Connected particles

In problems with two or more connected particles, draw a large diagram in which the particles are

clearly separate. Then put in all forces on each particle: don’t forget Newton’s third law there

will be some ‘equal and opposite’ pairs of forces.

Example: A lift of mass 600 kg is accelerating upwards carrying a man of mass 70 kg. If the

tension in the lift cables is 7000 N find the acceleration of the lift and the force between

the floor and the man’s feet.

Solution: Draw a clear diagram with all forces on lift AND all forces on man.

Draw a second diagram showing the combined system, that is, the man and the lift as

‘one particle’.

N.B. If the normal reaction on the man is R newtons then this means that the lift floor is

pushing up on the man with a force of R newtons,

therefore the man must be pushing down on the lift floor with an equal sized force

of R newtons.

Hint: Draw a LARGE lift and put the man in the middle (not touching the floor).

Example: A truck of mass 1300 kg is pulling a trailer of mass 700 kg. The driving force

exerted by the truck is 1500 N and there is no resistance to motion.

Find the acceleration of the truck and trailer, and the force in the tow bar between the

truck and the trailer.

Solution: Draw a clear diagram, separating the truck and the trailer to show the forces on

each one.

Draw a second diagram showing the combined system, that is, the truck and the trailer

as ‘one particle’.

If the force in the tow bar is T N then this force will be pulling the trailer and pulling

back on the truck, since the truck is accelerating.