It is not difficult to calculate the diameter of the Earth's core knowing its density, the mantle and the average density of the Earth (which, by the way, is the largest in the Solar System: 5.5). There is still too much information about the bark, because it is so fine that we can despise it. That's what Earth has in common, a globe and a soap bubble: the thinness and fragility of their respective "skins". And the main objective of the problem posed last week was to highlight the extreme relative thinness of the earth's crust: if the Earth were the size of a soccer ball, the crust would be as thin as an eggshell. Hence, we can despise it and solve the problem "in the manner of Fermi", as does our "prominent user" Manuel Amorós:
"One way of roughly calculating the solution would be to notice the narrowness of the crust compared to the radius of the Earth, and neglect that layer. With the two unknowns x the inner radius e and the total radius, we obtain immediately that y3 = 3.5×3. Since the cube root of 3.5 is approximately 1.5, we deduce that x is 2/3 of the radius of the Earth. "
Stars, bubbles and balloons
Both a planet – or another star – as a balloon or soap bubble take the spherical shape (slightly distorted in the case of the balloon because of the swelling spout) because the forces involved force them to maximize the volume / surface ratio, and The sphere is the solid with the smallest surface area for a given volume. The forces are not the same, but they obtain the same result: the gravity in the case of the stars, the surface tension of the water in the bubbles, and the atmospheric pressure in equilibrium with the elasticity of the rubber) in the case of the balloons.
The soap bubbles are fascinating objects from the physical and mathematical point of view, as we will see in some future delivery. Its almost perfect sphericity, as pointed out by a reader, contrasts with the usual silhouette of water droplets, which also owe their shape to surface tension. Why are they geometrically different?
And the familiar children's balloons, whether full of air or helium, can also be very instructive, at the same time surprising. What happens if we focus a balloon with a fan and make its air blast on it?
Another counterintuitive behavior of balloons can be observed inside a moving car:
In the backseat of your car, which you drive at a uniform speed along a stretch of straight road, a child holds a balloon full of helium floating around the center of the roof. Suddenly you turn to the right; What does the balloon do?
Carlo Frabetti He is a writer and mathematician, a member of the New York Academy of Sciences. He has published more than 50 scientific dissemination works for adults, children and young people, among them Damn physics, Damn mathematics or The big game. He was a screenwriter The Cristal ball