Recent content by GiorgioPastore

Now I see my mistake. I was considering the change of level from the bottom of the submerged object. In such a case, objects with the same mass but different shapes may have different distances from the bottom to the water's free level. However, such a distance is not directly related to the...

Then you are assuming that the balls are completely submerged in water. That would be a simpler case. But with tennis balls, they are only partially submerged, which requires a more thorough analysis.

Archimedes' Principle gives the exact volume of water displaced by a submerged or partly submerged body. Where the displaced water goes depends on the geometry. Do you think that the level of the free surface of a fluid in a cylindrical container varies in the same way as a function of the...

You should take into account that this is just an approximation for the height change. A more accurate calculation should account for the geometry of the region occupied by the displaced water. Using the formula for the volume of a spherical cap ( https://en.wikipedia.org/wiki/Spherical_cap )...

Not exactly. The statistical mechanics entropy is explicitly defined for finite-size systems. The properties of thermodynamic entropy are recovered from statistical-mechanics formulae only in the thermodynamic limit. Without the thermodynamic limit, there is no overlap. For example, the nice...

Although calling the Dirac delta "distribution" is quite widespread in the Physics community, I prefer to call it a generalized function, reserving the term "distribution" for the corresponding functional (as in Schwartz or in the Gel'fand papers and books).

From my post, you can obtain the quantitative relation between ##v_1## and ##v_2##. Without that, it is impossible to say whether ##\theta_1<\theta_2## or the other way around. The final answer is very simple (it corresponds to equating the mechanical energy in the two half spaces). However...

A possible schematization for this problem is the x-dependent three-dimensional potential function $$ U(x)=U_1+(U_2-U_1)\frac{\left(1+\tanh\left( \frac{x}{w} \right)\right)}{2}. $$ Over an interval controlled by the width ##w##, ##U(x)## goes from values very close to ##U_1## at negative values...

Do you mean at T=0 K? In such a case, I agree. But this just says that the only possible state of a system in equilibrium with a thermostat at 0 K is the ground state. It has nothing to do with the possibility of cooling a system to absolute zero. At any other temperature, all the available...

If the 3rd law is stated as "the zero temperature cannot be attained", I agree: it is trivially related to the fact that the "laws" are principles, taken from experience, that we want to consider as the starting point from which all the consequences of Thermodynamics can be obtained. However...

I think the simplest way to get the result is by using the triangle with sides 2, 11, and AB in the modified figure below. The length of segment AB is twice the height of an equilateral triangle of side x, and the angle between the side of length 2 and that of length 11 is ##2 \pi/3##. From the...

Opinions, like definitions, are not right or wrong. They can be useful or useless. From my experience in teaching Physics, I can say that names, although they do not modify Science, do play a role in the learning process. Some names do not help to grasp the concept. Who, staying at the normal...

It is not a problem for me. It is a problem for people who translate "fictitious forces" as "illusion" without further explanation. The problem exists, as evidenced by the original post in this thread.

Using inertia in place of mass is another confusing thing for beginners. Moreover, historically, the term "vis inertiae" is different. Newton conceived of "inertia" as "the innate force possessed by an object which resists changes in motion", Among "pseudoforce" and "fictitious," there is an...

It doesn't matter to somebody, no problem. Other people, mostly those who are involved in teaching Physics, understand the difference.