M10.5MechanicsStretch

Connected Particles

When two objects are connected — a car towing a trailer, or a lift and its load — they move together with the same acceleration. You can analyse the whole system at once, or each particle separately to find the connecting force.

30 min Video by Zeeshan Zamurred Forces and Motion

Edexcel AS Level Maths: 10.5 Connected ParticlesWatch the full walkthrough before the notes below.

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What you'll be able to do

Recognise that connected particles share an acceleration
Analyse the system as a whole
Analyse each particle to find the tension/thrust
Apply this to tow-bars and lifts

Shared acceleration

Connected particles (joined by a string, tow-bar or in contact) move with the $same acceleration$ . The connection exerts equal and opposite forces (tension or thrust) on the two parts.

Whole-system method

To find the acceleration, treat both particles as a $single object$ . The internal connecting forces cancel, so you use the total mass and the external driving force.

F_{driving} = (m_{1} + m_{2}) a

Treat the system as one mass to find

a

a = \frac{3000}{1000 + 500}

Answer

2

m/s²

Single-particle method

To find the $connecting force$ (tension in the tow-bar), apply $F = ma$ to just $one$ particle, using the acceleration found above.

1On the trailer, the only forward force is the tension:

T = ma = 500 \times 2

Answer

T = 1000

Tip — System method → acceleration; single-particle method → the connecting force.

Formula recap

a = \frac{F}{m _{1} + m _{2}}

Whole-system acceleration.

T = ma (one particle)

Connecting force.

same a for both

Connected ⟶ shared acceleration.

Common mistakes to avoid

Including the internal tension when using the whole-system method.

Internal forces cancel for the system; use only external forces and total mass.

Using total mass when finding the tension on one particle.

For the connecting force, apply F = ma to a single particle.

Key takeaways

Connected particles share the same acceleration.
Whole-system (total mass, external force) gives the acceleration.
Analysing one particle gives the connecting tension/thrust.

Test yourself

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