Addition of Vectors
The purpose of this exercise is to introduce the student to a variety of ways of determining the
vector sum of a series of vectors. The Instructor will assign a set of vectors for each group, each
vector expressed in polar form. The student should compare and contrast the various methods,
discuss limitations, etc. as part of the laboratory report.
Methods:
1. Component Method (Analytical): Express each vector in terms of components. Sum
the x components to determine the x component of the resultant. Sum the y components
to determine the y component of the resultant. Use these components for the resultant to
determine the magnitude and direction of the resultant.
Vector
V1
Assigned Vectors
Magnitude
Direction
Vector Components
Vx
Vy
V2
V3
V4
V5
R
2. Computer Method: Use the vector addition spreadsheet to add the vectors. Include a
printout of the spreadsheet with your report. Note that the spreadsheet includes a
graphical representation of the vector addition.
3. Force Table: When a set of forces acting on an object all act through the same point,
the net force on the object is the vector sum of the individual forces. The set of forces
corresponding to the assigned vectors are created by using counterweights attached to
strings that radiate out from a central point. The pulleys are set at the appropriate angles
by using the markings on the force table perimeter. The Equilibrant (E) is determined by
adding an additional counterweight, adjusting the weight and direction so that the ring at
the center of the force table is balanced (the central ring is centered). The Equilibrant is
the opposite of the resultant so R = E, so that the experimental value for the resultant
has a magnitude equal to the magnitude of the equilibrant, and a direction 180
R
E
4. Graphical Method: Add the vectors graphically by drawing them to scale on graph
paper using a ruler and a protractor. The length of the resultant is measured using the
ruler and the direction of the resultant is measured using the protractor. The student must
choose an appropriate scale so that the drawing fills the paper.
Results:
Method
Magnitude
Analytical
Computer
Force Table
Graphical
Direction
Resultant
x-component
y-component