A-level Mathematics M1 Force as a Agent

 10 June 03:48   Candidates should be able to:

    (a) accept that force is a agent and use arrowed curve to represent armament in one or two dimension(s);

    (b) accept that resultant is the sum of two or added forces, and acquisition resultants by artful instead of by drawing;

    (c) breach vectors into their apparatus to account the consequence and administration of the resultant (by un-breaking the apparatus into a vector)

    - Diagram of a vector

    All two dimensional armament and all motion of altar in two dimenions may be torn down into their corresponding x and y components. The

    sum of one or added armament acting on an item of accumulation is accepted as a vector. A agent has two properties, administration and magnitude. The consequence of a agent is represented by the breadth of the vector. The administration of a agent is represented by the bend of the resulant vector. For an anglular altitude of a agent to be useful, it haveto be abstinent from a advertence point, accepted as a accustomed line. Usually, vectors will be abstinent from 0 degrees, that is, the x-axis on the encartesian alike system. Agenda that vectors are usually represented in en:degrees as against to en:radians. As apparent below, two separate and connected armament acting aloft an item may be represented as a individual vector.

    Vectors may be activated to all assessable backdrop of movement (such as force, acceleration, connected movement). Some problems will ask for the apprentice to add calm agent apparatus or actuate an alien basic of a resultant vector. This may be acheived with about affluence graphically by accurate altitude with a adjudicator and en:protractor; about some times this is not feasable. In this case is acclimated to account vectors. Back two-dimensional vectors are create of beeline components, simple triangle geometry may be acclimated to account resultant angles and magnitudes.

    As said earlier, vectors may be mathematically represented.

    
ight | = F = sqrt

    $heta\; =\; arctan\; left\; (\; frac\; y\; x$
ight )

    (put in a table)

    $x\_1\; =\; F\_1\; cos\; heta\_1$

    $y\_1\; =\; F\_1\; sin\; heta\_1$

    $x\_2\; =\; F\_2\; cos\; heta\_2$

    $y\_2\; =\; F\_2\; sin\; heta\_2$

    $x\_R\; =\; x\_1\; +\; x\_2$

    $y\_R\; =\; y\_1\; +\; y\_2$

    
ight | = sqrt

    $heta\_R\; =\; arctan\; left\; (\; frac$
ight )

    
ight | = sqrt

    - (maybe appearance with column-vector notation)