VECTORS

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 Visit the following site and get an understanding of vectors and scalars.

 Purpose: To determine  the resultant and equilibrant of two or more vectors using  the component method.

                        analytically and to verify the results using a force table.

Apparatus: force table with pulleys, mass hangers, mass set, string, level

Theory: a) analytical method (component method)

Direction of the resultant, A_R, measured from the X - axis depends on the signs of Fx and Fy. 

In general, A_R = tan^-1  (abs(F_y/F_x)). Correction have to be made, however, depending in which quadrant it is. Use the table below as a guide.

When one or both the components are negative go the the appropriate quadrants and determine A_R.

The equilibrant is given by:

magnitude = magnitude of the resultant.

Direction for the equilibrant is always directly opposite to the resultant. It is very easy to read this from the force table. You should also calculate it using  the table above.

  Procedure

  Analytical Method 

Use the analytical (component ) method and find the magnitude and the direction of the resultant. The Equilibrant  is  always   directly opposite to the resultant. Use the force table to figure out where it should be and then verify it with you calculation. 

  Force Table Check

Addition of two vectors:

1) Use a level to make sure the force table is leveled.

2) Mount a pulley on the 0 degree mark and suspend a 50 gram mass hanger. Mount a second pulley on the 90 degree mark and suspend a 100 gram mass (hanger and a 50 gram mass).

3) Set up the equilibrant on the force table and test the system for equilibrium.

4) Remove all the masses from the force table.

5) Mount a pulley on the 20 degree mark and suspend a 50 gram mass. Mount a second pulley on the 120 degree mark and suspend a 250 gram mass.

6) Set up the equilibrant on the force table and test the system for equilibrium. 

7) Remove the equilibrant mass.  

 Addition of three vectors:

1) Mount a pulley on the 300 degree mark and suspend a 300 gram mass (masses 50 gram and 250 gram are already there).

2) Set up the equilibrant on the force table and test the system for equilibrium.

3) Remove all the masses from the force table.

  Addition of four vectors:

1) Mount a pulley on the 30 degree mark and suspend a 100 gram mass. Mount a second pulley on the 140 degree mark and suspend a 150 gram mass. Mount a third pulley on the 200 degree mark and suspend a 125 gram mass. Mount a fourth pulley on the 300 degree mark and suspend a 200 gram mass.

2) Set up the equilibrant on the force table and test the system for equilibrium.

3) Remove all the masses from the force table.

 Vector resolution:

1) Mount a pulley on the 30 degree mark and suspend a 300 gram mass over it.

2) Find the magnitudes of the components along the 0 degree (X- axis) and 90 degree (Y-axis) directions. 

3) Set up the above components as they have been determined. Move the 300 gram mass to, 30 + 180 = 210 degrees, which is the direction of the equilibrant. Test the system for equilibrium.

A = 12 i -35 j + 55 k and B = 5 i + 25 j - 40 k where i, j, and K are unit vectors along X, Y, and Z axes.

(Hint: Always add or subtract vectors component wise. The use Pythagorean theorem to get the magnitude.) 

a) Calculate the magnitude of vector A.

b) Calculate the magnitude of vector B.

C) Calculate the magnitude of the vector A + B.

D) Calculate the magnitude of the vector A - B.

Conclusion: (Reread the purpose of the experiment and write a conclusion that addresses the purpose. Was the purpose or goal met by what you did?)