2-9. The plate is subjected to the forces acting on members A and B as shown. If θ = 60 o, determine the magnitude of the resultant of these forces
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1 2-9. The plate is subjected to the forces acting on members A and B as shown. If θ 60 o, determine the magnitude of the resultant of these forces and its direction measured clockwise from the positie x axis.
2 2.17. The cable exerts a force of 600 N on the frame. Resole this force into components acting (a) along the x and axes and (b) along the y and u axes. What is the magnitude of each component?
3 2-25. The jet aircraft is being towed by two trucks B and C. Determine the magnitude of the two towing forces B and C if the resultant force has a magnitude R 10 kn and is directed along the positie x axis. Set θ 15 o.
4 2-9 Cosine law: (500)(400) cos lb Ans R Sine law: sin sin( 60 α) 400 α 10.9 o Ans
5 2-19. The horizontal force 500 N acts to the left at A on the two-member frame. Determine the magnitudes of the two components of directed along the axes of members AB and AC.
6 2-17 (a) Sine law: x 600 sin 45 sin 60 x 490 N Ans y 600 sin 75 sin 60 y 669 N Ans (b) Sine law: u 600 sin 15 sin 120 u 179 N Ans y 600 sin 45 sin 120 y 490 N Ans
7 2-19 Sine law: AC 500 sin 45 sin 75 AC 366 N Ans BA 500 sin 60 sin 75 BA 448 N Ans
8 2-24. Three chains act on the bracket such that they create a resultant force haing a magnitude of 500 lb. If two of the chains are subjected to known forces, as shown, determine the orientation θ of the third chain, measured clockwise from the positie x axis, so that the magnitude of force in this chain is a minimum. All forces lie in the x-y plane. What is the magnitude of? Hint irst find the resultant of the two known forces. orce acts in this direction The jet aircraft is being towed by two trucks B and C. Determine the magnitudes of the two towing forces B and C if the resultant force has a magnitude R 10 kn and is directed along the positie x axis. Set θ 15 o If the resultant R of the two forces acting on the jet aircraft is to be directed along the positie x axis and hae a magnitude of 10 kn, determine the angle θ of the cable attached to the truck at B such that the force B in this cable is a minimum. What is the magnitude of force in each cable when this occurs?
9 2-25 Sine law: C 10 sin 15 sin 145 C 4.51 kn Ans. B 10 B 5.96 kn Ans. sin 20 sin 145
10 2.4 Addition of a System of Coplanar orces - Resultant of more than two forces by 1. Successie application of Parallelogram Law 2. inding components of each force along specific axes Adding these components algebraically orming the resultant inding components - Resole each force into its rectangular components &, which lies along x & y axes. x y x & y axes : Horizontal & ertical or inclined but orthogonal perpendicular to one another By parallelogram law: x + y x + y - sense of direction of each components is represented graphically by the arrowhead. or analytical work: Need a notation to represent the sense of the direction.
11 notations Scalar Cartesian ector Scalar Notation: o for computational purposes not for graphical representation. Cartesian Vector Notation: Cartesian unit ectors î, ĵ : directions of x, y axes, respectiely. - dimensionless magnitude of unity - sense (arrowhead) analytically + or depending on pointing along + or (e) axes. x y î x ĵ y x î + y ĵ î x + y ( ĵ) î ĵ x y
12 Coplanar orce Resultants: Resultant of coplanar forces 1. resole each force into its x & y components. 2. add respectie components using scalar algebra - sketch components on x & y axes they are collinear 3. resultant is formed by adding resultants of x & y components using parallelogram law. Ex. * Using Cartesian ector notation 1 1x î + 1y ĵ 2 2x î + 2y ĵ 3 3x î 3y ĵ Resultant R Rx î + ĵ Rx (1x 2x + 3x ) ( 1y + 2y 3y ) x * Using Scalar Notation ( y) positie + Rx 1x 2x 3x 1y + 2y Resultant R 3y Rx +
13 In general where R Rx î + Rx x ĵ y Sign Conention: components with directional sense along (+e) axis are positie scalar. components with directional sense along ( e) axis are negatie scalar. and ice ersa the component means along +e axis. Signs of the components of the resultant specify their sense. - Sketch components Rx & Using Pythagorean theorem Resultant magnitude + R 2 Rx 2 Direction angle θ orientation direction & sense from trigonometry θ tan 1 Rx
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