Recent content by jbriggs444

Indeed. We teach elementary school students using integer ratios and decimal fractions. As a pure mathematician, I tend to shy away from decimals. But when communicating with laymen, it is handy to fall back on a shared background of decimal fractions that have only finite precision. I am...

Are you comfortable with long division using pencil and paper? My generation was taught how to do this. There is no problem in principle with carrying out this process using infinitely long decimal expansions. Just do it to ten decimal digits and compute ten (or so) digits of the quotient. Go...

Global conservation of mass is a feature of classical mechanics. Local conservation of stress energy is a feature of general relativity. I am currently at an age where my height is almost certainly decreasing over time.

Height is not conserved. Nor is it usually additive. That makes it less meaningful and less useful to speak about height "moving". We can and often do speak of a mass flow rate. Mass is conserved and [in common circumstances] localized. We can meaningfully speak of its motion. If an aircraft...

Nor do I. To the extent that energy is localized and conserved, it may be sensible to speak about energy moving. We could, for instance, speak about energy moving across an ocean in an oil tanker. Does the "path of least resistance" take into account the political and military situation in the...

When someone speaks of freedom from censorship as a virtue, I like to think back to Usenet. The lesson learned there was that unmoderated open access discussion groups do not work. It was fine when it was just the nerds chattering back and forth to each other. Once the barrier to entry became...

Right. You are asked for velocity. You have determined the [coordinate] acceleration. That is all you need. The various forces required to produce that acceleration do not enter in.

The professor is still wrong. Let us grant that the intended threshold for pilot unconsciousness is 6g of coordinate acceleration. This is then 7g of experienced proper acceleration at the bottom of the loop. But that 7g of experienced proper acceleration is not equal to the ##\frac{v^2}{r}##...

Loss of consciousness results from proper acceleration, not coordinate acceleration. Proper acceleration is how much the plane's acceleration deviates from free fall. Coordinate acceleration is the plane's acceleration in a chosen reference frame. Probably the rest frame of the ground. The...

Yes.

When the question asks for mass, do you understand it to mean relativistic mass or invariant mass? Obviously one can discard the idea that invariant mass is meant immediately. The invariant masses are always in the ratio of one to four regardless of velocity. Never one to three. You understand...

Let me be sure I understand. For this calculation we are abstracting away the interaction zone between the falling portion and the static portion and making blind assertions about the behavior there. Your particular blind assertions are that energy is not conserved and that the tensions from...

The static portion has velocity zero. The falling part has velocity ##v##.

A good way to approach infinite quantities in physics is to model them as the limit of finite cases as some parameter is increased without bound (or decreased toward zero). So we take the limit of a flexible ribbon and a tight curve as both flexibility and tightness increase without bound. That...

In line ##\LaTeX##:: ##a_1 = \frac{4 m_2 m_1 + m_0 ( m_1 - m_2 )} {4 m_2 m_1 + m_0 (m_1 + m_2)} g## Which should render as ##a_1 = \frac{4 m_2 m_1 + m_0 ( m_1 - m_2 )} {4 m_2 m_1 + m_0 (m_1 + m_2)} g## I tossed in some white space in the unrendered LaTeX for what I think is better readability...