In the second example, I happened to write the displacement x2 in relative to x1. But we should consider absolute displacement of node 2, and for that, we must change the potential energy stored in the second spring to the value corresponding to a displacement of (x2 - x1). Thank you.
That was impressive! Great help. Thank you ❤️❤️❤️ I would like to put a question. You explained potential of external force system with an analogy to gravitational potential energy. Can we visualize it with a direct force? For example, consider I am pulling spring with my hand. What is external force system in that case? And how does potential energy of external system changes with displacement? Can potential energy of external system ever increase?? If so, where does the potential energy get stored?
Thank you @Binit. Very good question. I thought video could get long and boring if I used other analogies too. But here is your answer: 1. ... can we visualize with direct force? = Yes. 2. ... what is the external force system in that case? = Here you are pulling spring with your hand. So YOU are the physical cause to that force. The external force system is no other that your body. The energy you have in your body which can be expensed to do work is the stored potential energy of the external force system. 3... and how does potential energy of external system changes with displacement? = One thing you should understand is that all work done in our systems (external or internal) are conservative type. Meaning, when work is done, although potential energy is expensed in the process, it can be immediately fully recovered by equal workdone in opposite direction. So when you are pulling something and displacement happens along the direction of your pull, the energy that is in your body gets expensed in the process. So, as I said, your body is the external force system, we say that the potential energy in external force system reduces. But, when you are pulling the spring tip and somehow displacement happens in the opposite direction, then your hand is going to get pulled towards the spring. When your hand is going to get pulled towards the spring, your body is also going to get pulled. But it depends on how you are pulling the spring.. if you are hanging on the spring, it will lift you up and hence your gravitational potential energy increases and if you are at rest then your hand will get stretched and there is a non conservative type of work done when your elbow rotates. But we are talking about conservative work done so it will make more sense when you are hanging on the spring or you take help of another conservative field as a support that you hold when applying your force to the spring. 4. ... can potential energy of external system ever increase? = Yes. When a single force acts on an elastic body like the first example in the video, then the force will always cause displacement along its direction. In that case the potential energy of the external force system decreases. But, if we have number of forces acting on different directions applied on an elastic body, then a small force could get displaced opposite to its direction when larger forces causes more displacement to their directions (also stiffness will play role for which force will cause more displacement). So, the potential energy of that small external force will increase. But, in total, the external potential energy will always be less or equal to zero (zero is when all external forces balance each other's displacements) 5. ...if so where does the potential energy get stored? = It's answer is in answer number 3. I hope you are more clear now.
i mean, i dont know is that ok to ask, but how ddi u come up with this analogy to explain the external work? is there any books that would help me understand all the other theories or is it by any other source?
Well I didn't actually find a simple and easy explanation of this concept in any particular textbook ... and this was the main reason I made this video that nowhere in even RU-vid did I find any satisfactory explanation... I searched about it in a number of books.. including a very old and original book of structural mechanics.. nevertheless I put some personal imaginations and analogies too. I'm sorry that I forgot the exact names of those books.. but thank you for your concern and I'm happy that you appreciate it 😊
Only conservative force can make potential energy. If you move a heavy stone 1 meter away & you got hungry. And now you turn it back to the initial position, you just get twice hungry. NOT conservative force.
