When a car is pulling a trailer, we can apply
where
is the resultant of all the forces on both car and trailer,
is the mass of the car plus the mass of the trailer, and a is the acceleration, which, since the cable between the cable and car is always assumed inextensible, is the same for both car and trailer, to the system as a whole – In the diagrams belowis the driving force...
where
is the total mass of car plus trailer.
or each individually...
Applying
for the trailer we obtain
(1)
Applyingfor the car we obtain
(2)
(1)+(2) gives
Notice that when we draw the force diagram for the car and trailer separately:
The tensions acting on trailer and car are equal and opposite. The tension is a force internal to the system so does not appear in the top diagram, which takes only external forces into account. That they are equal and opposite is a consequence of Newton's 3rd Law.
The accelerations are the same for car and trailer, the cable is inextensible and are the same as in the first diagram.
and
are the same in the first and second diagrams.