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Experiment#5 – Vector Addition Experiment

Purpose

The goal of this experiment is to determine the equilibrant vector necessary to maintain static equilibrium in a system containing three other force vectors. This experiment will allow the students to practice both the graphical and algebraic method of vector addition.

Equipment

•     A thin board

•     A spool of thread

•     A large split ring with four attached smaller split rings

•     Three super pulleys with clamps

•     A spring scale

•     Ruler

•     Protractor

Procedure

Part 1: Construct and use a force table

1.      Print out a sheet of polar graph paper and tape it to the center of the board.

2.      Attach the three super pulleys to the edges of the board so that they are aligned to point back to the center of the polar graph paper.

3.      Cut off three sections of thread long enough to extend from the center of graph paper to over the a super pulley plus an extra few inches.

4.      With the large split ring on a flat surface, tie the three sections of string to three of the smaller rings on the large split ring and tie the remaining three thread ends to masses from the box of masses.

5.      While holding the large split ring in the center of the sheet of polar graph paper, drape each mass over one of the mounted super pulleys and check to see that the threads do not cross each other.

6.      Adjust the height of each of the pulley wheels so that the thread extend from the split ring out to the pulleys horizontally just above the surface and check to see that the pulleys are aligned with the center of the large split ring.

7.      Check to see that the spring scale is calibrated for horizontal measurements and attach it to the fourth ring on the large split ring (the one without thread).

8.      Pull on the spring scale with the proper amount of force and in the appropriate direction to keep the large split ring in the center of the polar graph paper.

9.      With a pencil, mark the outer edge of the polar graph paper where the spring scale and the three thread lines cross the edge of the paper.

10.  Next to each of the thread markings, write in the amount of mass used and next to the spring scale marking, write in the equivalent amount of mass used to  grams).

11.  Remove the polar graph paper from the flat surface and write in 0°, 90°, 180°, 270° and 360° on the +x axis, +y axis, –x axis, –y axis and the +x axis respectively.

12.  Label the thread markings as vectors V₁, V₂, and V₃and the spring scale marking as vector V_E.

13.  Determine the bearing (angle) of each string line and spring scale marking on the polar graph paper.

14.  Covert each of the mass measurements (in grams) into a resulting force, F_g, (in N).

15.  Record your results below

Part 2: Performing the Graphical Vector Addition

1.      Determine the length (cm) needed formapping the three vectors,V₁, V₂, and V₃listed above by using the scaling factor that 0.098 N is equivalent to 1.0 cm.

│V₁ │ =               cm

│V₂ │ =               cm

│V₃ │ =               cm

2.      Do a quick check to see that, in starting at the center of the rectangular graph paper, the vectors when mapped will not leave the page. If parts of the vector map leave the page then re-scale the three vectors and list the scaling factor below.

Scale factor:               N =              cm

3.      Using a ruler and a protractor, map the vectors listed above onto the graph paper in a head-to-tail manner and determine the resultant vector (V_R). Start by mapping the first vector (V₁) from the center of the rectangular graph paper ( 12.5 cm down and 9.5 cm to the right).

4.      Once all the vectors are mapped onto the graph paper and clearly labeled, draw in the resultant vector V_Rby starting from the center and extending a straight line out to where the V₃ vector left off.

5.      Using a ruler and protractor, determine the magnitude of direction of V_R.

│V_R │ =               cm at             °

6.      Using the scaling factor from above, convert the magnitude of the resultant vector (V_R) back into Newtons (N).

V_R =                N at            º

7.      The equilibrant vector (V_E) is defined as the vector used to maintain static equilibrium in the system.  The equilibrant vector is equal in magnitude but opposite in direction to the resultant vector.  Determine the equilibrant vector from the resultant vector determined above.

V_E =                N at       º

Part 3: Performing the Algebraic Vector Addition

1.      On a sheet on scratch paper, convert V₁, V₂, and V₃ (in Newtons) into their corresponding rectangular (x and y) components and algebraically determine V_R.

V₁ =                 N î +          N ĵ

V₂ =                 N î +          N ĵ

V₃ =                 N î +          N ĵ

____________________________

V_R =                 N î +          N ĵ

2.      Keeping in mind that the equilibrant vector (V_E) is equal in magnitude but opposite in direction to the resultant vector.  Determine the equilibrant vector from the resultant vector determined above.

V_E =                 N î +          N ĵ

3.      Convert the resultant vector and the equilibrant vector back in polar coordinate notion.

V_R =                            N at            º

V_E =                            N at            º

4.      Compare the three equilibrant values obtained (force table, graphical method and algebraic method) ranking them from most reliable to least reliable and justify your ranking order.