The Addition of Forces & Newton’s First Law, Parallelogram Method - Physics Assignment Help

Assignment Task

Object:
To learn to add force vectors by the parallelogram method and by the resolution of forces into rectangular components. These methods will then be used for several systems in equilibrium (zero acceleration). 
To verify the equilibrium condition ΣF=0 (Newton’s First Law).
Apparatus: 
Force board with string, set of hooked weights, 8-1/2” x 11” white paper, meter stick, triangle, digital scale, tape, and an unknown mass. Ruler and protractor.
Procedure:
The forces which we will work with within this experiment are provided by gravity acting on masses marked in grams. The magnitude of these forces in Newtons may be obtained by converting grams into kilograms and multiplying by 9.8 m/s2 (F = mg). A force is a vector quantity that can be represented by an arrow, the length of which represents the magnitude of the force, while the direction indicates the direction in which the force acts.
Part A:
Two forces represented by vectors may be added by the parallelogram method (see Figure 2). The diagonal of the parallelogram is a vector defining the resultant of the two forces, i.e. the single force which will produce the same effect as the two forces which are being added together.
In Part A you will find the resultant of adding forces F1 and F3 and comparing the results to the downward force F2, which should ideally be exactly opposite R and the same magnitude.
Adjust the loads m1, m2, and m3 on the force board as shown in Figure 1 until equilibrium is obtained (the knot, point B is at rest) and the angle ABC is somewhat greater than 90º. Place an 8-1/2”x11” sheet of paper behind the string on the board and after shifting the weights a few times to minimize the effects of friction, make dots at points A, B, C, and D behind the string on the paper. The paper should be placed so that point B falls a little below the center of the paper so that space is available on the upper portion of the paper for drawing a parallelogram.
Record the values of m1, m2, and m3 in Data Table 1. Calculate the magnitude of each of the forces and record their values.
Remove the paper from the force board. For this online lab, display the PDF file with the data on your screen, take a sheet of paper (preferably copier or printer paper) and hold it over the screen, and place dots on the paper representing points A, B, C, and D.
Using a ruler, the next task is to draw vectors. To do this you must choose a scaler factor, SF, to represent the forces on your drawing.

Scale factors may be unfamiliar, so consider the following examples. Suppose one of the forces is 2N. If we choose SF = 10 m/N, then our force would be represented by a line that is length = (2N) (10 m/N) = 20 m long. This is not going to fit on the page, so we want something smaller. Suppose, instead, that we choose SF = 0.1 mm/N. The line representing the force will then be length = (2 N) (0.1 mm/N) = 0.2 mm long. This is too small to be drawn accurately with most rulers and measurements of the resulting diagram would be inaccurate. The scale factor should be somewhere in between these extreme values. Start by using 4.0 cm to represent 1.00 N of force (i.e. SF = 4 cm/N). If the diagram does not fill most of the paper, increase the scale factor. If the diagram is too large, make it smaller.

Record the final lengths you have chosen for ?1, ?2, and ?3 in the data table. You must now construct a parallelogram to scale. The scale drawing will look similar to the one shown in Figure 2. Draw straight lines from point B, through points A, B, C, and D that go clear to the edges of the paper. Now measure off the distance ?1 along with AB which corresponds to the load F1 according to your chosen scale factor. You will get the most accurate results by choosing a scale that will give the largest possible parallelogram without going off the paper. Now measure off a distance along with BC equal to ?3. Attach arrows to represent the direction of the forces, complete the parallelogram and draw the diagonal BE. Point E is located at the intersection of the line drawn from the tip of vector F1 parallel to BC, with the line drawn from the tip of F3 parallel to AB. Parallel lines can be drawn from the tip of F3 parallel to AB. Parallel lines can be drawn by sliding the triangle along with the meter stick or other straight edge.
 

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