Apply a force so it won't move?

[mistabry]

Homework Statement

A box of mass m = 4.5 kg rests on a larger box of mass M = 26.0 kg, which is at rest on a frictionless surface. The coefficient of static friction between the two boxes is μs = 0.51. An ideal string runs between the two boxes around a fixed pulley. What is the maximum force F that can be exerted on the lower box without causing the boxes to slide?

Homework Equations

f_s=μ*|N|

The Attempt at a Solution

I drew 2 free body diagrams. For first mass, I had Tension point left, Force point right, Normal force up, W down. For second mass, I had Tension point left, Friction point right, Normal force up, W down.

I would think since the surface was frictionless, T = F = f_s, but that didn't work out so well D;

 

[PhanthomJay]

In your free body diagram of the bottom block, you left out a force. Which one??

 

[mistabry]

Is there like another tension added to the bottom block going right?

 

[PhanthomJay]

Well, a pulling force F acts right, and you already identified it. Look for a contact force at the top of that lower block that acts horizontally. Think about Newton's third law.

 

[turbo21]

hey mistabry i got the answer here:
https://www.physicsforums.com/showthread.php?t=443079

it's not the exact same problem, but it's similar.
basically use F - T - Fs = 0. because the sum of the forces need to equal 0 since its not moving.
T = Fs, so just find Force.

The weight of the second box is neglible, because the floor is frictionless.

Thanks PhantomJay for helping the other guy in the thread i linked lol.