7. Motion of bodies in contact
Case (A) :
Two body system :
Let a force F be applied on mass m₁.

Free body diagrams: (vertical force do not cause motion, hence they have not been shown in diagram)

For A	For B
F – f = m1a	f = m2a

⇒ and
(i) Here f is known as force of contact.
(ii) Acceleration of system can be found simply by
Note:
If force F be applied on m₂, the acceleration will remain the same, but force of contact will be different i.e.
Case (B) :
Three body system :

Free body diagrams :

For A	For B	For C
F – f1 = m1a	f1 – f2 = m2a	f2 = m3a

⇒
and

f₁ = contact force between masses m₁and m₂
f₂= contact force between masses m₂ and m₃
Remember :
Contact force is different if force F will be applied on mass C