Vectors

Distance and Displacement

Distance and DisplacementDistance is the total path length. It is full described by magnitude (size) alone. Displacement is the direct length from a starting point to a finish point. To describe displacement both magnitude and direction must be given.

ExampleA woman walks 3 km due North (000) and then 4 km due East (090). Find her (a) distance travelled              (b) displacement, i.e. how far is from where she started?Using a scale diagram (1 cm = 1 km) draw an accurate scale diagram as shown above.  (a) Distance travelled = AB + BC = 7 km  (b) Measuring AC - 5 cm      Convert using the scale gives the magnitude of the displacement = 5 km       Use a protractor to check angle BAC = 53 degrees east of north.                       => displacement = 5 km (053)

Vectors and Scalars

Addition of Vectors

When vectors are being added, their magnitude and direction must be taken into account. This can be done using a scale diagram and adding the vectors 'tip to tail', then joining the starting and finishing points. The final sum is known as the resultant, the single vector that has the same effect as the sum of the individuals.

Vectors at right anglesIf the vectors are at right angles then it may be easier to use Pythagoras to find the resultant and trigonometry to find an angle.

Addition of more than two vectorsUse a scale diagram and ensure that each vector is placed " tip to tail " to the previous vector. The resultant vector is the vector from the starting point to the finishing point in magnitude and direction.

Resultant of a number of forcesThe resultant of a number of forces is that single force which has the same effect, in both magnitude and direction, as the sum of the individual forces.

Rectangular Components of a Vector

Any vector, v can be split up into a horizontal component Vh and vertical component Vv.

Distance and Displacement

Vectors and Scalars

Addition of Vectors

Vectors at right angles

Rectangular components of a vector