Newton's three laws, force diagrams, weight, normal reaction, tension, friction, and connected particles over a pulley.

What this dot point is asking

WJEC wants you to state and apply Newton's three laws, draw clear force diagrams, identify weight, normal reaction, tension and friction, and solve problems involving connected particles linked by a string over a smooth pulley. This is the heart of the mechanics section and combines with the kinematics equations to find accelerations, speeds and distances.

The answer

Newton's three laws

The second law is the workhorse: resolve forces into a chosen direction, find the resultant, and set it equal to $ma$.

Force diagrams and the standard forces

A force diagram shows every force acting on the body as an arrow. The forces you meet at AS are:

On a horizontal surface with no vertical acceleration, the normal reaction balances the weight, so $R = mg$.

Friction

A body on the point of moving, or already moving, has friction at its maximum value $\mu R$.

Connected particles

For two particles joined by a light inextensible string over a smooth pulley, the string has the same tension throughout and the particles share the same acceleration magnitude.

Examples in context

Example 1. A lift accelerating. A person of mass $70\,\text{kg}$ stands in a lift accelerating upward at $2\,\text{m s}^{-2}$. The normal reaction (what a scale reads) satisfies $R - mg = ma$, so $R = m(g + a) = 70(9.8 + 2) = 826\,\text{N}$, more than their weight of $686\,\text{N}$. Newton's second law explains the heavy feeling on acceleration.

Example 2. Friction limiting motion. A $10\,\text{kg}$ crate sits on a floor with $\mu = 0.3$. The maximum friction is $\mu R = 0.3 \times 10 \times 9.8 = 29.4\,\text{N}$. A horizontal push of $25\,\text{N}$ is below this, so the crate does not move; a push of $35\,\text{N}$ exceeds it, so the crate accelerates. The friction inequality decides whether motion starts.

Try this

Q1. A $2\,\text{kg}$ object has a resultant force of $10\,\text{N}$ acting on it. Find its acceleration. [2 marks]

• Cue. $F = ma$: $a = \dfrac{10}{2} = 5\,\text{m s}^{-2}$.

Q2. Find the weight of a $6\,\text{kg}$ mass (take $g = 9.8\,\text{m s}^{-2}$). [1 mark]

• Cue. $W = mg = 6 \times 9.8 = 58.8\,\text{N}$.

Q3. A block on a rough horizontal surface has normal reaction $40\,\text{N}$ and $\mu = 0.25$. Find the maximum friction. [2 marks]

• Cue. $F = \mu R = 0.25 \times 40 = 10\,\text{N}$.