Discussion and hints:
As the force F is applied to block C, a pair of friction forces act on the crate at feet A and B. These friction forces create a net counterclockwise (CCW) moment about the crate’s center of mass. In order to prevent tipping, the normal forces at A and B must create an equal but opposite (clockwise, CW) moment about the center of mass. This CW moment will result in a reduction of the normal force at the leading foot at B. When this normal force at B is reduced to zero, the foot at B will lift off block C, causing the create to tip. Your goal in this problem is to determine the value of F that is required to make the normal force at B a zero, or NB = 0.
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw individual free body diagrams of the crate and the block. Please note that since the crate does not slip on the block, fA ≠ μNA.
Step 2: Kinetics (Newton/Euler)
Write down the Newton/Euler equations for the crate using your FBD above. Take care in choosing the reference point for your moment equation. In order to use the “short form” of Euler’s equation, this point should be either a fixed point or the body’s center of mass. Note that there are no fixed points on the crate. From these equations, you will find the normal force and the friction force at A. From the Newton equation for the block, you can relate the friction force at A to the applied force F.
Step 3: Kinematics
Do you need any kinematics here?
Step 4: Solve
Set NB = 0 in your above equations and solve for the applied force F.
Any questions?