Forces and equilibrium

Need to know

What you need to know

• Draw the object as a simple shape or particle.
• Draw the weight (W = mg) acting vertically downwards from the centre of mass.
• If the object is on a surface, draw the Normal Reaction (R) acting perpendicular to the surface.
• If a string or rope is attached, draw a Tension (T) force pulling away from the object along the string.
• If there is friction, draw the frictional force (F) acting parallel to the surface, opposing the direction of motion or potential motion.
• Include any other applied forces (pushes or pulls) given in the problem.

Explanation

The Balancing Act of Forces

1. A force is a vector, having both magnitude and direction. We can split any force into two perpendicular 'component' forces, which is essential for analysing forces that aren't purely horizontal or vertical.
2. For an object to be in equilibrium (balanced), the net force must be zero. This means the sum of all force components in any direction must be zero; for example, total force up equals total force down.
3. Friction is a force that opposes sliding, but it has a limit. When an object is on the verge of slipping, it's in 'limiting equilibrium', and the friction force is at its maximum value, given by $F_{max} = \mu R$.
4. To solve any forces problem, always start by drawing a free-body diagram. This means drawing the object by itself and adding arrows to represent every single external force acting on it, such as weight, tension, and reaction forces.