Introduction and Equipment To begin our study of the addition of vectors and vector components, we are going to analyze three forces that are in equilibrium. To do this each group need one washer, three 1-meter strings, three 20-N spring scales, and a sheet of unlined paper. Procedure The first task is to attach all three strings through the washer. We will do this by folding the string in half, passing the folded end into the washer, and threading the rest of the string through the fold. Now arrange the three string-loops around the washer, but do not tighten them. Now tie a knot in the ends of each of the three string-loops and hook a spring scale onto each end. One student in the group will now pull on two of the ends so that the spring scale readings are greater than 5 N but less than 15 N. The second team member will hold the third string-loop and its spring scale, adjusting the position of the string's loop on the washer until the spring scale reading is between 10 N and 20 N. When equilibrium has been reached, the third member will slip a piece of unlined paper under the washer and use dots to mark the center of the washer as well as the positions of each string. This student should also record next to each string's line the force reading on each spring scale. When your data is finished, you may release the strings. While your teacher is creating a xerox copy of your "data lines and values" for each group member, record these magnitudes in the table below. Analysis Each student will now work independently on their xerox copy of the data. Start by onnecting the dot for each string-loop to the dot representing the center of the washer. These are shown as red lines in the diagram below. Using the measurements that you recorded for your forces, use a scale of 1 cm = 1 N to draw in the lengths of your three force vectors. Start each vector on the dot representing the center of the washer and end each vector by placing an arrow at its exact length. Do not let the tip of the arrow exceed the required length. Next, using the longest vector as your "x-axis," drop perpendiculars from the tips of each of the other two vectors to the "x-axis." Use a protractor to make sure that the lines are really at 90º. Measure the lengths of these y-components and record them in the table below. HINT: To be in equilibrium, the y-components should "cancel" - that is, the y-component of the vector above the "x-axis" should be the same length as the y-component of the vector below the "x-axis." Now measure the distances along the extrapolated, or dotted section, of your "x-axis" marked off between the dot representing the center of the washer (our origin) to where each y-component's perpendicular strikes the axis. Record these lengths in the table below. HINT: To be in equilibrium, the sum of the lengths of the x-components of the two shorter vectors should equal the length of the longest vector which provided the orientation of your "x-axis." |