Leaning Ladder

Small ladder against wall with variable load and inclination.

What it shows: 

A small ladder is leaned against a vertical wall. A weight can be moved up succeeding steps to find when the ladder will slip and fall down. The forces holding the ladder in equilibrium are in consideration here.

How it works: 

A short (4 foot) step-ladder leans against the wall. The reaction of the wall may be considered horizontal, tangential friction being negligible (the edge of the ladder is covered with a sheet of teflon ... the rollers in the illustration are no longer used). The ladder is leaned against the wall at such an angle that it just does not slip. What are the forces holding the ladder in equilibrium? Now a large weight (14.5 kg = 32 lb) is placed on the first step. What are the forces? The weight is moved up to succeeding higher steps until the ladder begins to slip and equilibrium has been lost.

leaning ladder

Setting it up: 

Use one of the side lecture hall walls between the blackboard and the side door. The plain cement floor is usually O.K. but if slippage is a problem, a sheet of masonite (rough side up) will make the friction between the floor and the base of the ladder more dependable (μ≈0.3). Duct tape the masonite to the floor ... otherwise it slips. Instead of measuring the angle of the ladder, use tanθ and measure the distance the bottom is from the wall and the top is from the floor.


This is one of those demonstrations where a little showmanship flair will liven it up considerably. The weight is quite heavy and the audience's anticipation of the Great Crash can be capitalized on. On occasion, the lecturer has substituted for the weight by cautiously climbing the ladder until it slips. While much more dramatic, it is of course more dangerous and is only recommended for the nimble footed. A board, butted against the lecture bench and ending about 15 cm from the foot of the ladder, can be used as a "stop" to prevent the ladder from crashing all the way down and preventing a serious fall.