Pasco Scientific ME-9447, Instruction Manual And Experiment Manual

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6
012-04715B Force Table
®
Component Method
Two forces are added together by adding the x- and y-components of the forces. First the
two forces are broken into their x- and y-components using trigonometry:
F
A
= A
x
x + A
y
y and B
x
x + B
y
y
where
A
x
is the x-component of vector F
A
and x is the unit vector in the x-direction. See
Figure 5. To determine the sum of F
A
and F
B
, the components are added to get the compo-
nents of the resultant F
R
:
F
R
= ( A
x
+ B
x
) x + ( A
y
+ B
y
) y = R
x
x + R
y
y
To complete the analysis, the resultant force must be in the form of a magnitude and a
direction (angle). So the components of the resultant (
R
x
and
R
y
) must be combined using
the Pythagorean Theorem since the components are at right angles to each other:
F
R
= R
2
+ R
2
tan
θ
=
R
x
R
y
And using trigonometry gives the angle:
Graphical Method
Two forces are added together by drawing them to scale using a ruler and protractor. The
second force (
F
B
) is drawn with its tail to the head of the first force (
F
A
). The resultant (
F
R
)
is drawn from the tail of F
A
to the head of F
B
. See Figure 6. Then the magnitude of the
resultant can be measured directly from the diagram and converted to the proper force using
the chosen scale. The angle can also be measured using the protractor.
Figure 5 Components
F
B
F
A
A
x
B
y
x
y
F
R
x
y
R
y
R
x
θ
F
B
F
A
F
R
Figure 6 Adding Vectors Head to Tail
θ