2 - 1 Engineering Mechanics Lecture 2 Composition and Resolution of forces

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

Sample Problem 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.

Sample Problem 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,

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

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Sample Problem 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

Sample Problem 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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Rectangular Components in Space The vector is contained in the plane OBAC. Resolve into horizontal and vertical components. Resolve into rectangular components.

Rectangular Components in Space With the angles between and the axes,

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Example :

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