We have a homogenous box on a surface with static friction μ=0.5. We apply a force on the top of the box at an angle 30 degrees to the horizontal (see picture) and we want to know for what values of P does the box slip and tip. I have drawn a free-body diagram here of the situation:
The Attempt at a Solution
I have found that for slipping, P=0.448mg but I need help to determine P for the box to tip. If we take the moment(torque) around point C we get;
(Pcosθ)d+(Psinθ)2d+(N_B)2d-mgd=0 and hence P = (mg-2N_B)/(cosθ+2sinθ). How can I get rid of N_B in this case?