Problem: Two masses are connected by a cord and placed on a cart as shown. What must the acceleration of the cart be (caused by the force F) so that the mass on the right does not fall? What are the normal forces on the masses? What is the tension in the cord? What must the force F be?

Solution: First, the free body diagrams...

You should study these carefully. For example, do you understand how the directions of the various normal forces were obtained? (Hint: Newton's Third Law was used.)

Writing Newton's Laws for body 2...

For body 1,

Substituting this back into the equation for N₂,

Using the free body of the cart,

You can also use a free body of the entire system. Can you see why the force F would not be (M + m₁ + m₂)(m₂/m₁)g? Try working it out!!