Force

Force

Force is a very important concept in engineering science. It may be described as an agent that produces motion, stops motion, or tends to change the existing state of motion of a body. In simple words, force can create, destroy, or modify motion.

Resultant Force

When multiple forces such as P, Q, R act on a particle at the same time, a single force that can replace all of them and produce the same overall effect is called the resultant force. The individual forces are known as component forces. The method of determining the resultant of these forces is known as the composition of forces.

The resultant may be found analytically, graphically, or by using the following laws:

  1. Parallelogram law of forces: “If two forces act simultaneously on a particle, their resultant can be represented in magnitude and direction by the diagonal of a parallelogram formed using the two forces as adjacent sides.”
  2. Triangle law of forces: “If two forces acting at a point are represented in direction and magnitude by two sides of a triangle taken in order, then the third side of the triangle (taken in opposite order) gives the resultant.”
  3. Polygon law of forces: “When several forces act on a particle, their resultant can be represented in magnitude and direction by the closing side of a polygon whose sides represent the given forces taken in order.”

Scalars and Vectors

1. Scalar quantities: These are quantities which have only magnitude such as mass, time, speed, volume, density, etc.


2. Vector quantities: These quantities have both magnitude and direction, for example velocity, acceleration, displacement, and force.

3. Since vectors have direction, while adding or subtracting vectors, their directions must always be considered.

Representation of Vector Quantities

Vectors are represented by straight lines. A vector has a starting point and a terminal point, with an arrow indicating its direction. The length of the vector line shows its magnitude according to a chosen scale.

Addition of Vectors

To add two vectors P and Q, follow the graphical method shown in Fig. 1.1:

  1. Take a point A and draw line AB parallel and equal to vector P.
  2. From B, draw BC parallel and equal to vector Q.
  3. Join A to C. The line AC represents the resultant (sum) of vectors P and Q.

Subtraction of Vector Quantities

To find the difference of two vectors P and Q, follow the steps shown in Fig. 1.2:

  1. Take point A and draw line AB equal and parallel to vector P.
  2. From B, draw BC parallel and equal in magnitude to vector Q, but in the opposite direction.
  3. Join A to C. The line AC now represents the required difference of vectors P and Q.

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