Posted in Science & Nature

Buttered Cat Paradox

Cats always fall on their feet. Buttered toast always seems to fall buttered side down. So what would happen if we tied a buttered toast on a cat’s back and then dropped the cat? Would the cat land on its feet or would the toast land on its buttered side?
Or would we achieve perpetual motion and anti-gravity simultaneously as they cancel each other and never touch the ground?

Although the paradox is obviously a humorous thought experiment, there is some truth to the separate adages. 
Cats have a natural righting reflex that allows them to twist their upper body so that they land on their feet. This gracious manoeuvre is developed as a kitten and actually involves quite complex physics where the cat is able to turn around without changing their net angular momentum. Since cats have a small body and very light body weight, their terminal velocity (100km/h compared to a human’s 210km/h) when falling is much less and allows them to absorb the shock easily when landing. Furthermore, when falling cats naturally spread their limbs out to slow their fall as much as possible. All these factors let a cat land safely on its feet even if dropped from a high place. Ironically, the lower they are dropped from, the more likely that the cat would fall on its back.

The other side of the paradox is slightly more complicated. The adage that toast falls buttered side first is actually an example of how if something bad can happen, it will happen. However, physicists have discovered that toast is more likely to fall on its buttered side.
When toast falls off a plate, it is highly likely to tip as it hits the edge. This causes it to rotate as it begins to fall. There are two explanations on why the buttered side is more likely to be facing down. Firstly, butter adds weight to one side and heavier objects fall faster in the face of gravity. Secondly, using experimental data it has been found that toast only rotates about 180 degrees by the time it falls the height of the table or person from where it was dropped from. 

Despite it only being a tongue-in-cheek thought, one can only wonder how many scientists have made some toast, buttered it, tied it to a cat and dropped the cat off a ladder.


Posted in Science & Nature

Murphy’s Law

In 1947, an aerospace engineer named Edward A. Murphy Jr was involved in high-speed rocket sled experiments led by the US Air Force. The aim of the experiment was to research the effect of sudden deceleration on the human body so to improve the safety of jet fighter pilots. To study this, a flight surgeon named Dr John Stapp devised a “sled” attached to a rocket that could be used on a long track. The rocket would propel the sled to a massive speed and brakes would induce as sudden deceleration. However, they found that the machines that were used to measure the G-force (force of deceleration relative to the force of gravity) were unreliable. Murphy proposed that they use electronic strain gauges attached to the harness of the test subject to measure the G-force, something he learned while working with centrifuges.

The idea was great but there was one problem: the gear kept failing, showing no reading whatsoever. Murphy soon found that the sensors were attached correctly but were wired backwards. This simple mistake frustrated Murphy, who blamed the incompetency of his assistant, stating that “if that guy has any way of making a mistake, he will.” This became the famous Murphy’s law, now simplified to “Anything that can go wrong will go wrong”.

Murphy’s law actually played a fundamental role in defensive design, where the worst-case scenario is always assumed and prepared for. Thanks to this system, the rocket sled experiment was successful and in 1954 Dr Stapp became the fastest man in the world – travelling at a speed of 1011km per hour and decelerating at a force of 46G (it was hypothesised that a human being could not survive past 18G). Not only did he survive (albeit with broken limbs, ribs, hernias, detached retina and temporary blindness), Dr Stapp went to build bigger rockets to further test the limits of the human body.

Interestingly, there’s another side to the Murphy’s law involving psychology. People suffer from a fallacy called appeal to probability, where they believe that because there is a possibility of something can happen, it will happen. The brain is surprisingly inefficient in dealing with probabilities and has a tendency to ignore that there is a relatively miniscule possibility and instead focuses on the absolute fact that there “is” a probability. This is the best explanation for why people are compelled to buy lottery tickets and why every student believes they will grow up to be rich and successful.