# Fridge about to tip, statics

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1. Feb 29, 2016

1. The problem statement, all variables and given/known data
say a fridge of width "w" and height "L" is being pushed on by a force F at an angle θ to the horizontal. This force is applied at a height of "h" above the ground.

I want to know what the max value of h can be such that the fridge doesn't tip and the coefficient of static friction is μ.

2. Relevant equations
ΣF = 0
Στ = 0

3. The attempt at a solution
The force can be found:

ΣFx = 0
Fcosθ - f = 0, where f(max) = μN

And

ΣFy = 0
N - mg - Fsinθ = 0

So

Fcosθ - μ(mg + Fsinθ) = 0
F = μmg/(cosθ - μsinθ)

This is my reasoning for the height, since only the horizontal component of F affects the perpendicular distance "h" to F, then:

Στ = 0 (about axis where the fridge is about to tip)
hFcosθ - mg(w/2) = 0
h = ½mgw/(Fcosθ)

2. Feb 29, 2016

### drvrm

How you are pushing? F acting below the horizontal at theta angle or above the horizontal?

3. Feb 29, 2016

Oups forgot to mention, the force is pushing above the horizontal, the vertical force is downward though

4. Feb 29, 2016

### drvrm

If you are pushing in a direction above the horizontal then sin component will point up -in the direction of N

so the sign of of F sin(theta) should change, if i am correctly following you!