Solving Friction Problem with Masses m and M

[Peter Lauer]

Hey guys, My first post, I'm not sure this is the right place to put my question...but here it goes:

A block of mass m stands on another block of mass M. Some force F starts pushing M to the right, initially both blocks move together then, as F increases the block with mass m starts to slide to the left. There is no friction between the floor and block M, just between M and m.
The solution is given by the equations :
Friction = ma
F-Friction = MA
a,and A are the accelerations for blocks m and M respectively.

So, I don’t understand why the block m slides to the left. Because by Newton’s third law, if block M is pushed by some force, the way I see it, friction pushes back, so M pushes m forward to the direction of force F,as m pushes back. So why mass m is moving backwards ? I'm pretty sure my application of the Third Law is wrong but why? The only way m could possibly go to the left, would be if M pushed m back then m would have no option but push M forward so the equations should be :
Friction = ma
F+Friction = MA
So what's wrong?

 

[Doc Al]

So, I don’t understand why the block m slides to the left. Because by Newton’s third law, if block M is pushed by some force, the way I see it, friction pushes back, so M pushes m forward to the direction of force F,as m pushes back. So why mass m is moving backwards ?

Mass m is only moving to the left with respect to mass M. With respect to the ground, it is of course being pushed to the right and thus moves to the right.

 

[Peter Lauer]

Mass m is only moving to the left with respect to mass M. With respect to the ground, it is of course being pushed to the right and thus moves to the right.

Waw. I got it ! I was trying to think of it in respect to the moving block M, not considering that it isn't an inertial reference... THANKS for the answer, really helpful!