LAB 3
Forces as Vectors
OBJECTIVES
1. Experimentally verify that vector methods describe the addition of forces.
2. Practice using vectors both graphically and analytically.
EQUIPMENT
Force Table, masses, mass hangers, rulers, protractors, paper, and calculators.
PROCEDURE
Part 1: Adding Two Perpendicular Vectors
Insert a nail through the washer and into the center hole in the force table (this keeps the ring
from moving when unbalanced forces are applied). Set one pulley at 0° (x-axis) and another at
90° (y-axis) on the force table. Then apply two forces to the center ring by hanging 25g and 45g
masses over the pulleys at 0° and 90°, respectively. Find the magnitude of the weight forces
(W) produced by these masses (m) using the equation W = mg. Note that for a given force, the
magnitude is given by W = mg and the direction is along the string direction. In your notes:
a. Draw a set of x-y axes and define a suitable scale (5 cm = 0.1 N) for drawing force vectors.
Use the "Graph paper" link on the lab page to get this graph paper. When you print the
page, be sure to set the "Page Scaling" to none.
b. Calculate your hanging masses (kg) into weight (N) using W = mg. Then convert your
weight into a length (cm) using the conversion factor (5 cm = 0.1 N). Record your results in
a table.
c. Graphically determine the magnitude and direction of the net force by drawing the vectors
tail-to-tip and measuring the magnitude (Rgraphical) and angle (graphical) of the resultant.
d. Analytically determine the magnitude Ranalytical and direction analytical of the net force by
creating a table of x- and y-components, adding the x-components to get the net xcomponent, adding the y-components to get the net y-component, and then finding the
magnitude and direction of the net force by combining the components.
e. Compare the magnitudes Rgraphical and Ranalytical and the angles graphical and analytical using the
percent difference:
%diff 
x
x graphical  xanalytical
graphical  x analytical

2
 100% .
Are the two methods consistent?
Part 2: Experimental Testing of Vector Addition
In theory, you should be able to balance the two forces in part (1) by applying a third force which is
equal in magnitude and opposite in direction (i.e. add 180o to the angle θ) to the sum you
determined above.
a. Translate the resultant R length (cm) back into a mass (grams) using a two step process: (i)
convert your centimeter length into a weight in Newtons; (ii) from your weight (N) get a mass
(grams) using W = mg where g = 9.81 m/s2.
b. Use the parallelogram rule to graphically add the three vectors (W 1, W 2 and inverse of R)
and show that the sum of these is zero.
c. Test your prediction experimentally, hang the predicted mass at the predicted direction.
Does the ring remain balanced when the nail is removed?
d. What is the sum of all three forces now acting on the ring?
Part 3: Resolution of a single force into components
On the force table, apply a single force (mass of 65 g) at an of 30o from the horizontal and
resolve this force vector into x- and y-components. Only do this analytically, not graphically.
a. Without converting the weight into a length, determine the x- and y-components of the
hanging mass of 65 g angled at 30o from the horizontal. Record your data in a table.
b. What two forces should be applied in the negative x- and y-directions, respectively, to
balance these components?
c. Experimentally test your predictions. Use the same procedure from Part (2).