# Homework Help: Maximum force so object on top wouldn't start sliding back

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1. Dec 13, 2016

### Arquon

1. The problem statement, all variables and given/known data
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

2. Relevant equations
Ffr = umg
F = ma

3. 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.

2. Dec 13, 2016

### Staff: Mentor

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

3. Dec 13, 2016

### Arquon

I got acceleration 7.5 m / s2. Then :
F = Ffr + 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 ?

4. Dec 13, 2016

### Staff: Mentor

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

5. Dec 13, 2016

### Arquon

Yeah, it's ok. Thank you !