A mass m ₁ is on top of another mass m ₂ , which in turn is supported by a frictionless horizontal surface. A light string is attached to m ₁ and pulled on the other end with a force F.

Suppose the surface between the two masses is frictionless. Find the acceleration of each mass. Suppose instead the surface between the two bodies is rough and the force is small enough that the mass m1 does not slide on m ₂ . Find the acceleration of each mass now.

If the coefficient of static friction between the two surfaces is ? _s , how big can F be before the top mass slides? If the coefficient of kinetic friction is ? _k , and the force, F, is large enough to cause sliding, find the acceleration of each mass.