Vectors, Forces and Moments
Representing physical quantities by vectors
A graphic representation of forces is a valuable tool in physics. Some explanations in
aeronautics require the use of such representation. A vector is a line where its length is
proportional to a quantity with an arrow on one side to indicate the direction of such
quantity. The quantity could represent weight, force, speed, etc.
Resolving vectors - The figure above illustrates vector resolution by components. In the first example, a boat crosses
a river without compensating for the current. Vector (a) represents the actual distance (D)
traveled. Vector (b) shows the distance traveled down stream while vector (c) represent the
distance traveled across. The actual speed (V), the speed across (v1) and the speed down
stream (v2) are proportional to the distances D, d1 and d2. It is stated that vector (b) and
(c) are components of vector (a).
Similarly, the second example illustrates two forces F1 and F2 exerted on a box. Vector (f} is a graphic representation of the resultant force F res.
Forces, Equilibrium and Moments
There are times that multiple forces act on a single
object. An object is said to be in an equilibrium when the sum of all the forces equals zero
. The model that interests us most is an object which has a single pivotal point.
The turning effect of an applied force about a pivotal point is defined as moment ( torque).
The moment is the product of a force and the distance from the point where the force is
applied to the pivotal point . Moments are expressed in lb.oft or kg.ometer in the
metric system. The idea is best demonstrated in above figure(a). If the force applied is F and
the arm is A then the moment that is affecting the bolt is:
In (b), a board placed on a pivot with two weights placed one on each end. For the board to
remain in an eqilibrium, the sum of moments must equal sero . In other words,
W1xL1 = W2o L2
W1xL1 - (-W2xL2) = 0.
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