“Method for breaking or not breaking eggs” — kinetic energy explained (April 1973)

In this document

The egg drop: establishing the principle

The note opens with a simple experiment: an egg dropped from a certain height suffers increasing damage with the height of the fall — resistance, cracking, crushing p. 8. Magès then shows that placing the egg in a rigid box changes nothing: at an equal drop height, the impact speed — and therefore the force sustained — remains identical p. 8.

He then introduces the concept of kinetic energy, illustrated by the image of the hammer and the nail: the energy doubles if the mass doubles, but it “quadruples” if the speed doubles p. 8.

Acceleration, deceleration, weight and mass

Page 9 details the difference between speed (m/s) and acceleration (m/s²), then distinguishes “mass” M from “weight” P, by introducing the acceleration of gravity g = 9.81 m/s² p. 9. In the margin are compared values of g: “9.8088 in Paris”, “9.7085 at the equator”, “9.8333 at the North Pole” p. 9.

The formula F = Mγ is set out, then applied to the case of gravity: P = M × 9.81 p. 9-10.

The egg calculation

Magès establishes the kinetic energy formula E = ½MV² = ½PV²/9.81 and the speed/drop height relationship V = √(2gh) p. 10. He applies these formulas to a 50-gram egg falling from 1.20 m: impact speed of approximately 4.85 m/s, kinetic energy of 0.06 kilogram-meters p. 10.

He then breaks this energy down into equivalent force/distance pairs: “0.06 kg over 1 m”, “0.6 kg over 0.1 m”, “60 kg over 1 mm” p. 10, to show that an acceptable force requires a sufficient braking distance.

The strap and egg protection

In paragraph 9, the egg is suspended in its box by a non-elastic strap capable of stretching without returning to its original state. With an egg withstanding 1.2 kg of force, 5 cm of braking travel is required for a 1.20 m fall p. 11. Magès also notes, “as a curiosity”, that a perfectly elastic strap would send the egg back towards the ceiling with the same energy, causing a second shock p. 11. Page 12, which is very damaged, contains a deceleration calculation γ = V²/2d = 235 (unit uncertain) p. 12.

Transposition to the horizontal trolley

Paragraph 10 transposes this reasoning to “a box propelled horizontally”: a trolley containing the egg, which hits the front partition during sudden braking (Fig 5-7, p. 13). The conclusion is explicit: “do not forget to fasten the egg to keep it intact” p. 13, signed “P Magès, April 1973”.

Context

This pedagogical analogy of the egg to explain kinetic energy and the importance of braking distance evokes, in the history of automotive safety, the principles underlying seat belts and crumple zones — but nothing in this document explicitly mentions the automobile or Citroën: the analogy remains, here, focused on the egg and the trolley.

Paul Magès, a Citroën engineer known for the hydropneumatic suspension, was also involved in passive safety issues within the manufacturer during the 1970s, a period when these subjects were gaining increasing importance in the automotive industry.

Archivist's perspective

This document appears to be a reworked version of a pedagogical demonstration that Magès had already sketched out a month earlier, as attested by the “Method for not breaking eggs” of 24 March 1973. The repetition of the same example, enriched with developments on acceleration and the formula F = Mγ, suggests an effort of progressive clarification before transposition to a case closer to the automobile — the trolley hitting an obstacle p. 13.

It is likely that this note prepares or accompanies the more technical reflections on passive safety developed in the same month of April 1973, notably the dialogue “Passive safety — The motorist and the technician” and the calculation notes on safety distances, dated 25 April 1973. The use of such a concrete and vivid analogy (the egg, the hammer, the nail) testifies to Magès's concern to make complex physical concepts accessible, probably for internal training or popularization purposes.