Force Table Vector Lab
Introduction:
Force is a vector quantity as is displacement, velocity and acceleration. When a body is in static
equilibrium (not accelerating), the vector sum of all the forces acting on the body must be zero: F = 0. In
this lab, you will analyze several forces that are balanced in equilibrium using the graphical method for
adding vectors, which is also known as the parallelogram method.
To graphically find the resultant of two vectors, use the parallelogram method as follows:
1. Draw the two vectors with a magnitude or size scaled to the actual value. For example, if the
force of vector A is 5N, then 5N may equal 5 cm.
2. Draw the angle between them using a protractor.
3. Redraw vectors A and B as in the diagram below such that they are parallel to each other. Use a
protractor and a ruler. Use the supplementary angle to obtain the proper directions for the
vectors.
4. Draw the resultant between where the tails of the two vectors meet to where they meet again at
the tips. The length and angle of this vector is the sum of vectors A and B.
A = 5.0N
B = 3.0N
 = 30
A = 5.0N
B = 3.0N
R
R = 7.8N
B = 3.0N
 = 150
A = 5.0N
For this lab, you will be using a force table. A force table consists of a stand holding a circular board with
degree markings around the outer rim. Three strings are tied to a ring at the center of the table; each
string passes over a pulley clamped to the edge of the board with a mass holder attached to the hanging
end. Masses placed in the holders create tensions (forces) in the strings attached to the ring. When the
vector sum of these tensions is zero, the ring will be in equilibrium such that it will be in a rest position
concentric with the center of the force table.
Purpose:
To develop the graphical method used in the resolution and composition of forces.
Pre-Lab:
Given two forces of 20N and 30N acting at a point and separated by an angle of 30, what is the net force
required to produce equilibrium? Solve both graphically and analytically (using coordinates) on a
separate piece of paper using a protractor, ruler and scientific calculator. Note: the force required for
equilibrium will need to oppose the resultant of these two forces.
Materials:
Force table
String/Ring assembly
3 pulleys
3 mass hangers
1 set of masses
Ruler
Protractor
Paper
Graph Paper
Procedure:
1. Place a center post in the hole in the top of the table and place the string/ring assembly over it. A pencil
or pen may be used in place of the center post.
2. Clamp the three pulleys to the table and guide the strings through them.
3. Place the hangers at the end of the strings of the string/ring assembly.
4. Choose three similar masses and place them on the hangers. Note: You must convert the mass from
grams to kilograms by dividing by 1,000. To determine force in Newtons, you must multiply this
value by g (the gravitational constant = 9.81 m/s2). Note: The mass of each hanger must be
accounted for as well.
5. Arrange the hangers such that the forces are now balanced and in equilibrium.
6. Remove the center post from the ring and place a piece of paper under the ring and strings.
7. Mark the paper with two points for each of the three strings such that a graphical analysis can be
conducted.
8. Repeat steps 4 – 7 with three different masses.
Analysis:
1. Summarize the data graphically. Use Forces A and B to find Force C.
2. What is the significance of the equilibrant? How does it relate to your graphical drawings?
3. Compare the values for the resultant vector determined both graphically for each trial. Are they similar or
different? i.e. Does the resultant of A and B equal C? See your percent error.
Error Analysis & Conclusions:
Three Equal Masses
Magnitude
Direction
( CCW from A)
% Difference in
Magnitude
Degrees Difference in
Direction
% Difference in
Magnitude
Degrees Difference in
Direction
Force A
Force B
Force C
Resultant
(Graphical)
Three Unequal Masses
Magnitude
Force A
Force B
Force C
Resultant
(Graphical)
Direction
( CCW from A)