VCE Physics Unit 2 2008 Vectors Page 1

VCE Physics Unit 2 2008 Vectors Page 1

Scalars and Vectors

Vectors are quantities that have a direction as well as a magnitude. To specify completely a movement from one point to another we have to give the length as well as the direction. Eg. 5 km. due North.

Scalars are quantities that have magnitude but no direction, eg. volume, mass, energy.

Vectors are represented by symbols in bold, or which have a line above or below them. Eg. v, ,. A vector can be represented graphically by an arrowed line whose direction represents the direction of the vector, and whose length represents the magnitude of the vector.

Eg. 5 km east 10 km east 5 km west

Adding Vectors

Once the vectors are drawn, addition and subtraction is as follows. Suppose we have to add two vectors,

v1 and v2 shown below

We add the two vectors by drawing a line to represent v1 and then on the end of this line we draw another to represent v2, making sure that the arrow heads are such that the vectors are drawn 'head to tail' as shown below.

The sum of the vectors is then the third side of the triangle. Note the direction of the arrow heads. The resultant vector, can be used to replace the two original vectors, it starts at the same point as v1 and finishes where v2 finishes.

If we wish to add more than two vectors, we simply place them all head to tail to form a polygon. The order of the addition does not matter. The 'resultant vector' will always be the same.

Rearrange these and add in another order, is the resultant the same?

Subtracting vectors

To subtract vectors we add the negative of the vector to be subtracted.

Eg. a - b = a + (-b)

Change in velocity

When an object collides with another and changes its velocity, its change in velocity is a vector quantity found by subtracting the initial velocity from the final velocity.

Change in velocity = final velocity - initial velocity

Dv = vf - vI

If a ball bounces off a wall, the change in velocity can be determined graphically in a vector diagram.

RESOLUTION OF VECTORS

In some situations it is convenient to replace one vector by two which are equivalent. This process is called resolving a vector into its components. It is normal practice to resolve the vectors into two components that are at right angles to each other.

EQUILIBRIUM

A body is in equilibrium when the vector sum of the forces acting on it is equal to zero. When forces act parallel to each other the equilibrium conditions are simple

F1

F3

F2

F1 + F2 + F3 = 0

When the forces are not parallel the situation is a little more complex, but is usually best solved by resolving all vectors into 'X' and 'Y' components and then using Fx = 0 and Fy = 0.