I read in many sites that the concept of mechanical energy is the ability of an object to do work, but how can an object do work? Isn't it rather the force applied to that object the one that produces work and not the object itself?. We can have an object that has mass $m$ and a constant speed $v$, with which, we can have kinetic energy $E_K = (1/2)mv^2$, but by work definition $W=\vec{F}d$ there's no work because there's no force applied. How is this explained mathematically?
Newtonian Mechanics – How Can an Object Do Work?
definitionenergyforcesnewtonian-mechanicswork
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Something that has a constant velocity[1] has a definite amount of kinetic energy. It would do work if it would exert a net force on something. Let's make a nice and simple model with two objects.
Let's call the first one a baseball. The baseball is flying through the vacuum[2], going it's merry little way. There is no net force on the baseball, and it has a definite amount of kinetic energy.
We have a second object too. A catchers glove. The catchers glove is stationary. It has no kinetic energy.
Right now, nothing is happening, no forces, no work, just a flying ball. But due to an astronomical coincidence, right as we're looking at this situation, the ball is approaching the glove, and hits it! The moment the ball hits the glove, we are in a different situation. The ball is exerting a force on the glove, and the glove on the ball[3]. This means the ball is no longer flying at a constant speed; it's slowing down. the catchers glove starts to move too - it's gaining the amount of kinetic energy that the ball is losing. It is said that the ball is performing work and the amount of work it performs is the amount of energy transferred between the ball and the glove.
Note however, that the ball started to do work only when it started to exert a force, and thus a force started to work on the ball[3].
So yes, an object with a constant speed/no net force working on it has kinetic energy, which is equivalent to the ability to do work - if it would exert force on something else, in which case it would no longer be true there is no net force working on it. So when it's still flying along at a constant speed, it has the potential to do work. As soon as it starts doing that work, it's no longer flying along at a constant speed.
You could, of course, make things more complicated, and add in a third body that exerts force on the ball equal and opposite to the force the glove exerts on the ball. In that case, there would still be a net force of zero on the ball, and it would not accelerate or slow down, but would still do work on the glove. That changes nothing fundamentally however, and would be equivalent of the third object exerting the force directly on the glove, with the ball taken out of the equation completely. It adds nothing to the understanding of the original question.
[1] or something on which no net force is working - these two statements are equivalent!
[2] yes, we are playing baseball in a vacuum. We're awesome like that.
[3] remember Newtons third law. If something is exerting a force on something else, that other thing is exerting a force on the first thing, equal in size, opposite in direction.
Don't be surprised that physics has a lot of definitions that are circular. Ultimately, we are just describing the universe.
Work and energy have been defined in a certain way in newtonian physics to explain a kinematic model of reality. This is a model, not reality - you will find no such thing in reality. However, in many scenarios, it is close enough to reality to be useful.
For example, let's say that a human has a 10% efficiency at converting food to mechanical work. So if you spend 1000 kJ of food energy to press against a wall, are you doing 1000 kJ of work, or 100 kJ of work, or 0 kJ of work?
In strict mechanical sense, you did no work whatsoever, and all of the energy you used was wasted as heat. If you instead used this energy to push a locomotive, you would have wasted "only" 900 kJ of the energy as heat, with 100 kJ being work. But the locomotive has its own friction, and it wil stop eventually, wasting all the energy as heat again. And overall, you did expend all those 1000 kJ of food energy that is never coming back.
All of those are simplifications. Kinematics is concerned with things that move. Using models is all about understanding the limits of such models. You're trying to explain thermodynamics using kinematics - this is actually quite possible (e.g. the kinematic theory of heat), but not quite as simple as you make it. Let's look at the fire example. You say there is no displacement, and therefore no work. Now, within the usual context kinematics is used, you are entirely correct - all of that energy is wasted, and you should have used it to drive a piston or something to change it to useful work.
Make a clear note here: what is useful work is entirely a human concept - it's all 100% relevant only within the context of your goals; if you used that "waste" to heat your house, it would have been useful work. It so happens that if you look closer, you'll see that the heat from the fire does produce movement. Individual molecules forming the wood wiggle more and more, some of them breaking free and reforming, and rising with the hot air away from the fire, while also drawing in colder air from the surroundings to feed the fire further. There's a lot of displacement - individual molecules accelerate and slow down, move and bounce around... But make no mistake, the fact that kinematics can satisfactorily explain a huge part of thermodynamics is just a bonus - nobody claimed that kinematics explains 100% of the universe. It was a model to explain how macroscopic objects move in everyday scenarios. It didn't try to explain fire.
For your specific questions, you really shouldn't ask multiple questions in one question. It gets very messy. But to address them quickly:
- There is no potential energy in the kinematic model. The concept is defined for bound states, which do not really exist as a concept in kinematics. In other models, you might see that there's a difference between, say, potential energy and kinetic energy - no such thing really exists in reality. You need to understand the context of the model.
- In a perfectly kinematic world, this is 100% correct. However, as noted before, kinematics isn't a 100% accurate description of reality, and there are other considerations that apply, such as the fact that humans have limited work rate, limited ability to apply force, and the materials we are built of aren't infinitely tough, perfectly inflexible and don't exist in perfect isolation from all the outside (and inside) effects. In real world applications of models, these differences are usually eliminated through understanding the limits of given models, and using various "fixup" constants - and if that isn't good enough, picking (or making) a better model.
- You're mixing up many different models at different levels of abstraction and of different scope so confusion is inevitable. Within the simplified context of kinetics, there is no concept of "potential energy". You simply have energy that can be used to do work, and that's it; it doesn't care about how that energy is used to do work, about the efficiency of doing so etc. In another context, it might be very useful to think of energy and mass as being the same thing - and in yet another, they might be considered interchangeable at a certain ratio, or perhaps in a certain direction, or at a certain rate. It's all about what you're trying to do.
- How is that equation useful? That's the only thing that matters about both definitions and equations. I can define a million things that are completely useless if I wanted to - but what's the point?
- Within the original context, those aren't considered at all. Within a more realistic context, both heat and sound are also kinematic.
The reason you have so much trouble finding the answer to your questions on physics sites and forums is that the question doesn't make much sense in physics. It's more about the philosophy of science, and the idea of building models of the world that try to describe reality to an approximation that happens to be useful to us. You think that those words have an inherent meaning that is applicable in any possible context - this simply isn't true. From the very inception of the idea of physics, people have known that it isn't (and never will be) an accurate representation of reality; and we've known for a very long time that, for example, different observers may disagree on the energy of one object. You just need to understand where a given model is useful, and pick the right model for the job. Don't try to drive a screw with a garden rake.
Best Answer
Energy is the ability or potential to do work. In the case of an object with kinetic energy it can do work by exerting a force on another object (but it does not have to do work). This force could be exerted by colliding with another object, or by gravitational attraction, or it could be an electromagnetic force etc.
No matter what the force is, the work done on the second object is $W=\int \vec F . \vec {d s}$, which simplifies to $W=\vec F . \vec s$ if $\vec F$ is constant. By Newton’s third law the second object exerts a force $-\vec F$ on the first object and so does work $-W$ on the first object. So the first object loses an amount $W$ of energy.