PHY101 Lab # 2
THE FORCE TABLE EXPERIEMNT
Object:
To study and verify the laws of composition and resolution of vectors by:
 graphical method and,
 using the force table.
Apparatus:
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force table,
pulleys,
standard weights,
metric ruler and
protractor.
Theory:
A vector quantity is one that has direction as well as amount or magnitude. Take force as an
example. To be properly described, the direction of a force, as well as its magnitude, must be
given. The same is true for velocity also.
An object may be acted upon several forces at one time, each varying in magnitude and
direction. Their combined effect on the object depends on both the magnitude and the direction
of the forces. If two forces, equal in magnitude, act on the object in opposite directions, they will
produce no change in the state of motion of the object, and are said to produce a state of
equilibrium. Their net effect on the object is zero. If, on the other hand, the directions of the two
forces are at right angles to one another, a single force, called the resultant, can be found which
will produce exactly the same effect as the original pair. More generally, any number of forces
acting at or through a single point can be combined as one force of appropriate magnitude and
direction – called the resultant.
After the resultant force is found – the direction of the vector representing the resultant is the
direction of the motion of the object. If you would want to achieve the state of equilibrium with
the resultant, than the force equal in magnitude but opposite in direction to the resultant must be
applied to the object. The force, which can be added to produce equilibrium is, called the
equilibrant or resultant force.
To represent a vector quantity by graphical means, you draw an arrow whose length is
proportional to the magnitude of the quantity in question (force, velocity, ... ), and whose
direction is given by an angle with respect to some particular reference line. The ratio of the
magnitude of the vector quantity to the length of the arrow is called the scale or the scale factor.
Scale factors should always be chosen for their simplicity and for ease of computation. For
example, to represent a force of 100 g, one might draw an arrow 5cm long. The scale chosen is
20 g = 1cm. An arrow 13.2 cm long then would represent a force of 13.2 times 20 or 264 g.
20cm
x

1cm
13.2cm
x  264 grams
One method using graphical method to add two or more vectors in order to find the resultant is
called the parallelogram method. Two arrows, representing the two vectors, with their “tails” at a
common point, are drawn to scale with the proper angle between them. The parallelogram is
completed with the two arrows at adjacent sides. The diagonal from the common point to the
opposite vertex represents the resultant of the two vectors, i.e., its length is proportional to the
magnitude of the resultant, and its direction may be specified by the angle it makes with either of
the two original arrows. See Figure 1.
Resultant
Vector B
Vector A
Figure 1. Addition of two vectors
An example with three vectors F1, F2, and F3 is shown in Figure 2.
F
F3
F2
F1
Figure 2. Addition of three vectors
Example of four vectors added is shown in Figures 3 and 4.
Figure 3. Four given vectors
Figure 4. Addition of
four vectors
The resultant R of this set is then found by drawing an arrow from the point O to the head of the
last vector D. The magnitude of R can be found from its length and the scale used. The direction
of R is found by measuring the angle R makes with the reference, in this case vector A, with a
protractor. The equilibrint E is equal in magnitude but opposite in direction to that of R. That is,
the direction of E is 180o from that of R. This method can be applied to any number of vectors,
including two. The sequence of plotting the vectors is completely arbitrary.
Procedure:
1. Use the parallelogram method to find graphically the amount and direction of the resultant of
the forces involve in the two cases indicated by the table of results in this handout. Indicate
the scale being used and label the diagrams completely. Remember, the larger the scale you
choose, in general the grater the accuracy for your graphical solution.
2. Level the force table. Place tow pulleys and hang weights from them at the locations
indicated by problem 1 in the table of results. Remember to take in account weight of a pan.
To check your graphical solution with the force stable, attach the equilibrant (resultant force)
to the system. The ring should remain center when the pin is removed and the table and ring
gently tapped. If necessary, make minor adjustments in magnitude and/or angle of the
equilibrant (resultant force). Record these results on the data sheet. If discrepancies between
graphical solutions and force table results are large, recheck the graphical solutions.
3. Place three pulleys and hang weights from them at the locations indicated by problem 2 in
the table of results as in procedure 2 above.
Report for this lab:
For this experiment, you are to prepare one page written report to be submitted at the begging of
your next lab period. This particular should consist of the following:
A. Fill in the table with the data and results obtained graphically and experimentally.
B. Answer the following questions:
1. What is the definition of equilibrium?
2. Can you place three forces of 5 g, 6 g, and 12 g. so they are in equilibrium. Justify your
answer.
3. Suppose the that the three pulleys were placed on the force table at an angle of 0 o, 60 o,
and 120 o, with respect to the common reference with 100 g. on each string. Find the
magnitude and the direction of resultant force.
Table of Results
The instructor will give the magnitude and the direction of vectors F1, F2, and F3.
FORCE - Vector
Two Vectors
Magnitude
Direction
(mass in g) (angle in o)
F1 or mass in g
F2 or mass in g
F3 or mass in g
Resultant
by graph
Resultant
by force table
Force Table
Three Vectors
Magnitude
Direction
(mass in g)
(angle in o)