We're now dealing with forces in two dimensions in conceptual physics. I teach everything graphically, with ruler and protractor: to add forces, we use the parallelogram method; to break forces into components, we just draw the components and measure their length.
To me, the important part of teaching this process is to maintain contact with physical reality. I never teach "vector addition" in the abstract. We're always adding forces, for the purpose of determining a resultant force.
I start everyone working on these worksheets. First, I give each student two random forces acting perpendicular to one another. I make sure that these forces are all between 0.1 and 2.0 N*. The student is charged with determining the amount and direction of the resultant force. Once I approve his work, he heads over to a force table, hangs the appropriate amount of mass from each pulley, and uses a spring scale to measure the resultant force.
* for two reasons: (1) using a scale where 1 cm = 0.1 N, virtually anything can fit on a standard page, and (2) the PASCO force table doesn't like more than 200 g hanging from a pulley.
See the picture above? It was taken by a student in order to show me his experimental result. You can see that the scale is hooked directly to the strings at the center of the table. The PASCO table is designed so that when the center tab is right inside the circle, the force table is in equilibrium, allowing for quite accurate results.
The student who took the picture above was assigned to add forces of 0.8 N on the x axis, and 0.9 N on the y-axis. I read the above pictured resultant as 1.25 N an an angle between 45 and 50 degrees, which is dead on to what he predicted.
In general, I'm happy with a student's experiment if I read within 0.2 N and 5 degrees of his prediction. The most common issues leading to incorrect results:
* failure to take into account the 5 g mass of the hangers
* uncalibrated scales
* pulling vertically downward on the scale, causing it to stick on a too-low force reading
These are all easily fixed. Freshmen need accurate results, and this force table gives them.
The next activity is essentially the same thing, but backwards: I give everyone a random resultant force, and they use ruler and protractor to find the components of the force, hence predicting how much mass they should hang on each hanger to measure the resultant.