What is the resulting force in physics

Resulting power

a) the site plan with forces F1 and F2 and the resultant FR.
b) Krafteck to determine the resultant
c) alternatively to b): the parallelogram of forces
d) Couple of forces - resultant equal to zero, but torque not equal to zero

The resulting power (short Resultant or Resultant) in mechanics is the vector sum of two or more forces that act on a physical system at the same or at different points. In the case of only two forces, it is given by the diagonal in the parallelogram of forces. If all forces act at the same point, the system reacts as if only the resulting force were acting at this point.

If the forces act at different points, the center of mass of the system reacts as if only the resulting force was acting on it (principle of the center of gravity). In the event that the resulting force is zero, the center of mass does not move at all or maintains its linear, uniform movement. Regardless of this, however, the forces can exert a torque that influences the rotating movement of the system. The best-known example of this is the couple of forces. Here the resulting force is zero.

If the system is a rigid body and the lines of action of the individual forces intersect at a point, then the resulting force, if it acts at this point of intersection, has the same effect on the body in every respect as all the individual forces combined (see static equivalence) .[1][2][3][4]

Procedure for determining the resultant

The resultant is determined by vector addition. There are various procedures for this.

Analytical procedure

The resultant is determined analytically from the following conditions:

  • The components of the resultant with respect to a Cartesian coordinate system are equal to the sum of the components of the individual forces and
  • the components of the moment of the resultant in relation to any point are equal to the sum of the components of the moments of the individual forces.

If the vector sum of the individual forces vanishes, the resulting force is zero. This is z. B. the case with a couple of forces (Figure d.); a single moment remains, whereby the law of leverage applies.

Graphic process

The force corner (Figure b.) Or the parallelogram of forces (Figure c.) Are used to graphically determine the resultant of two forces.

The three-force method is used to determine the resultant or to determine a third, unknown force if two of three forces are known. The resultant with two or more forces can be z. B. also determine with the help of the rope corner method.

The four-force method according to Karl Culmann, like the Cremonaplan, is used to graphically determine the resulting beam or bar forces, for example when dimensioning trusses.

Individual evidence

  1. ↑ Thanks, thanks: Technical mechanics, Springer, 7th edition, 2013, p. 20.
  2. ↑ arches: Technical mechanics, Springer, 31st edition, p. 38.
  3. ↑ Gross, Hauger, Schröder, Wall: Technical mechanics - statics, Springer, 11th edition, 2011, p. 50.
  4. ↑ Böge (Ed.): Mechanical engineering manual, Springer, 21st edition, 2013, p. B12f.