# A train with lots of trucks

Think about a train of several trucks being pulled along a horizontal track by an engine. If the engine is accelerating the train then all the trucks must be accelerating at the same rate. If this were not true the train would either stretch or squash itself!

Consider the forces in the link between the engine and the first truck and in each link along the train. The engine has to pull all the trucks and so therefore the force in the first link (1) will be large. However the link between the last but one truck and the one at the end (2) only has to accelerate the final truck and so the force in that link will be much smaller.

So for the line of trucks the forces between each pair of trucks will be different. You should be able to understand this by thinking about the picture (Figure 1).

However if the last truck was fixed to the ground and the engine simply pulled on the carriages without them being able to move the forces in all the links would be the same!

Example problem
The engine pulls five carriages with an acceleration of lets say 4 ms-2 - this must be the same for the whole train. If this were not so the train would fall apart. Each carriage has a mass of 2000 kg.

Now using Newton's Second Law (F = ma) the force between the engine and carriage 1 must be (5x2000)x4 = 40000 N. The force between carriage 1 and carriage 2 is (4x2000)x4 = 32000 N.
That between carriage 2 and carriage 3 is (3x2000)x4 = 24000 N and so on.

So you see as you go down the train further from the engine the forces needed to pull the remaining part of the train get less.

## schoolphysics Newton's Second Law and trains animation

To see an animation of the acceleration of different trains please click on the animation link.

A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS USB