Vector Addition
When two or more forces act at the same time on an object and their vector sum is
zero, the object is in equilibrium. The diagram below illustrates three concurrent forces
acting on point P. Because point P is not moving, the three forces produce no net force
on point P, and the system is in equilibrium. In this experiment, you will determine the
vector sum of two of the concurrent forces, called the resultant, and investigate the
relationship of the resultant to the third force.
Spring
Scale
Mass
1. Set up the apparatus as shown above. With a protractor, very carefully measure each
of the three angles at the intersection of the three strings. Record these as well as the
values on the spring scale, and the mass.
2. Convert the mass to a force (weight) measurement by multiplying by 9.80 m/s2.
3. Using the angle measurements, construct a scale drawing on a blank piece of paper.
4. Using either the parallelogram method, or the head to tail method, add the two vectors
that were measured by the spring scale. Make sure to draw out all the steps. Record your
results in the data table provided.
5. Also calculate the resultant vector using vector math. Show your work on the side of
your drawing. Record your results in the data table.
6. Perform error and deviation calculations using the weight as your accepted magnitude,
and 180 opposite the direction of your weight as the accepted angle.
Graphical
Method
Magnitude of
Resultant
Vector (N)
Direction of
the Resultant
Vector (o)
Calculated
Method
Accepted
Value
Relative
Error
Relative
Deviation