Physics problem : dynamics with friction

[3ephemeralwnd]

Homework Statement

A cube of titanium with a mass m = 0.1 kg is placed on the rough, sloping side of a triangular block of mass M = 1 kg , which itself rests on a horizontal frictionless table. if the coefficient of static friction is 0.4, determine the minimum horizontal force F applied to M that will cause the small block m to slip.

The attempt at a solution
I've drawn out the FBDs for m and M and even m+M (ignoring all internal forces between m and M), but i can't really relate them to each other in order to solve the problem

Any help would be appreciated :)

 

[ehild]

The attempt at a solution
I've drawn out the FBDs for m and M and even m+M (ignoring all internal forces between m and M), but i can't really relate them to each other in order to solve the problem

Any help would be appreciated :)

Do not ignore the forces between m and M, and show your work.

ehild

 

[3ephemeralwnd]

I didn't totally ignore the forces, the internal forces between the two masses I included in the FBD of M and m, but i also drew a FBD that represented the entire system as a whole (M+m) in which i didn't inlcude the internal forces.

Im just not sure how to continue from here, I have all the FBDs, now what?

 

[ehild]

Find the conditions that the block and slope move together. You know that F=(M+m)a. Find the horizontal and vertical components of the forces acting on the block. These forces are gravity (mg), normal force (N) and static friction (Fs). The resultant of the vertical components is zero. That of the horizontal components has to be ma=Fm/(M+m). The force of friction can not exceed μN. If Fs=μN the block starts to slip.


ehild