6
Addition of Vector Forces
Purpose:
To practice vector addition by putting objects in equilibrium.
Use the graphical method and
component method of adding vectors to show the sum of the forces equal zero.
Apparatus:
Force table, String, Hanging masses, Protractor, Ruler, graph paper.
Background on Vectors:
Vectors are used to indicate size and direction of such things as forces, velocities, accelerations
etc.
The direction of the vector is specified by an angle from one of the primary axes.
The magnitude is
indicated by its length.
Figure 1 below illustrates this idea of a single vector.
θ
(x,y)
x
y
Scale
1 cm = 1 Newton
Figure 1.
A force vector defined by the length of the vector and the angle
θ
.
The magnitude of a single vector can be determined by measuring the vector and using a scale to
determine the actual magnitude.
The magnitude can also be determined mathematically
by using the
Pythagorean theorem, and measuring the x and y components
2
2
y
+
x
=
R
r
.
(eq. 1)
The angle which the vector makes relative to the x axis can be found by using
o
180
arctan
±
⎟
⎠
⎞
⎜
⎝
⎛
=
x
y
θ
.
(eq. 2)

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