Resultant Vector of Mechanics
A number of forces acting on a structure can be reduced to a single resultant force, then this concept can assist in simplifying problem. Calculate the resultant force depends on the amount and direction of the gayagaya. Some way or method to calculate the resultant force, namely:
1. Method force vector addition and subtraction.
2. The method of triangular and rectangular-many vector style.
3. Method force vector projection.
For more details, here described each of the components of the method / how to find the resultant force.
1 Method force vector addition and subtraction
This method uses the concept that two or more styles contained in the working line of the same style (inline) can be directly added together (if the same direction / direction) or subtracted (if the opposite direction).
Figure 2.11 The sum of the vector in the same direction and aligned into a resultant force R
2. The method of triangular and rectangular-many style vector
This method uses the concept, if the forces that work are not aligned, it can be used the way Paralellogram and Triangle Style. The method is suitable if the force-style is not much.
Figure 2.12. Two resultant force vectors that are not aligned
However, if there are more than two styles, it must be composed of a polygon (polygon) style. The forces then arranged in a row, following the clockwise direction.
3. The method of triangular and rectangular-many style vector
Figure 2.13. The resultant of several vectors style is not unidirectional.
If it has been established in terms of closed-many, then the solution is no net force or resultant force is zero. But if formed polygon is not closed, the lid line is the resultant force.
4. Method force vector projection
Projection method uses the concept that the projection of the resultant vector of the two forces on each axis is equal to the sum of the projections of each component on the same axis. As an example can be seen in Figure 7.
Figure 2.14. Projection Axis
Xi and X are respectively the projection style Fi and R on the x-axis. while Yi and Y are each projection style Fi and R on the y-axis. Where :
Xi = Fi. Cos αi; X = R cos αi; then X = ΣXi Yi = Fi. Sin αi; Y = R sin αi; then Y = ΣYi
Thus the method is not actually limited to two vectors style, but it could be more. If the only known vectors of force and the resultant force will be sought, then by knowing the cumulative number of components projection axis, ie X and Y, then the Pythagoras theorem can be searched value of the resultant force (R), wherein:
