I don't get it. ##(E_3')^2-(Mc^2)^2=(cp_3')^2## is exactly the form of ##(E'^2)-(cp')^2=(Mc^2)^2##.
You may read p.169-172 of "Special Relativity" by A.P. French. The idea is like this: In Newtonian mechanics, we know by experiments that a specific type of collisions can be described by the...
By substituting the above expression for ##p_3## and ##\gamma=M/m## into the expression for ##\cos\theta## (equation (10)), we can obtain
$$\cos\theta_{max}=\sqrt{1-\left(\frac{m}{M}\right)^2}$$
and hence ##\sin\theta_{max}=m/M##.
The textbook is "Special Relativity" by A.P. French.
I finally took the time to do the calculations. Surprisingly it is not as tedious as I thought. Here are my calculations:
\begin{align}
p_1^2 &= (\gamma^2-1)M^2c^2 \\
p_1 &= \sqrt{(\gamma^2-1)}Mc \\
E_4=E_1+mc^2-E_3 &= \gamma...
Equation (12) (and hence (16)) is wrong, I should have used relativistic velocity addition (I found it difficult to get out of the habit of using Galilean velocity addition).
But why is equation (17) wrong? The rest energy (##Mc^2##) is an energy-momentum invariant, i.e...
Homework Statement
Homework Equations
Conservation of linear momentum
Conservation of energy
Energy-momentum relationship: ##E^2-(m_0c^2)^2=c^2p^2##
Lorentz transformation of energy: ##p=\gamma(v)(p'+vE'/c^2)##
##\mathbf{p}=\gamma(v)m_0v##, ##E=\gamma(v)m_0c^2##
The Attempt at a Solution
My...
I created a small app simliar to what you wanted (but not in pdf format). It organizes notes hierarchically by using expandable and collapsible panels. It was written in browser-based front-end languages (HTML, CSS, JavaScript) so that it can run on different platforms, in exchange for...
OK. Let me try to answer my own question. If there is no friction, the "hands" will continue to move out until tension of arms holds it. If we think of the "hands" as two masses sliding along a frictionless infinitely-long arm at opposite ends, then the two masses will continue to move out until...
I don't understand... Let me try to analyze the situation in this way:
Ignore the translational K.E. of the hands (e.g. the boy is spinning very fast, and he pulls his hands very slowly).
When the boy pulls in his hands:
decrease in P.E. + work done by muscles to pull hands in + work done...
Did you study classical mechanics right after calculus/ODE/LA, without reading a calculus-based general physics textbook like Freedman or Halliday (as most universities require)? Is thermodynamics and statistical mechanics necessary? Do we need to study particle physics before learning QFT? For...
You must be very talented to learn so quickly! Do you solve most of the problems in the textbooks, or just a selected few? Have you ever encountered difficulties such as those that I mentioned in the first post? If you have, would you mind sharing how you overcome them?
Thank you very much, SolsticeFire. Have you ever encountered "knowledge gaps" between textbooks and research papers, because the textbooks available are not advanced or up-to-date enough? Is backtracking among research papers via the references a good way to overcome this hurdle (for a...
Why do you think so? I really can't see the point of doing exercises without being able to verify my answers. But for the proof-type exercises, I can try to solve them and ask for help online as you have suggested. For the advanced topics, I suspect that it is not very likely to get answers...
I wholeheartedly agree with this, ZombieFeynman, but my ultimate goal is to understand how the universe originates and evolves as much as possible. I do look forward to learning about specific phenomena such as the nuclear processes in stars, but to me they are much less important. That's why I...
Thank you very much BiP. My undergrad degree is computer engineering. I think you are in a much better position than me: Since some of your relatives are physicists, you can call for their help when you have questions on physics.
The web sites you gave me are of introductory level. This is...