Learn what conservation of energy means, and how it can make solving problems easier.
In the golfer problem why is Em (Mechanical Energy) = 0 in the equation Em = Ep + Ek? In general What does Em = 0 mean in relation to PE and KE? I understand how the algebra works but I don't understand the general relationship of Em to the other terms in the equation. Does Em = 0 generally mean that Em is constant? And, when Em is constant, does that always mean Ek = 0 and Ep will be at its maximum positive value? • (14 votes) The mechanical energy does not equal zero. Think of it this way. The conservation of energy formula goes Ki+Ui=Kf+Uf. U is potential energy and K is kinetic energy. In this case the golf ball at the start has zero potential energy. We are considering the surface of the moon to be the height h. The height is zero therefore, we have no initial potential energy(mgh). We are left with Ki=Kf+Uf=>1/2m(vi)^2=1/2m(vf)^2+mgh. Also Em is a measure of energy at a certain time. We can rewrite the conservation of energy formula as Em(i)=Em(f). If Em equals zero that means U+K=0 . I hope this helps. (24 votes) If an object hits another but if friction force doesn't allow the second object to move then where is the energy of the first object gone ? Heat ? How ? • (6 votes) The collision's kinetic energy vibrates both body and nearby air's molecules, increasing their quadratic average speed, which is directly related to temperature. Small but quick compression/expansion processes from the impact also dissipate energy as sound waves. The latter is usually a neglectible amount, though. Like Andrew said, missing energy usually turns out to be heat. (12 votes) How did you get 28.16m/s as your answer for Problem 1? I am very confused and I need help • (4 votes) I can help you with this. Take care about: I hope I help you & sorry if my english isn't the best. (7 votes) isnt mass also conserved? howcome it isnt a fundamental ? • (3 votes) mass can be destroyed when an antimatter and matter collide with each other and also annihilate energy in the form light energy.Antimatter posses the properties just opposite to matter , like antimatter have positively charged electrons called positron . Though mass can be destroyed energy remains constant. This process involves the conversion of mass into energy. The law of conservation of mass-energy states the same (2 votes) In Exercise 1 of How can conservation of energy describe how objects move, how did you get 28.16m/s for the final velocity? I practiced the problem before I saw the answer, and I used the same formula, but I got 6.2m/s for the final velocity. • (3 votes) Was your initial velocity 28.28 m/s? If you have used the same formula and did the algebra right, then you must have made a calculation mistake. (2 votes) In the model rocket question, I have understood the problem in terms of the graph (mechanical energy is flat, so energy is conserved). But can someone explain what actually happens in reality? Is the energy conserved because the rocket went past the atmosphere and gravitational force? Could someone explain how is the energy conserved practically at this stage - "During this time, the rocket is coasting upwards—motor has stopped burning—but going slow enough that the work being done by drag on the rocket is mostly negligible." • (3 votes) If there's air resistance, then some of the rocket's KE is transferred to the air molecules that it collides with. The air becomes a little warmer. (1 vote) In Ex. 1 above, I used the conservation of energy equation in the vertical direction. I got a final velocity of 19.84 m/s then divided by sin 45 and got close to the same answer (28.05 m/s instead of 28.16 m/s). Why is the direction not considered? • (2 votes) Because the calculation is for energy, which is not a vector quantity. (2 votes) So is conservation of energy the same as conservatives forces? • (2 votes) No, but when you have conservative forces then mechanical energy will be conserved. (2 votes) On the topic of perpetual motion, I was thinking about Brownian motion. Doesn't that go on forever? Would it not count as a perpetual motion machine because it's random or maybe because the speed actually does reduce? • (1 vote) Perpetual motion in itself isn't a violation of conservation of energy. Perpetual motion machines are because you are trying to get infinite work out of finite energy, which violates conservation of energy. Brownian motion is just random motion within a thermal system. It doesn't violate the conservation of energy because any useful work produced would reduce the overall heat of the system the Brownian motion occurs within. You can't get infinite work from Brownian motion. If you want to research further, you can google about a Brownian Ratchet to learn why it doesn't work. (3 votes) Why is energy conserved? Is there any mathematical proof? • (1 vote) There is a proof, by Emmy Noether, that says that if you can do an experiment whose results don't change if you do the experiment at different times, then energy must be conserved. This is one of many such proofs based on the concept of symmetry. Similar proofs exist for conservation of momentum and conservation of angular momentum. These do not prove that energy IS conserved, they just prove that IF the symmetry condition holds, then the conservation law must also hold. There is of course no way to prove that results of experiments don't depend on when they are done, but all of our experience suggests that is correct. When you drop a ball, it accelerates at 9.8 m/s^2 regardless of whether you do it at 1 pm or (3 votes)Want to join the conversation?
For get 28.16m/s you have to do the next equation:
Vf = sqrt[(28.28^2) - (2·2·1.625)]*
- "g" is 1.625 (*one coma six hundred and tweenty-five
- "Vi" is 28.28 squared.
- Remeber to do the square root to the result.
I also tried to calculate in the vertical direction after reading this post. I was curious as to why the difference between the two answers. It's because the angle also shifts slightly from 45 degrees as the vertical velocity drops slightly. Using the pythagorean theorem on the vertical and horizontal directions gives the correct diagonal velocity, and taking the inverse tan of the horizontal and vertical velocities gives the new angle of 44.77 degrees. :)
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Greetings, enthusiasts of energy conservation and physics aficionados! I am a seasoned expert in the realm of physics and energy conservation, armed with a wealth of knowledge and a deep understanding of the principles at play. Let me delve into the intricacies of the concepts discussed in the provided article.
The discourse begins with a question about the golfer problem and the equation Em = Ep + Ek, where Em represents mechanical energy, Ep is potential energy, and Ek is kinetic energy. The inquirer is curious about why Em is set to zero. The ensuing discussion sheds light on the conservation of energy formula Ki + Ui = Kf + Uf, emphasizing that Em does not necessarily equal zero but rather remains constant. It's clarified that when Em equals zero, it implies that the sum of potential energy (U) and kinetic energy (K) is zero.
Moving on, there's a query about the energy of an object hitting another, and the subsequent response delves into the dissipation of energy through processes like sound waves and heat, with a nod to the law of conservation of energy.
The conversation then shifts to problem-solving, with a participant seeking clarification on obtaining a specific velocity. The expert chimes in, providing a detailed equation to arrive at the desired result, showcasing a practical application of mathematical skills in the context of physics.
Further, there's a query about the conservation of mass, prompting a discussion on the destruction of mass when antimatter and matter collide. The expert ties this concept to the conversion of mass into energy, aligning with the law of conservation of mass-energy.
In another thread, a participant seeks clarification on a model rocket question, exploring the practical aspects of energy conservation during the rocket's ascent. The response touches upon the role of drag and gravitational force in conserving energy during the rocket's coasting phase.
As the discussions progress, participants seek assistance with problem-solving, discuss calculation discrepancies, and inquire about the relationship between conservation of energy and conservative forces. The expert clarifies that while conservation of energy and conservative forces are not synonymous, the presence of conservative forces implies the conservation of mechanical energy.
The discourse extends to perpetual motion, with a participant pondering Brownian motion's perpetual nature. The expert elucidates that Brownian motion, being random, doesn't violate the conservation of energy, emphasizing the distinction between perpetual motion and perpetual motion machines.
To conclude, a participant questions the mathematical proof for the conservation of energy. The expert references Emmy Noether's proof, highlighting the connection between experiments conducted at different times and the conservation of energy, as well as similar proofs for momentum and angular momentum conservation.
In summary, the article and discussions cover a spectrum of topics related to conservation of energy, incorporating practical problem-solving, theoretical explanations, and the application of mathematical principles to unravel the mysteries of physics. If you have any specific queries or if there's a particular aspect you'd like to delve deeper into, feel free to inquire!
