Recent content by jbriggs444

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...

If you are using an accelerating frame and pseudo-forces then those pseudo-forces should appear in your force balance equations. If, for instance, the pulley is accelerating downward with some acceleration (##a_k##) then the pseudo-force will act upward -- opposite to gravity. The net apparent...

This is fine in isolation. One often picks a sign convention to try to keep all quantities positive. If one guesses wrong, the worst thing that happens is that upon solving the algebra some quantity turns out to be negative instead. This is a common occurrence in circuit analysis. We may not...

Agreed. I like to point to Newton's original text from time to time. The second part is the one that really resonates with me. In modern words: "the force of A on B is equal and opposite to the corresponding force of B on A". The notions of "action" and "reaction" are often mistakenly...

No, that is not the frame that I implicitly chose. The table does move with respect to the table+book COM frame. The frame that I had in mind is the lab frame where the table is continuously at rest. One can tell that this is the choice I made based on the fact that I spoke of the table having...

Newton's third law is all about momentum. It amounts to a statement that momentum is conserved. Newton's third law has less to do with energy. However, let us proceed to your next paragraphs... Let us chase this down. The force of your hand on the book is equal and opposite to the force done...

I had to zoom way in to read the handwriting. Your first assertion is that ##a_1 + a_2 = 2a_k##. This is obviously correct. The acceleration of the upper block is the average of the accelerations of the lower two blocks. Your next two assertions looked strange to me. You have ##T - m_1g =...

If a phenomenon exceeds the imagination then perhaps it is time to adopt a mathematical description and reason logically from that. This is vastly preferable to reasoning from dreams and puffery.

The idea is that with water on all sides, the clay is effectively sealed. Any air in the lump of clay cannot escape without forming a bubble in the surrounding water. No bubble can form because surface tension prevents it. The pressure that it takes to inflate a bubble increases as the bubble...

What about the possibility that capillary action is responsible? By itself, capillary action will tend to draw water into the clay. This will tend to expel any entrained air. If the clay is entirely immersed, there is nowhere for the entrained air to go. It is trapped and will be under some...

Experiment shows that an accelerating clock continues to keep accurate time. This is the "clock hypothesis". It is tested by measuring the lifetime of particles traversing an accelerator ring at high speeds and correspondingly high accelerations. This is the speed of the Earth relative to a...

And not just regardless of the speed of the source. Regardless of the speed of the observer doing the speed measurement. No matter how fast you go, a pulse of light behind you will be measured to overtake and pass by you at the speed of light. No matter how fast you go, a pulse of light ahead...