s) Using the method of Polygon of Forces, Parallelogror Forces and the Algebraic
ID: 1656409 • Letter: S
Question
s) Using the method of Polygon of Forces, Parallelogror Forces and the Algebraic Method, Find the resultan indicated below? (For 1a) and 1b), an approxima solution is adequate ensuring questions on the examination) of the Forces te graphical adequate time to complete all Given the force system below: A4(100 N) 225° c (200 N) B (150 N) 5a) Using the Method of Polygon of Forces draw the resultant R Where R is A+B C 5b) Using the Method of Parallelogram of Forces, draw the resultant R Where R is A + B C Sc) Find the i) Magnitude and ii) Direction of the Resultant Force using the Algebraic Method, Where R A BExplanation / Answer
5b.)We have used the phrase resultant in stating the requirement for static equilibrium of an isolated particle – the resultant of all forces acting on the isolated particle must vanish. Often we use resultant to mean the vector sum of a subset of forces acting on a particle or body, rather than the vector sum of all such forces. we can say “the resultant of the two cable tensions, F and FC acting A at point B in the force vector -W”. The resultant is constructed using the so called parallelogram law for vector addition. FA + FC can then be read as -W, the vector equal in magnitude to the weight A C vector W but oppositely directed.
We can also speak of a single force vector as being the resultant of its components, usually its three mutually perpendicular (or orthogonal) rectangular, cartesian components.The vector F has components F , F and F . x y z The latter three mutually perpendicular vectors are usefully written as the product x of a scalar magnitude and a unit vector F y indicating the direction of the vector component. The three unit vectors are often indicated by i, j and k and that is the convention we will follow in this text. The vector resultant or sum can be written out as
F F= x + Fy + Fz or, equivalently F = F i + Fy x j + Fzk
Note the convention for designating a vector quantity using bold face. This is the convention we follow in the text. In lecture it is difficult to write with chalk in bold face. It is also difficult for you to do so on your homework and exams. In these instances we will use the convention of placing a bar (or twiddle) over or under the letter to indicate it is a vector quantity.
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