DIAGNOSTIC QUESTION: Predict how much is the magnitude of the force that balances two perpendicular forces of 24 pounds and 32 pounds applied as shown in the picture shown above; write your answer in the space provided:  

PROCEDURE:  

Arrange three persons per group. Manipulate the balances or the rubber bands on a free flat surface. Take two portions of thread and tight them to the o-ring. Secure each balance or rubber band to the free ends of the threads. Reproduce the setting shown in the picture by applying perpendicular forces of F₁ = 3 units and F₂ = 4 units by pulling from the threads. 

NOTE: always ensure that the o-ring remains stable with respect to some reference point at the surface, and the applied forces remain perpendicular. The edges of a sheet of paper can be used. This means the applied forces will be in equilibrium.

Answer the following questions:

1. Explain what you should do in order to obtain equilibrium through the third force applied (wiht no movement in the O-ring).

 2. Now experiment with the forces and find the the direction and value of an equilibrant force F_e that counterbalances the other two applied forces. Write also the two applied forces and their units of measurement.

F₁:      F₂:     F_e: include units

specify the direction of this F_e with respect to one of the applied forces:

3. If you would have to replace the forces F₁ and F₂ by only one force F_r that balances the force F_e, how should be the magnitude and direction of F_r as compared with F_e ?.

4. Now double the forces F₁ and F₂ and find the new equilibrant force (F_e2). Write the values and units of the new forces in the spaces provided:

   F₁:      F₂:        F_e2:    include units

5. Again double the applied forces F₁ and F₂ and find the new F_e3:

F_e3:         F₁:      F₂:     include units.

 In this activity you balanced two perpendicular forces F₁ and F₂ by using another force F_e that equilibrated them. You also noticed that these two forces could be replaced by a resultant force F_r. This resultant force is really the sum of the two forces. The equilibrant force functioned like a subterfuge for finding the sum of forces F_r.  Then, We say that,

6. This activity revealed that when perpendicular, the sum of a force of 3 pounds with a force of 4 pounds results in a force of   pounds (see question 2.).

SUMMING FORCES VS. SUMMING NUMBERS

7. From your results compare the sum of numbers with the sum of forces as you experimented in this activity. Use the following table and write in the boxes:

We can also study other kind of vector: the displacement. To see this activity press here.

Give your own conclusions about what you have learned in this activity:

 ASSESSMENT QUESTION

Predict how much is the magnitude of the force that balances two forces of 24 lb and 32 lb applied as shown in the above figure:

.

WHAT WE LEARNED

From this activity you have learned about an important mathematical entity having important physical applications in the real world. This entity is called a vector and this activity showed that vectors follow particular sum rules. Also you recognized that a vector has a value (the amount of the measurement), and a direction. An important discovery was that summing vectors is not the same as summing numbers. When summing vectors, the direction is important and this affects the result of this sum; that is, a vector is correctly expressed when both its value and its direction are specified. Examples of vectors include forces, displacements, velocities, accelerations, and certain combinations of these.

This activity was developed under support of PR-LS-AMP, 2000.

Name:    "email":  

Gerson R. Revised: February 11, 2007