# Toppling Stack problem

## Homework Statement

The Toppling Stack

There is a stack of N boxes (rectangular solids) on a level frictionless table. Each box has the same uniform density, has the same mass M, and has the same dimensions L x W x H. The bottom box is pulled with a constant force F parallel to the table. The dimension H is perpendicular to the table and perpendicular to F; the dimension L is parallel to the table and is parallel to F; and the dimension W is parallel to the table and perpendicular to F. The coefficient of friction between the boxes is mu_s. Assume the acceleration due to gravity, g, is constant for the entire stack. The bottom box is Box 1, the box directly on top of Box 1 is Box 2, ..., the top box is Box N.

If F is large enough, some boxes will fall by toppling over (not sliding off).

a) Show mathematically that the separation should occur between the Box 1 and Box 2.
b) What is the minimum value of F which will cause the boxes to fall. Answer in terms of g, H, L, M, N, and / or W.
c) Find the minimum value of mu_s which will make falling over impossible without sliding first. Answer in terms of g, H, L, M, N, and / or W.

The three parts can be done separately.

F=μkN

## The Attempt at a Solution

I drew a picture of 4 boxes and labeled the forces but I don't know how to proceed further...