Introduction
The objective for the current chapter is to investigate the effects of forces on particles:- replacing multiple forces acting on a particle with a single equivalent or resultant force
- relations between forces acting on a particle that is in a state of equilibrium
The focus on particles does not imply a restriction to miniscule bodies. Rather, the study is restricted to analyses in which the size and shape of the bodies is not significant so that all forces may be assumed to be applied at a single point.
Resultant of Two Forces
- force: action of one body on another; characterized by its point of application, magnitude, line of action, and sense.
- Experimental evidence shows that the combined effect of two forces may be represented by a single resultant force.
- The resultant is equivalent to the diagonal of a parallelogram which contains the two forces in adjacent legs.
- Force is a vector quantity.
Vectors
- Vector: parameters possessing magnitude and direction which add according to the parallelogram law. Examples: displacements, velocities, accelerations.
- Scalar: parameters possessing magnitude but not direction. Examples: mass, volume, temperature
- Vector classifications:
- Fixed or bound vectors have well defined points of application that cannot be changed without affecting an analysis.
- Free vectors may be freely moved in space without changing their effect on an analysis.
- Sliding vectors may be applied anywhere along their line of action without affecting an analysis.
- Equal vectors have the same magnitude and direction.
- Negative vector of a given vector has the same magnitude and the opposite direction.
Rectangular Components of a Force: Unit Vectors
- May resolve a force vector into perpendicular components so that the resulting parallelogram is a rectangle.Fx & Fy are referred to as rectangular vector components
- Vector components may be expressed as products of the unit vectors with the scalar magnitudes of the
vector components
