## Galileo’s inclined plane | science game

Galileo’s (possibly mental) experiment to refute the theory, discussed last week, has generated some controversy. Here is what Jesus Nella had to say about her:

“It is a surprising argument by reduction to the absurd: if the Aristotelian theory is correct, two contradictory conclusions will be drawn. On the one hand, on the one hand, the lighter stone will slow down on the other (while the heavier stone will accelerate the first). On the other hand, together they will both form more weight than each separately. Thus, the whole must fall more slowly than the heaviest alone (for the first reason) and must also fall faster (for the second reason).”

Regarding the Madrid Foucault pendulum, Gabriel Espin gave an accurate account:

“The Royal Madrid Observatory is located at (according to Google Maps) 40408 degrees latitude; when applying the pending formula, the time used for the full cycle is 37,024 hours or 37 hours 1 minute 26 seconds.”

Going back to Galileo, much is said about his experiences – real or mental – at the Tower of Pisa, where he dropped objects from above; But it was actually an inclined plane, not a tower, which allowed him to make accurate calculations when the bass fell. If we let a ball roll on an inclined plane, its weight – perpendicular – is divided into two forces: one perpendicular to the plane that makes it stick to it and the other parallel to the plane that makes it slide; The less inclined the plane, the less this second force is (until it becomes zero in the horizontal plane), therefore, by means of a suitable inclination, gravity can be observed working in slow motion, so to speak, which greatly facilitates measurements. With an inclination of 30º, for example, the force that causes the ball to descend on the plane is half its weight, because it is proportional to the sine of the angle of inclination (sin 30º = 1/2).

### sloping roof

We have a daily example of an inclined plane over roofs (although usually not very flat), so we can get one of them to pay Galileo the Great a little tribute in the form of bus-fall problems:

A little chicken sits on top of a gabled slate roof and lays a spherical egg (round eggs are not rare among first-time chickens), which rolls 4 meters across the roof and falls to the ground from a height of 8. 30 roof. Does the egg break? Another yes: How fast does it get to Earth?

It’s still more difficult:

Next to the chicken is a television antenna on its base attached to a rope that extends under the ceiling and hangs two meters from the edge. The little inexperienced cyclist would mistake it for a huge worm and click at the point where it attaches to the antenna until it breaks and the rope slips through the ceiling and falls. What is the velocity of the rope the moment its lower end touches the ground?

In both cases, roof friction (a slippery stone) and air resistance are neglected.

Carlo Frappetti Writer, mathematician, and member of the New York Academy of Sciences. He has published more than 50 popular scientific works for adults, children, and youth, including “Damn physics”, “Damn maths” and “The great game”. He was the screenwriter of “La bola de cristal”.