A ladder against a wall: which angle is safe

What the experiment shows

The ladder’s weight presses on the floor and the wall. The flatter the ladder, the harder its foot is pushed outward, until floor friction can no longer hold it.

How to run it

1. Press “Run” and watch both ladders.
2. In the editor make the shallow ladder steeper — from which angle does it stand?
3. Increase the floor friction (rubber feet).

Questions to discuss

• Why do ladder feet have rubber pads?
• Why is a ladder on ice dangerous at any angle?

The science

A ladder stands while floor friction balances the push from the wall. With equal friction μ at floor and wall the limiting angle from vertical is tan α = 2μ/(1 − μ²). For μ = 0.3 that is about 33°.

Try it at home

Lean a ruler on a box on a smooth table and tilt it more and more until it slips.

What to change in the editor

• Put a weight at the top of the ladder.
• Make the wall slippery (friction 0).