What are vector quantities any why they are important?
Answers
A VECTOR is a universal component that can be used to quantify how a FORCE, or ACTION, is applied to a structure, truss, beam or a number of other applications we will encounter.
Using the scenario of a golf club striking a golf ball, a few ways that we can apply VECTORS are:
· A VELOCITY VECTOR can describe the velocity motion of a golf ball
· A DISTANCE VECTOR can help determine how far away and in what direction a golf ball lands
· A FORCE VECTOR can describe how hard and in what direction the golf club strikes the golf ball
When performing engineering calculations and analysis utilizing VECTOR MECHANICS, we assume that the bodies and particles of interest are RIGID BODIES, and will not deform under load.
STATICS is the study of VECTOR MECHANICS that deals with bodies under action of forces that are either at rest or move with a constant velocity.
DYNAMICS is the study of motion of bodies under accelerated motion.
VECTORS are commonly represented in VECTOR NOTATION, where a SCALAR is used to represent the component of each quantity with respect to a particular axis or direction.
A vector representing 3 components, or dimensions, can be expressed in VECTOR NOTATION as:
Let’s highlight some of the more important CHARACTERISTICS of note:
·A SCALAR is a mathematical quantity that retains a magnitude only, whereas, a vector is one that possesses both magnitude and direction.
·The SENSE of a vector is the SIGN OF THE MAGNITUDE, or the direction in which the vector is acting. The sense is the part of a vector that indicates whether a football thrown is coming towards you or away from you.
·The POINT OF APPLICATION is the physical location on the object or in space where the vector is acting. The LINE OF ACTION represents the line space on which the vector is acting.
·The HEAD is the vector’s sense and is indicated by the arrowhead.
·The TAIL of the arrow typically depicts the vector’s point of application.
·The SHAFT is the actual line-length of the arrow representing the vector’s magnitude, where a longer vector drawing implies a large action and vice versa.
·The LABEL of the vector helps to label or distinguish the vector from other vectors in the analysis.
Two vectors are said to be the same if they have the same MAGNITUDE and DIRECTION. However, they can be anywhere in space, and do not need to have the same point of application.
A NEGATIVE VECTOR is a vector with the same magnitude, but OPPOSITE DIRECTION.
TYPES OF VECTORS:
FIXED – A FIXED (OR BOUND) VECTOR has a UNIQUE POINT OF APPLICATION specified and therefore can’t be moved without modifying the conditions of the problem. An example is the action of a force on a deformable body or the weight vector from the center of gravity of a body:
FREE – A FREE VECTOR does not have a CONFINED ACTION or associated with any particular line in space. An example of movement of a body without rotation. These vectors are usually moments and couples that result in a specific action but may be freely moved around the object without changing the original behavior.
SLIDING – A SLIDING VECTOR has a UNIQUE line in space, or LINE OF ACTION, which must be maintained, but NOT A UNIQUE POINT OF APPLICATION. An example is an external force on a rigid body such as that impulse in dynamics.