Experiment 4
Force Table
Thursday’s 12:001:50 PM
Experiment date: February 9
th
, 2017
Submission date: February 16
th
, 2017
Purpose
The purpose of this experiment is to learn how to add a set of vectors using three methods
experimental, analytical, and graphical to find the resultant vector. We are going to use a force
table to find the equilibrium force and angles for these three measurements:
1)
´
F
1: 200g at 30.0
o
;
´
F
2: 200g at 120.0
o
2)
´
F
1: 150g at 30.0
o
;
´
F
2: 150g at 150.0
o
;
´
F
3: 150g at 180.0
o
3)
´
F
1: 250g at 30.0
o
;
´
F
2: 200g at 120.0
o
;
´
F
3: 150g at 180.0
o
Theory
The equipment that will be used is a force table, weight hangers, slotted weights (mass),
protractor, and a compass. We need to know that a scalar quantity is different than a vector
quantity. A scalar quantity is a quantity that can be specified by its magnitude alone such as time
(t), mass (m), volume (V), etc. A vector quantity is a quantity that must be specified by both its
magnitude and direction such as force (
´
F
), velocity
(
´
v
)
, acceleration
(
´
a
),
etc. There
are several representations of a vector. For example
´
F
,
is a symbol that has an arrow at the
top which
indicates that force is a vector, and
F =

´
F
∨
¿
indicates its magnitude. A graph is
also used to represent a vector. On the graph is an arrow, whichever direction the arrow is
pointing to, is the direction of the force.
´
F
Also, the length of the arrow is proportional
to the magnitude of the force. The components of a vector are
´
F
=
´
F
x
+
´
F
y
=
F
x
^
x
+
F
y
^
y
where
^
x
and
^
y
are unit vectors (or direction vectors), which are used to indicate the directions of
the
x
and
y
axes respectively. A unit vector is a vector of the length 1, i.e.,

^
x
 = 
^
y

≡
1
The two components of
´
F
are
F
x
= F
cos
θ
and
F
y
= F
sin
θ
The magnitude of
´
F
is
F
=
√
F
x
2
+
F
y
2
The direction of
´
F
is tan
θ = F
y
/ F
x
or
θ =
tan
1
(
F
y
/ F
x
)
However, a vector can be moved from one location to another in space as long as its magnitude