Force as a Vector

Abstract

The term force was defined in Chapter 2. We saw there how this definition was adequate to use when modelling motion in one dimension. However, whenever we wish to introduce a force into a problem in mechanics in two or three dimensions, we need to be specific in its description in terms of its magnitude, direction and point of application. While we are concerned with the particle model, the point of application will have no significance, as it is described as the particle’s position. Here are some examples:

• 1 A force of 10 N which pushes a cart along a horizontal plane. Its magnitude is 10 N and its direction is specified to be horizontal and in the direction of the push.

• 2 A weight of 500 N. Automatically, in specifying weight, we have allocated a vertically downwards direction to the magnitude 500 N.

• 3 A tension of 10 N in a string. By the definition of tension, the force of magnitude of 10 N is directed away from the centre of the string along its length.