The figure shows a uniform crate resting on a horizontal surface. Determine the minimum pushing force that leads to tipping.?

The crate has a square cross section and a weight of W = 592 N, which is uniformly distributed. At the bottom right edge of the surface is a small obstruction that prevents the crate from sliding when a horizontal pushing force is applied to the left side. However, if this force is great enough, the crate will begin to tip and rotate over the obstruction.


Because l (lower case L) looks identical to I (capital i), I will use L instead of the lower case of a script L used in the figure. I do not know how to use view a. In view b, Lw = Lp/2. Remember that the crate is square, so a diagonal from the pivot to the point where the force is applied is at a 45 degree angle to horizontal. The weight can be modeled as if it exists at the middle of the mass because it is uniformly distributed in the crate. The weight provides a CCW torque: 592 N*Lp/2 . The applied force P provides a CW torque: P*Lp*sin45 (sin45 because the location that the force is applied can be visualized as at the end of a diagonal from pivot to the opposite corner). The crate will begin to tip when force P is slightly more than the value that would balance the above torques. 592 N*Lp/2 = P*Lp*sin45 P = (592 N*Lp/2) / (Lp*sin45) = 592 N/(2*sin45) = 418.6 N