Mechanics: Statics Force 1 Draft for Information Only
ForcesThe effect of force on an object can be characterized by its point of application, magnitude, and direction. As force has both magnitude and direction, it is a vector quantity. The unit of force is Newton. Force Vectors A force vector can be represented by an arrow with the length of arrow represents the magnitude of the force, the angle between the arrow and the coordinate axis defines the direction of force indicated by the line of action, and the arrow head indicates the sense of direction. Forces in a Plane When more than one force act on a point, they can be replaced by a single resultant force with teh same effect on the point of action. The resultant force can be determined by means of vector addition.
Force decomposition From the parallelogram Law, force can be resolved into two components. When the two components are perpendicular to each other in the form of a rectangle, they are called rectangular components. or Assumed two unit vectors, i and j, with unit magnitude along the x and y axis. Then , , and , imply The two components of the force vector can be obtained by and The magnitude of the force vector can also be obtained by
And the direction of the force vector can also be obtained by Force Equilibrium According to Newton's first law of motion, when a particle is in equilibrium, the resultant of all the forces acting on it is zero. That is And graphically in the form of force polygon, , imply When there are only three applied forces, the problem can be reduced to a force triangle and be solved by trigonometry. Analytically, forces can be resolved into rectangular components to form the equations of equilibrium. Imply Therefore, and ©sideway ID: 110400006 Last Updated: 30/4/2011 Revision: 0 Ref: References
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