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If a 1200 kg1200\text{ kg} car pulls an 800 kg800\text{ kg} trailer down the road, does the connecting tow-bar experience the entire pulling force of the engine, or just a fraction of it?
To solve this, we model the setup as a coupled dynamical system — two connected bodies whose motion is governed by Newton's second law, which states that net force equals mass times acceleration (Fnet=maF_{\text{net}} = ma).
Why can we treat both vehicles as a single combined mass when finding the acceleration?

The Whole System Method

In mechanics problems, a light, inextensible tow-bar means the connector has zero mass and cannot stretch, forcing both vehicles to move with the exact same acceleration aa.
In 1687, Isaac Newton formulated his third law of motion, stating that interaction forces between two bodies are equal in magnitude and opposite in direction. Because the tow-bar pulls backward on the car with tension TT and forward on the trailer with equal tension TT, these internal forces sum to zero when considering the whole system.
How do we apply these separate equations to calculate both the acceleration and the tension with real values?

Worked Example: Accelerating Car and Caravan

A car of mass 1200 kg1200\text{ kg} tows a caravan of mass 800 kg800\text{ kg} along a straight horizontal road. The car exerts a driving force of 3000 N3000\text{ N}, while constant resistance forces of 400 N400\text{ N} and 600 N600\text{ N} act on the car and caravan, respectively.
First, apply Fnet=maF_{\text{net}} = ma to the whole system horizontally to find the acceleration:
3000−(400+600)=(1200+800)a  ⟹  2000=2000a  ⟹  a=1.0 m/s23000 - (400 + 600) = (1200 + 800)a \implies 2000 = 2000a \implies a = 1.0\text{ m/s}^2