1. Set up three newton (spring) balances as in Fig. 3.7. Each newton balance is connected to the same centre point (O), which is at rest.
2. Take any two balance vectors and draw them on the paper.
3. The resultant of these two vectors will be equal but opposite in direction to the third force. This is shown in Fig. 3.7 where the resultant of the forces from A and C are shown equal and opposite to balance B (equal and opposite to B).
FIG 3.7
Resolving a vector into perpendicular components
Resolving a vector is the reverse process of finding the resultant of any two vectors.
NOTE
If you recombine the x and y vectors, the resultant will be the same as the original vector.
We can use the parallelogram law to resolve a vector into perpendicular components (also known as orthogonal components). Any given vector can be broken down into an x (horizontal) component and a y (vertical) component, as shown in Fig. 3.8. Both components originate from the tail of the original vector.
y A B O C paper sticky tape pull
x
FIG. 3.8 Resolving a vector into perpendicular components
Calculating the magnitudes of perpendicular vectors
Suppose vector F has been resolved into two perpendicular components x and y and that F makes an angle q with x (Fig. 3.9). The magnitude of x and y will be: x = F cos p
y = F sin p
From your Junior Certificate Maths course, remember that cos q = sin (90° – q ). If q = 30°, x = F cos 30° and y = F sin 30° (or y = F cos 60°).
y
These can be shown using trigonometry: cos q = Adjacent
Multiplying both sides by F gives: F cos q = x x
FIG. 3.9 Calculating magnitudes of perpendicular vectors
So 26 FUSION Similarly: sin q = Opposite F sin q = y.
