2.2. Forces

All too often my students decide to either drawing skip these diagrams when solving Mechanics problems or to rush them, missing the key points. I can't emphasise enough just how useful these diagrams can be when solving problems, particularly when stuff starts getting harder (e.g. looking at circular motion or analysing torques on an object).

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The key things you need to remember:

• The length of the force arrows are proportional to their magnitude.

• The force arrows should start at their point of action (e.g. from the surface for friction/ reaction force, from the CoG for the weight)

• If an object is in equilibrium (balanced forces), then the sum of vector components in any direction (e.g. vertical and horizontal) will also be in equilibrium (more later)

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Let's start with a simple example, of a ship slowing down in the sea. We can see the various forces and their relative sizes through the lengths of each arrow. A few key points about these diagrams

• Notice that in the vertical direction, the buoyancy and weight forces are equal, therefore there is no acceleration in that direction.

• In the horizontal direction, the drag force is greater than the thrust vector, therefore the resultant force is backwards, causing an acceleration in that direction.

• Occasionally it can be useful to annotate a velocity (or acceleration) onto these diagrams for clarity. However, these are NOT forces so make sure they are separate.

• The situation diagram shows the forces acting from their point of action. e.g. the thrust force acts from the propeller, the weight from the CoG etc.

• The Free Body Diagram is often drawn as a point as in diagram 2) (thereby ignoring the geometry of the object).

• The vector polygon allows us to clearly visualise in which direction the resultant force (and therefore acceleration) acts.

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