Statics lecture 3 part A Coplanar Force Resultant|scalar notation / Cartesian notation{online class}

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CHAPTER OBJECTIVES
• To show how to add forces and resolve them into components using the Parallelogram Law.
• To express force and position in Cartesian vector form and explain how to determine the vector’s magnitude and direction
.• To introduce the dot product in order to determine the angle between two vectors or the projection of one vector onto another.

Determine the x and y components of F1 and F2 acting on the boom
shown in Fig. 2–18a. Express each force as a Cartesian vector.
SOLUTION
Scalar Notation. By the parallelogram law, F1 is resolved into x and
y components, Fig. 2–18b. Since F1x acts in the –x direction, and F1y acts
in the +y direction, we have
Ans.
Ans.
The force F2 is resolved into its x and y components as shown in
Fig. 2–17c. Here the slope of the line of action for the force is
indicated. From this “slope triangle” we could obtain the angle , e.g.,
, and then proceed to determine the magnitudes of the
components in the same manner as for F1. The easier method, however, consists of using proportional parts of similar triangles, i.e.,
Similarly,
Notice how the magnitude of the horizontal component, F2x, was
obtained by multiplying the force magnitude by the ratio of the
horizontal leg of the slope triangle divided by the hypotenuse;
whereas the magnitude of the vertical component, F2y, was obtained
by multiplying the force magnitude by the ratio of the vertical leg
divided by the hypotenuse. Hence,
Ans.
Ans.
Cartesian Vector Notation. Having determined the magnitudes
and directions of the components of each force, we can express each
force as a Cartesian vector.
Ans.
F2 = 5240i - 100j6 N Ans.
F1 = 5-100i + 173j6 N
F2y = -100 N = 100 NT
F2x = 240 N = 240 N :
F2y = 260 Na 13 5 b = 100 N
260 N F2x = 12 13 F2x = 260 Na 12 13 b = 240 N
u = tan-1(12 5 )
u
F1y

[kylequerijero]

This is correct but why do they use sine in books. In the book they show F1x as -200sin(30). What is the explanation behind this?