Mr. Kovall's Neighborhood

Lab 1:  Addition of Forces

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(Revised 7-24-03)

Purpose:                                                                                                                                                                        

     To determine experimentally the relationship between the resultant of two force vectors and a third force vector which are in equilibrium.

Materials:

     Force board, linked newton scales, straight edge, protractor, paper.

Procedure:

Click on button for photographic detail of the apparatus: AddForcLbApp1.jpg (17854 bytes)

  1.  Place unlined paper on force board and tape in place.

  2. Attach the linked newton scales to the force board, placing varying amounts of tension on each.  Don't make an effort to adjust the spacing between the scales in a symmetrical manner. (Fig. 1)

  3. Record the magnitude of the force designated on each scale next to the scale so that you can refer to this value later in the lab. (Fig. 2)

  4. Using your pencil, place a distinct dot in the exact center of  the ring.  This point will later represent the "origin" of three opposing force vectors. (Fig. 3)

  5. With a pencil, lightly trace the front of each scale, the edge which is closest to the ring.  Continue tracing around to include a tiny portion of each side of  the scale as well.   Your tracing for each scale should look like a bracket ( ] ).    Detach and remove the set of scales from the force board. (Fig. 4)

  6. Bisect each of the three lines representing the front of each newton scale, lightly marking the center of each.

  7. Draw a line from each marked point described above to the dot  placed earlier in the center of the metal ring.  The three lines converging on the dot represent force vectors. These lines represent the newton scales, in magnitude and in direction.  (Fig. 4)

  8. Rotate your sheet of paper so one of the force vectors points horizontally to the right.  Construct an x-axis through this vector.   Using your protractor, construct a y-axis through the point where the three force vectors converge.  

  9. The force vector resting on the positive x-axis is to be considered the "accepted value" during the mathematical portion of this lab.  Label this vector "A".  Moving counterclockwise, label the next force vector "B", and the third force vector "C".

  10. Using the protractor, determine the angle each of the two opposing force vectors, B and C,  make with the x-axis.

  11. Lightly construct a parallelogram for vector B and vector C, denoting their respective x-axis and y-axis components, labeling as Bx, By, Cx, and Cy, respectively. NOTE: The parallelogram for vector B and vector C must be neatly drawn on the original lab project sheet.

  12. Calculate the magnitude of each of the four vector components using sinø and cosø trigonometry functions.  

  13. Determine the sum of Bx and Cx; identify as XBC.  Determine and sum of By and Cy; identify as YBC.

  14. Compose vectors XBC and YBC  into the resultant vector "R".

  15. Determine the angle between vector R and its nearest x-axis as ø. Determine the angle between vector R and the positive x-axis as øR. 

  16. Allowing  the magnitude of force vector "A" to serve as the accepted value, determine the % Error of  vector R.

  17. Each lab partner must complete his or her own  project as described above.

    

Definitions:

     Resolution -

     Composition -

     Resultant -

     Vector -

     ø - 

    øR -

      øE - 

     Scalar -

     Equilibrant -

     Directional bearing -

 

Sample calculations:

     In this section, each student must individually show the math steps as described in the procedure.  Show this work in a neat, orderly fashion.  Include diagrams to accentuate the various vectors leading to the final relationship between vector A and vector R.  Include appropriate units.

     

3 Sources of Potential Lab Error:

 

Conclusion:

  1. Compare and contrast force vectors "R" and "A" to determine the relationship between them.

  2. State the magnitude and direction of vector R and vector A, and explain the significance of these values.

  3. What type of equilibrium exists between vector R and vector A?  Explain.

  4. What is the significance of the angle theta between vector R and the x-axis?

  5. Explain the relationship that exists between vectors B and vector C.

 

Practice Problems:

  1. Determine the resultant vector equivalent to 17.5 Nt vector A acting northward, 6.4 Nt vector B acting N30ºE, and 10.5 Nt vector C acting eastward.

  2. At least ONE short answer problem will be assigned to each group from problems #3, 4, 5, 8, 9, 13 listed on the "Short Answer Vector Problems" handout associated with Lab 1.

 

Individual Extra Credit:

     Each student must provide the directional bearing for his or her own vector R