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Inquiry: Composition of Forces

Purpose: To find the resultant of two forces acting at an angle and to show that the equilibrant of the two forces is equal to the resultant but acts in the opposite direction.

Procedure:

Two different forces often act simultaneously on a body at the same point. The angle between these two forces may be between 0 and 180 degrees. The resultant of these two forces is the single force, which could be substituted for them without altering the effect they produce. If the two forces act at an angle, the resultant is equal to the diagonal of the force parallelogram of which the two forces are the sides. The equilibrant of two or more forces is the single force, which can produce equilibrium with them. It is equal in magnitude, but it is opposite in direction of the resultant.

  • Using the small force table, place three different weights on A, B & C.

  • Use all the weights given or your error will be huge.

  • Adjust the angles so the system is in equilibrium, which means if you pull the pin out of the center ring it will not move.

  • You can think of A & B as your two forces acting on point P. The third force PC would then be the equilibrant.

  • Record all three forces and the angles in a data table in your notebook.

Drawing Directions;

  1. Use the scale (1cm = 1N) and draw the forces PA, PB, and PC in your notebook with the correct angle between them.

  2. Then construct a parallelogram out of the two forces (PA & PB) and draw in the diagonal. Label the diagonal PC1.

  3. From your scale determine the magnitude of PC1 and record.

  4. Also measure the angle APC1 with a protractor and record.

  5. Finally, extend the force line, PC, beyond P a distance equal to PC and label this segment PC2.

  6. Measure the segment PC2 and measure the angle APC2.

  7. Calculate % errors between PC1 and PC2 as well as between the angles APC1 and APC2.

  8. Consider PC2 and angle APC2 to be the theoretical values.

Inquiry Questions:

  1. A 12.0 N force at 70.0º is added to a 17.0 N force at 160.0º. What is the magnitude of the equilibrant force?