Force required to tip block backwards

[simonx]

Homework Statement

There is a 2-D block with height H, width W, and mass M. (H > W)
A force F is applied from behind the block at a height 0.1H from the ground. If the coefficient of friction is μ, what does the force F need to be to cause the block to tip backwards?

Homework Equations

F x r

The Attempt at a Solution

I know that if the we are interested in tipping the block forwards, then we set Fxr = mgxr and solve for F. Since the question asks for when it tips backward, how do you find the solution?

 

[tiny-tim]

welcome to pf!

hi simonx! welcome to pf!

if the block was accelerating with a force applied at ground level, "the weight would gradually shift to the back", ie the reaction force from the ground would get nearer the back

at a certain acceleration, the reaction force reaches the back, so there is no longer any torque to keep the box from rotating, and the block is free to tip

here, the external force is at height H/10, so that's an extra torque, and the tipping acceleration must therefore be greater