Syed Waqas Ali

Q: This Question is About Mechanics(Math)...:

Explain: "Resultant of Two Forces Acting at a Point With Diagram"

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answers: 1

Expert:

MiksNm

The system of forces, the lines of action of which intersect at one point, is called the system of converging forces.

The simplest system of converging forces is formed by two forces applied to a body at one point. According to the third axiom of statics, their resultant is expressed by the diagonal of a parallelogram built on given forces and called the parallelogram of forces. The rule for finding the resultant is called the parallelogram rule. There are two ways to determine the magnitude and direction of the resultant of two forces: graphical and analytical. Let's consider each of them in turn.

Let two forces F1 and F2 be applied at point A of a rigid body, the lines of action of which form an angle α. We draw the given forces on the chosen scale and construct a parallelogram ABCD on them. The diagonal AC of this parallelogram determines the resultant of the given forces in magnitude and direction. The module of the resultant R is determined by measuring the diagonal AC on the scale of forces, and its direction is determined by measuring the angle β between the resultant R and the force F1, or the angle γ between the resultant R and the force F2.

Consider triangle ABC. The side AB of this triangle is equal to the force F1, the side BC is geometrically equal to the force F2, and the side AC is the resultant of the two given forces. It follows that the resultant of two forces can be determined by the law of the triangle of forces. To build this triangle, it is necessary to set aside a vector geometrically equal to the force F2 from end B of the force F1, that is, a vector of the same length as the force F2, parallel to it and directed in the same direction. The closing vector drawn from the beginning of the force F1 to the end of the force F2 is the resultant of the two given forces.

Attention should be paid to the fact that the sides of the triangle, representing the given forces, always have one direction (clockwise or opposite), while the resultant has the opposite direction, i.e. closes the power triangle.

To determine the resultant of two forces in an analytical way, it is necessary to construct a force triangle schematically, that is, without respecting the scale of forces, and determine the modulus and direction of the resultant from the solution of the force triangle.

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