.Eng.
20 Applications Cable Stayed Bidge S. Kenny, Ph.D., P.Eng.
21 Applications Offshoe Platfom Foundation Connections S. Kenny, Ph.D., P.Eng.
22 Applications Towing S. Kenny, Ph.D., P.Eng.
23 Compehension Quiz 2-01 Scala o Vecto? Foce Vecto Time Scala Mass Scala Position Vecto S. Kenny, Ph.D., P.Eng.
24 Compehension Quiz 2-02 Q: Is this the coect application of the paallelogam law to detemine the esultant foce vecto (F R )? F 1 = 4 kn X F R sin ( ) sin F R = 4 kn 90 F 2 = 10 kn F R = 6.93 kn Y 4 kn S. Kenny, Ph.D., P.Eng.
25 Compehension Quiz 2-02 (cont.) A: No Tip-to-Tail tiangle constuction technique F 1 = 4 kn X 30 θ 1 θ R = 180 ( ) = 120 F 2 = 10 kn θ R θ 2 F R Y F 1 = 4 kn S. Kenny, Ph.D., P.Eng.
26 Compehension Quiz 2-02 (cont.) Detemine Resultant Foce Magnitude Cosine Law 2 2 FR FR = F + F 2 F1 F2 cosθ 1 2 R = 30 F 1 = 4 kn θ 1 F 2 = 10 kn F R θ R θ 2 Y F 1 = 4 kn θ R = 120 X F 2 2 ( 4 kn) + ( 10 kn) 2 ( 4 kn)( 10 kn) cos kn R = = Theefoe F R = 12.5 kn S. Kenny, Ph.D., P.Eng.
27 Compehension Quiz 2-02 (cont.) Detemine Resultant Foce Diection Sine Law F1 sinθ = θ 1 F R sinθ R 4 kn sin kn 1 o 1 = sin = Theefoe 43.9 fom hoizontal (clockwise) 30 F 1 = 4 kn 43.9 θ 1 F 2 = 10 kn F R θ R θ 2 Y F 1 = 4 kn θ R = 120 X S. Kenny, Ph.D., P.Eng.
28 Example Poblem 3-01 Detemine the component magnitudes (F X and F Y ) of the 700-lb foce esultant (F R ) F R = 700 lb Y F Y θ X F R = 700 lb Y Vecto Tiangle θ R F x 60 θ Y 30 X X S. Kenny, Ph.D., P.Eng.
29 Example Poblem 3-01 (cont.) Detemine Inteio Angles of Vecto Tiangle θ Y = = 30 α = = 60 θ X Y θ X = α = 60 θ R θ Y α 30 θ R = = 90 X S. Kenny, Ph.D., P.Eng.
30 Example Poblem 3-01 (cont.) Detemine the component magnitudes (F x and F y ) of the esultant 700-lb foce F Y F 60 R = 700 lb 90 F x Y F X = sinθ X FR sinθ R = 700 lb sin60 sin90 = 606 lb FR 700 lb FY = sinθy = sin30 = 350 lb sinθ sin90 R X S. Kenny, Ph.D., P.Eng.
31 Example Poblem 3-02 Poblem 2-12 fom Hibbele (2007) The component of foce F acting along line aa is equied to be 30 lb. Detemine the magnitude of F and its component along line bb. Given: S. Kenny, Ph.D., P.Eng.
32 Example Poblem 3-02 (cont.) Poblem 2-12 fom Hibbele (2007) Daw foce vectos F a = 30lb θ F b F θ b F b a F a = 30lb a b θ 2 = θ b = 60 θ F = θ 1 - θ b = = S. Kenny, Ph.D., P.Eng.
33 Example Poblem 3-02 (cont.) Poblem 2-12 fom Hibbele (2007) Magnitude of F & F b fom sine law F a = 30lb F θ 1 = θ a = 80 F b F = sinθ Fa sinθ 30 lb sin40 sin80 F = = a 19.6 lb θ 2 = θ b = 60 θ F = 40 F Fa = sinθb sinθ a 30 lb = sin60 sin80 b = 26.4 lb S. Kenny, Ph.D., P.Eng.
34 Vecto Summation Methods Studied Paallelogam Law Vecto tiangle constuction Sine law Cosine law Limitations Resultant of multiple vectos detemined though successive summation of two vectos Cumbesome fo lage systems S. Kenny, Ph.D., P.Eng.
35 Repesentative Poblems Hibbele (2007) Textbook Poblem Set Concept Degee of Difficulty Estimated Time 2-1 to 2-10 Vecto Addition Paallelogam Law Easy 5-10min 2-11 to 2-19 Vecto Addition Paallelogam Law Medium 10-15min 2-20 to 2-24 Vecto Addition Paallelogam Law Easy 5-10min 2-25 to 2-30 Vecto Addition Paallelogam Law Medium 10-15min S. Kenny, Ph.D., P.Eng.
36 Refeences Hibbele (2007) en.wikipedia.og S. Kenny, Ph.D., P.Eng.
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