1. 2 - 1 Engineering Mechanics Lecture 2 Composition and Resolution of forces 5-12-2016

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10. COMPOSITION OF FORCES 2 - 10 Trapezoid rule for vector addition Triangle rule for vector addition B B C C Law of cosines, Law of sines,

11. Sample Problem 2.1 2 - 11 The two forces act on a bolt at A. Determine their resultant. SOLUTION: Graphical solution - construct a parallelogram with sides in the same direction as P and Q and lengths in proportion. Graphically evaluate the resultant which is equivalent in direction and proportional in magnitude to the the diagonal. Trigonometric solution - use the triangle rule for vector addition in conjunction with the law of cosines and law of sines to find the resultant.

12. Sample Problem 2.1 2 - 12 Graphical solution - A parallelogram with sides equal to P and Q is drawn to scale. The magnitude and direction of the resultant or of the diagonal to the parallelogram are measured, Graphical solution - A triangle is drawn with P and Q head-to-tail and to scale. The magnitude and direction of the resultant or of the third side of the triangle are measured,

13. Sample Problem 2.1 2 - 13 Trigonometric solution - Apply the triangle rule. From the Law of Cosines, From the Law of Sines,

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15. Sample Problem 2.2 2 - 15 a)the tension in each of the ropes for  = 45 o A barge is pulled by two tugboats. If the resultant of the forces exerted by the tugboats is 5000 N directed along the axis of the barge, determine

16. Sample Problem 2.2 2 - 16 Graphical solution - Parallelogram Rule with known resultant direction and magnitude, known directions for sides. Trigonometric solution - Triangle Rule with Law of Sines

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19. Rectangular Components in Space 2 - 19 The vector is contained in the plane OBAC. Resolve into horizontal and vertical components. Resolve into rectangular components.

20. Rectangular Components in Space 2 - 20 With the angles between and the axes,

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23. 2 - 23 Example :

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