Maximum force so object on top wouldn't start sliding back

[Arquon]

Homework Statement

Box B is on top of box A. Box A has a mass of 1 kg, B has 0.3 kg. Coefficient of friction between ground and box A is 0.5, between box A and B : 0.75. With what maximum force can I pull box A without box B sliding back ?

m₁ = 1 kg
m₂ = 0.3 kg
u₁ = 0.5
u₂ = 0.75

Homework Equations

F_fr = umg
F = ma

The Attempt at a Solution

I got that the force of friction between box A and ground is 6.5 N ( (m₁ + m₂)u₁g )
Between box A and B friction is 2.25 N. ( m₂u₂g )
So the total force of friction box A receives is 8.75 N. But I can't work out what is the maximum force with which I can pull box A without having box B falling off.

 

[Doc Al]

Between box A and B friction is 2.25 N. ( m2u2g )

That's the key.
Hint: What's the max acceleration that box A can have before it starts to slide?

 

[Arquon]

I got acceleration 7.5 m / s². Then :
F = F_fr + ma = 6.5 + 9.75 = 16.25 N ( for friction I used friction between box A and ground, and m = 1.3 kg)

Is this correct ?

 

[Doc Al]

I got acceleration 7.5 m / s². Then :
F = F_fr + ma = 6.5 + 9.75 = 16.25 N ( for friction I used friction between box A and ground, and m = 1.3 kg)

Is this correct ?

Looks good to me. (Assuming it's OK for you to use g = 10 m/s^2.)

 

[Arquon]

Yeah, it's ok. Thank you !