What is a free body diagram? Two blocks of masses m₁ and m₂ are tied by a light string on a smooth horizontal table. A force F pulls m₂. Draw the free body diagrams and find the acceleration and the tension in the string.

1. 1 · Define. A free body diagram shows one body separated from its surroundings, with all the external forces on it drawn as arrows.
2. 2 · Draw the diagrams. [m₁ and m₂ in a line with a string between them. FBD of m₁: T forward, m₁g down, normal force up. FBD of m₂: F forward, T backward, m₂g down, normal force up]
3. 3 · Vertical balance. For each block, the normal force equals the weight, so there is no vertical motion.
4. 4 · Whole system. Only F acts horizontally on both blocks together: F = (m₁ + m₂)a, so a = F/(m₁ + m₂).
5. 5 · Block m₁. Only T acts on it horizontally: T = m₁a = m₁F/(m₁ + m₂).
6. 6 · Check with m₂. F − T = m₂a gives the same values.
7. 7 · Real-life link. A railway engine pulling coaches works the same way: the coupling next to the engine carries the largest tension.
8. 8 · Close in one line. So a = F/(m₁ + m₂) and T = m₁F/(m₁ + m₂), which is less than F.

Scoring tip: Draw a separate diagram for each block. Marks are given for the diagrams and for each force equation, even if the algebra slips.