Recent content by jbriggs444

Why did the astronomer put meat in his shower?

Are we arguing about the definition of "mechanical advantage" or are we nattering about a choice of reference frame and where to draw the lines for "effort" and "load". Isn't it irrelevant in any case since we agree about all of the forces and the net effect? The rest is just words. [Me, I...

The author has not given us the radius of the basin at the bottom. This is a hint that the radius is large enough to be irrelevant. From this we can conclude that the fluid level in the basin will rise slightly, but not significantly as a result of the process.

Looked it up. Work of a homeless guy in Austin by the name of "David". He specializes in weird signs like this.

You will need to be more specific about this. Are you suggesting that the midpoint of the string is pinned to the table? So that the tensions in the two half-strings are different. Or are you suggesting that the table is equipped with circular frictionless rails? So that the tension in the...

This aligns with my experience as well. The principle useful skill I obtained in college was in learning how to learn. Secondarily, I learned some terminology and fundamental principles in various fields. I ended up wearing about ten hats over time. Most of those hats involved learning new...

We might imagine achieving this by counter-balancing local gravity with an implausibly massive awning suspended overhead. The gravitational potential beneath the awning would be the same (to a good approximation) as the gravitational potential nearby. So zero effect on time dilation. For a...

It may be a language issue, but "equiprobable" is not the correct term to use. If ##V_x## is a random variable then we could speak of the probability that ##V_x## falls within a particular range. We could speak of the probability that ##V_y## falls within the same range. Or ##V_z##. If the...

It is not gravitational field strength (local gravity) that matters. What matters is gravitational potential. Or, almost equivalently, escape velocity. If one works through the math, the escape energy from a planet is the product of surface gravity times planetary radius. Both Earth and Pluto...

If one takes the limits ##\lim_{t \to \infty} x(t) = \infty## ##\lim_{t \to \infty} y(t) = 1## ##\lim_{t \to \infty} \frac{x(t)}{y(t)} = 0## ##\lim_{t \to \infty} \text{arctan} \frac{x(t)}{y(t)} = 0## If you then try to play naive arithmetic games with infinities and limits, you get...

“It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so. “ – Mark Twain

I see no contradiction. I see consistency. The probability that ##10^{23}## independent samples drawn from a normal distribution with mean zero will all share the same sign is ##\frac{1}{2^{10^{23}-1}}##. This is effectively impossible. And agrees with what I said. The probability that...

I read this as "given any distribution which is symmetric about zero, the distribution mean will be zero". That is a true statement about the distribution. Nonetheless, the following statement is false: "Any finite sample drawn from a symmetric distribution will have a sample mean of zero" An...

1. Google AI is not an acceptable reference. [See the rules here. Search for "ChatGPT and AI-generated text"] 2. If Google AI says this then Google AI is wrong. AI is frequently wrong but plausible. Hence the rule above. 3. I do not believe that Google AI says this. However since Google AI is...

How is it possible? Why should it not be possible? Why the surprise? It is very difficult to respond to an open ended question like this. You need to be specific about your concerns. Or, as has been aptly suggested, use a textbook and take a course. No. If we choose a frame of reference where...