Thank you very much for the detailed and easily understandable explanation. I am taking an online Mechanics course and I realized its quite difficult to learn Physics through only a textbook or online articles. This definitely saved me a lot of time and frustration.
It is important to know that the calculations are made at the bottom h=0 so v is the velocity of the mass along the bottom point when it is launched at rest from an angle \theta. This is not the formula for the velocity or kinetic energy at any point of the trajectory of the pendilum. Great video openened my eyes!
Math adventures, Excellent! Thanks for the comment, and keep up with the physics! You might also like my new website: www.universityphysics.education Cheers, Dr. A
+Noah Meyer Thanks for the props Noah! I did not have to write everything backwards. See this link: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-CWHMtSNKxYA.html Cheers, Dr. A
could one calculate theta without knowing the initial theta angle? just knowing the value of the initial force in relation to the weight of the object where the angle would be equal to the arc tangent of the relationship between the initial force to the weight
The purpose of the tension is two-fold, for a pendulum. 1. It needs to oppose the radially-outward component of gravity 2. It needs to cause centripetal acceleration to keep the bob following a circular path To solve part 1, it needs to at least be as large as m*g*cos(theta). To solve part 2, we also need to add onto it, m*v^2/L This means, that in total, the tension will equal: Ft = m*(g*cos(theta) + m*v^2/L) given a simple pendulum with a bob mass of m, a length L, and in a uniform gravitational field of g. The values of theta and v are transient throughout this problem, since v is greatest when theta is zero, and v is zero when theta is at its max. So you would determine v as a function of theta through conservation of energy, in order to get a concise expression for Ft in terms of theta.
Unsure if this is a stupid question or not but I was wondering from your (Matt Anderson) perspective are you writing everything inverted onto the board so we see it normally on the video .
When the swing is raised and released, it will move freely back and forth due to the force of gravity on it. The swing continues moving back and forth without any extra outside help until friction (between the air and the swing and between the chains and the attachment points) slows it down and eventually stops it. WHAT THEN IS THE FORMULA TO KNOW THE TIME WHEN IT PRACTICALLY STOPPED?
That's a great question and quite a tough one to answer. But you're absolutely right, friction and air resistance will cause it to stop eventually. Maybe I'll make a video about it. Cheers, Dr. A
@@yoprofmatt Thanks Doc A. I have been pre-occupied with this idea as the same with the UNDAMPED condition with the RLC circuits both SERIES and PARALLEL, I just can't make the PHYSICS connection of the 3 DAMPING factors involved... Please show all the MATHEMATICAL STEPS going though the mathematics. Than You for Your Response.
@@yoprofmatt I just want to know the difference of both angles in respect of gravity but according to you/physics, it is nothing to do but the friction and air resistance. So it means the friction and air resistance are the important things to eliminate to get the pendulum swing longer? Thanks for the answer 🙏
would we not conserve the energy like ; mgh + 1/2 mv^2 = mgh + 1/2 mv^2 . where in initialy there was no kinetic energy so initial kinetic energy is zero . so; 1/2 mv^2 = mgh + 1/2 mv^2
Your words are right, but the math is wrong. Initial kinetic energy is zero. But final potential energy is also zero. If h is the height at which it started, relative to the bottom of the swing, then you just get mgh=1/2 mv^2. See the 2:20 mark. Cheers, Dr. A
No, for work to be done there must be some displacement (W=F.∆d). As tension acts along the radial axis, and the pendulum's distance from the centre does not change, tension does no work.
Because it is treated as a simple a point mass, and its size is insignificant. You can calculate what 1/2*I*omega^2 is, for a point mass on a negligible mass rod of length L, and you will find that 1/2*I*omega^2 also equals 1/2*m*v^2.
The Pendulum starts at an initial height h. Which is also Ei = mgh. Ef is when it's at the bottom so you are correct 1/2 mv^2 is when it's the bottom but were confused about Ei and Ef it seems
It starts out by claiming/declaring that Ei = Ef. That is why it is never true at all in the actual world. Just on paper only. Any person who is paying attention will just keep on going minding his own business and that includes yourself. And any attempt to to bring other issues such as friction, air resistance is still false. There is so much more and all that is just left out. First can anyone define what is this thing and whoever came up with it...."closed system"? Does it even exist? If it doesn't, it is finished. And if it does exist... that is another can of worms...
Do you believe that energy can not be created? I do not think so. If so, why it exist? It means that energy can be created right?. If energy can not be created, then it will not be there. Think about it.....
Dr Lucky, Thanks for the comment. In physics we like to talk about theories that relate to experimental predictions and ultimately experimental results. If we cannot test it, it's not physics. Since all the energy in our universe was released by the Big Bang, you might say that the Big Bang "created" energy. But that would imply that you could see what was there before the Big Bang. And unfortunately, we have no way of seeing anything before the Big Bang. Thus that does not qualify as physics. So this is our current understanding: The total energy in the universe is a fixed quantity. We cannot create more, nor destroy it. We can simply move it around. Cheers, Dr. A p.s. Physics, like all science, is constantly evolving. Just because our current understanding is this does not mean our future understanding will be the same.
Dr Lucky, I don’t believe energy can be created, it can only be changed in form. At least on earth. But I also believe that our knowledge of physics has us stuck in a box. Although I believe we are 90% correct, there are things we do not know. Perpetual motion is not possible, however there are ways to use physics and combining known forces to convert energy. So extended motion is a factual thing, just look down at the rotating earth. So I believe that some day we will find a way to get over unity without defying physics, and maybe even leaving the laws of thermal dynamics in tact. But it seems that our teachings are holding us back.