PHYS 1301 1L2
Ex. 4 The Addition and Resolution of Vectors: The Force Table
I.
Objective
Physical quantities are classified as either scalar or vector quantities. The
distinction is simple. A scalar quantity is one with magnitude only—for example,
speed and temperature. A vector quantity, on the other hand, has both magnitude
and direction. Such quantities include displacement, velocity, acceleration, and
force—for example, a velocity of 15 m/s north or a force of 10 N along the + x-
axis. Vectors are generally written using a boldface capital letter with an over
arrow, for example,
⃗
F
. A nonboldface letter, F, indicates a magnitude.
Because. Vectors have the property of direction, the common method of addition,
that is scalar addition, is not applicable to vector quantities. To find the resultant
or vector sum of two or more vector, special methods of vector addition are used,
which may be graphical and/or analytical. The chief methods of there will be
described, and the addition of force vectors will be investigated. The results of
graphical and analytical methods will be compared with the experimental results
obtained from a force table. The experimental arrangements of force will
physically illustrate the principles of the methods of vector addition.
II.
Theory
A.
Methods of Vector Addition: Graphical
Triangle Method
The vectors are placed “head-to-tail which would be
⃗
R
=
⃗
A
+
⃗
B
As long as the direction stays pointed in the same way, the vectors may move
around.
⃗
R
would be the vector sum and the magnitude of it would be relative
to the length of the vector arrow. The direction would be at the angle that is
proportional to
⃗
A
.
Polygon Method
When three vectors are being added,
⃗
R
=
⃗
A
+
⃗
B
+
⃗
C
. This method is basically
the head to tail method twice applied. To find the length and the angle can be
determined by the resultant of the vector
⃗
R
and in order to get that a graphical