Force Problem Homework: Calculating Mass and Friction Coefficient

[anon1]

Homework Statement

A mass "b" is placed on top of a larger mass that is 2.4 times the mass of the smaller one as shown. The coefficient of friction between the larger block and the surface is 0.35. A horizontal force acts on the larger block.

a) What force would be necessary to maintain an acceleration of 4.0 m/s²? (in terms of "b")
b) What would be the minimum coefficient of static friction necessary to keep the smaller block from slipping?

Homework Equations

a = F_net / m
F_f = µF_N
F_netx = F_a + F_f
F_nety = F_g + F_N

The Attempt at a Solution

F_g = ma
F_g = 3.4b (9.81)
F_g= 33.354b N [down]

F_nety = F_g + F_N
0 = 33.354 N [down] + F_N
F_N = 33.354b N [up]

F_f = µF_N
F_f = (0.35)(33.354b N)
F_f = 11.6738b N

F_netx= F_a + 11.6738b N

I don't know how to get F_netx from here, and I don't know if this is right so far4.0 m/s²= F_net / 3.4b

Also I don't understand part b)
Thanks for the help

 

[haruspex]

F_netx = F_a + F_f

No, F_netx = F_a. You want to find F_app, where F_netx = ƩF = F_app + F_f.

Also I don't understand part b)

The smaller mass is to accelerate at 4m/s². What force is necessary to achieve that? Where is that force coming from?

Btw, I recommend working entirely symbolically, only plugging in numbers when you get to the final equation. It makes it easier to find errors, and much easier for others to follow.