Connected Blocks — Newton's Second Law Train

Train Setup

Number of boxes 4

Mass per box 3.0 kg

Friction coefficient μ 0.25

Applied Force

Pull force F 300 N

Rope break tension 600 N

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Acceleration

0.00 m/s²

Total friction

0 N

Tension at link 1 (front rope)

0 N

How it works

N identical boxes of mass m sit in a line on a floor with kinetic-friction coefficient μ, joined by short ropes. A single force F pulls the front box forward. While every rope stays taut and unbroken, the whole train shares one acceleration — Newton's second law applied to the entire system:

a = (F − μ·N·m·g) / (N·m)

Each individual rope, though, only has to carry the boxes behind it. Isolating the sub-chain of k boxes behind a given link (its own free-body diagram) gives that link's tension:

T_k = k·m·a + μ·k·m·g

The link right behind the front box carries the most mass and therefore the highest tension — it is always the first to fail. If F is large enough (or the rope weak enough) that this tension exceeds the rope break tension, the link snaps: the front box shoots off alone under F (now only fighting its own friction), while the rest of the train — no longer pulled — decelerates under friction alone (a = −μg) until it stops.

If F is below the total static friction μ·N·m·g, the whole train stays put (a = 0) — this is why parked trains of crates don't slide at the slightest push.
Raising N or m raises both the inertia and the friction resisting the pull, so a is set by their ratio, not either alone.
Raising μ lowers a and raises every link's tension, since the whole train must now fight a stronger drag.

Pull force F Rope (tension shown by color)

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