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How to Solve a Multi-Atwood Machine Assembly

Introduction The figure on the right shows a “double-double” Atwood machine with three ideal pulleys and four masses.  All pulleys are released from rest simultaneously.  Which of the choices below describes the angular motion of the top pulley P after some time has elapsed and why? It rotates clockwise with increasing angular speed. It rotates…

Epsilontic – Limits and Continuity

Abstract I remember that I had some difficulties moving from school mathematics to university mathematics. From what I read on PF through the years, I think I’m not the only one who struggled at that point. We mainly learned algorithms at school, i.e. how things are calculated. At university, I soon met a quantity called…

The Poor Man’s Milli-Ohm Meter

Introduction In a previous article on measuring battery internal resistance, a simple technique for low-resistance measurement was outlined. In this article, the technique has been modified and expanded somewhat although the basic method remains the same. It is about as simple as it gets – one passes current through a reference resistor in series with…

Differential Equation Systems and Nature

Abstract “Mathematics is the native language of nature.” is a phrase that is often used when it comes to explaining why mathematics is all around in natural sciences, especially in physics. What does that mean? A closer look shows us that it primarily means that we describe nature by differential equations, a lot of differential…

How to Apply Newton’s Second Law to Variable Mass Systems

Introduction The applicability of Newton’s second law in the oft-quoted “general form”  $$\begin{align}\frac{d\mathbf{P}}{dt}=\mathbf{F}_{\text{ext}}\end{align}$$ was an issue in a recent thread (see post #4) in cases of systems with variable mass.  The following example illustrates the kind of confusion that could arise from the (mis)application of Equation (1): A rocket is hovering in place above ground…

How Quantum Information Theory Solves “the only mystery” of Quantum Mechanics

In Chapter 37 of “The Feynman Lectures on Physics Volume 1,” Richard Feynman famously wrote that the mystery of wave-particle duality in the double-slit experiment is: a phenomenon which is impossible, absolutely impossible to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only…

Opinion: When Pro Scientists Explain Using Pop Science

Abstract There is so much to say about the many endeavors by professional scientists to explain to us the world. The list is long: Carl Sagan, Harald Lesch, Neil deGrasse Tyson, Sabine Hossenfelder, Michio Kaku, and I even saw Roger Penrose and Steven Hawking on tv. The list is – of course – considerably longer…

How to Measure Internal Resistance of a Battery

Introduction A commonly encountered school-level Physics practical is the determination of the internal resistance of a battery – typically an AA or D cell. Typically this is based around a simple model of such a cell as a source emf in series with a small resistor. The cell is connected to a resistive load and…

Why There Are Maximum Mass Limits for Compact Objects

In this article, we will look at why there are maximum mass limits for objects that are supported against gravity by degeneracy pressure instead of kinetic pressure. We will look at the two known cases of this, white dwarfs and neutron stars; but it should be noted that similar arguments will apply to any postulated…

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