Marquis de l'Hôpital

Imagine a pulley system with a beam, a rod, and a rope. How far can the weight drop? Let's dive in!

marquis de l hopital question

We have a beam (AB) that is 1 meter long. Connected to it is a rod (AC), which can pivot freely at A.

At the other end of the rod (C), there's a pulley that can spin freely. A rope is tied at B, goes over the pulley at C, and then hangs straight down to a weight at D.

Given that:

The rod AC is 40 cm (0.4 m) long
The total rope length (BC + CD) is 1 meter

What is the greatest depth that D can reach below the beam AB?

Based on Marquis de l'Hôpital (1661-1704) Analyze des Infiniment Petits

From a paper on optimization using the TI83 Calculator

Roger Fentem - College of St Mark and St. John