Mechanical models and force diagrams

What you’ll learn

• Translate modelling assumptions into equations.
• Distinguish mass, weight, force and acceleration.

Understand the idea

A model retains the features needed for a question and deliberately ignores others. A particle has mass but no relevant size; a rigid body keeps its shape; a light string has negligible mass; an inextensible taut string keeps a fixed length. These assumptions explain why connected particles can share acceleration magnitudes.

A force diagram should show only forces acting on the chosen object. Weight acts vertically downward, a smooth contact supplies a normal reaction, and a taut string pulls along its own direction. Use SI units and state the value of $g$; these lessons use $9.8\,\mathrm{m\,s^{-2}}$ whenever gravity enters a calculation.

Key formulae

$$W=mg$$

$$1\,\mathrm N=1\,\mathrm{kg\,m\,s^{-2}}$$

$$\sum\mathbf F=m\mathbf a$$

Worked example

A $4\,\mathrm{kg}$ book rests on a horizontal table. Model it as a particle and find the normal reaction. Take $g=9.8\,\mathrm{m\,s^{-2}}$.

1. The forces are weight $4g$ downwards and reaction $R$ upwards.
2. The book is in equilibrium, so $R-4g=0$.
3. Substitute $g=9.8$ to obtain $R=39.2$.

Answer: $R=39.2\,\mathrm N$.