Understand Potential Energy: Definition, Examples & More

[MIA6]

1. I don't really get the definition of "Potential energy", on my book, it says The energy that an object has owing to its position or condition is called potential energy. Why does it relate to position? (I know the distance involved in formula) Can you give me a definition that is easy to understand. In my opinion, i think it means an object has stored an energy and has the potential to move but it hasn't. Btw, how can i know if an object has potential energy or not.
2. In Elastic potential energy,Hooke's law: F=kx. k is known as the spring constant. I don't get what spring constant means? The resistance of the spring? My teacher said an ideal spring doesn't have mass. WHY? I think every object has a mass? WHy it is called 'ideal' spring?
3. I represent vector in bold. Fel=-kl Why here there is a negative sign? IN the study of mechanics, the sign of a vector is usually determined by the direction? Up and right is positive, down and left is negative?

Thanks a lot for answering.

 

[mgb_phys]

it says The energy that an object has owing to its position or condition is called potential energy.

If you lift an object up against gravity - you have done some work to put the weight up there, you can get that energy back by lowering it (think of water in a hydroelectric dam). While it is up there it has potential energy because there is energy inside it that can be extracted but it isn't doing anything at the moment. This is what potential means in general.

2. k is known as the spring constant. I don't get what spring constant means?I think every object has a mass? WHy it is called 'ideal' spring?

Think of it as the 'springiness', it is a meaure of how hard it is to compress the sping, strong springs have high K and so need more force to compress them and so store more energy.
An 'ideal' spring is an imaginary thing used in simple physics calculations, it means that the you should ignore the mass of the spring when making the calculations - there is of course no such thing as a mass less spring.
In introductory physics courses you will also come across 'smooth' slopes - where you ignore friction and 'point' masses where you assume an object has zero size even though it has mass.

Many of these words and phrases were closer to their english meaning 200/300 years ago when the ideas were first being worked out, now their meaning is slightly different to everyday use and it is a bit confusing.

 

[MIA6]

but how do I know if an object has the potential energy? When it is at rest, it has? For example, How much work must be done to accelerate a 1200-kg car from rest to a speed of 2.0m/s, assuming there is no friction? In my book, it says PE is zero. WHY? Is that because of the formula PE=mgh?? since there is no height here, so it's zero?

 

[mgb_phys]

It has potential energy when you can move it to another position and as a result get energy out.
So a car on top of a hill has potential energy because you can roll it down the hill and get energy out. A car at the bottom of the hill hasn't because you have to put energy into move it anywhere.

 

[MIA6]

It has potential energy when you can move it to another position and as a result get energy out.
So a car on top of a hill has potential energy because you can roll it down the hill and get energy out. A car at the bottom of the hill hasn't because you have to put energy into move it anywhere.

You said 'Get the energy out', it means a car has originally stored an energy, but it will not come out until we do something about it? I don't understand your last sentence, a car at the bottom of the hill hasn't what? potential energy? why?

 

[mgb_phys]

Sorry I was trying to put it in more everyday language than talking about point masses and heights.

Imagine a weight on the end of a pulley - starting on the floor.
You put energy into the system to raise the weight up - right?
The weight at the top of the pulley now has potential energy only because of it's position, there hasn't been any physical change in the weight.
If you let the weight go the pulley turns and you can use this to extract the energy you put in when you raised it (less any friction losses etc)

A more correct definition would be the energy an object has as the result of it's position in conjuntion with a restoring force. In the case of the weight that force is gravity. It is called potential energy because it is locked in the weight with the potential to be used. You could use the older term latent (hidden) energy if you prefer.

 

[MIA6]

Sorry I was trying to put it in more everyday language than talking about point masses and heights.

Imagine a weight on the end of a pulley - starting on the floor.
You put energy into the system to raise the weight up - right?
The weight at the top of the pulley now has potential energy only because of it's position, there hasn't been any physical change in the weight.
If you let the weight go the pulley turns and you can use this to extract the energy you put in when you raised it (less any friction losses etc)

A more correct definition would be the energy an object has as the result of it's position in conjuntion with a restoring force. In the case of the weight that force is gravity. It is called potential energy because it is locked in the weight with the potential to be used. You could use the older term latent (hidden) energy if you prefer.

ok, since when we mention potential energy, we always talk about position. sorry, I still have some problems here. I just feel very confused about the concept of position in relating to potential energy. In your example, if I put energy to raise the weight up, then the weight is lifted. What do you mean by it hasn't been any physical change in the weight? you mean the weight itself doesn't do anything actively? Then, if I extract my energy in raising the weight, then what happens?

 

[heafnerj]

A single object cannot have potential energy. Only groups of interacting objects can have potential energy.

 

[Astronuc]

Potential energy is related to an object's position within a force field, e.g. a graviational field, electric field, . . . . When one moves horizontally in gravitational field, one moves in a constant potential so there is no change in potential energy.

The spring constant simply relates the force of a spring to the deflection from some equilibirium point or zero displacement where there is no force.

 

[CompuChip]

Actually, potential energy is a sort of "trick" to use conservation of energy. When we have a closed system (for example, car on slope, or me and weight) the total amount of energy always stays the same. Yet, when I lift a mass above my head, and drop it (beside me, not on my head of course) it gains kinetic energy (according to $\tfrac12 m v^2$). Of course, by conservation of energy, this is exactly the energy it took me to lift the thing in the first place (ignoring air resistance and the like). In other words: when lifting it I put some energy inside the object, which is converted to velocity (kinetic energy) when I drop it. But until I drop it, the energy must be stored somewhere. This is now what we call the potential energy. You see, it's kind of like a bookkeeping trick. At all times, the total energy in the system must be the same (this is conservation of energy). If I drop a brick from some height, at the bottom it will have some kinetic energy -- and hence total energy -- E. Just before I dropped it, it didn't have kinetic energy though, but the total energy should still be E (I don't "make" energy during the fall, or something like that). That's the potential energy, which it gets just by being about to be dropped, basically. Somewhere halfway through the fall, the brick does have kinetic energy, but it's not at its final velocity yet. A part of the potential energy has been converted to kinetic energy, but the sum of the two is still E.

In numbers, suppose a mass m hits the ground with a velocity $v_0$. Then it's kinetic energy is $E_k = \tfrac12 m v_0^2$ and potential energy $E_p = 0$, hence total energy $E = E_k + E_p$. Before it fell, it must have had the same total energy, but it wasn't moving, so $E_p = \tfrac12 m v_0^2$ and $E_k = 0$. Halfway the fall, neither $E_p$ nor $E_k$ are zero, but the sum is still E.

Actually, from the above you (could/should) see that it's actually useless to talk about an object "not having potential energy", as potential energy itself is not observable. What we can measure, is a difference in potential energy. In the case of the mass, if it has kinetic energy $E_k$ when it hits the ground, we can define it to have potential energy $E_p$ at the top and it will have a potential energy $E_p - E_k$ at the bottom; it's common to pick $E_p$ such that this is zero though. I don't know if this works confusing or not, if so - please forget it until you understand the rest written here.

 

[heafnerj]

*sigh* I'm very disturbed, but not at all surprised, by what I'm reading here. No one seems to know how to correctly define potential energy.

 

[dontdisturbmycircles]

Potential energy is the energy available within a physical system due to an object's position in conjunction with a conservative force which acts upon it.

- http://en.wikipedia.org/wiki/Potential_energy

After reading the posts here, what aren't you understanding so people here can better explain it? I supplied a 'definition', but this was already pretty much stated word for word by Astronuc.

For the negative sign on Hooke's law, it is a consequence of the vector nature of forces. It is there because the force on the mass on the end of the spring is opposite in direction relative to it's displacement, hence $$F_{e}=kx$$ would be mathematically incorrect due to the vector nature of forces as stated before.

 

[pardesi]

suppose a force field is conservative
then there exists atleast a $$U$$ such that $$\vec F=- \nabla U$$
such a U is called the potential energy function...
but the best and most logical way would be say for gravitational field which is conservative is
the change in potential energy of a system of particles is the amount a work by the internal forces in changing the configuation of the particles from say a certain
i to f.

 

[turdferguson]

Potential energy is energy of position relative to an arbitrary reference point. It depends on the system of objects and what you define the zero point to be

 

[CompuChip]

We can keep on explaining forever, I think the TS should point out where the problem is. As I see it, the posts in this thread are quite clear and supplementary, about everything is said.
So what exactly don't you understand?

 

[MIA6]

Actually, potential energy is a sort of "trick" to use conservation of energy. When we have a closed system (for example, car on slope, or me and weight) the total amount of energy always stays the same. Yet, when I lift a mass above my head, and drop it (beside me, not on my head of course) it gains kinetic energy (according to $\tfrac12 m v^2$). Of course, by conservation of energy, this is exactly the energy it took me to lift the thing in the first place (ignoring air resistance and the like). In other words: when lifting it I put some energy inside the object, which is converted to velocity (kinetic energy) when I drop it. But until I drop it, the energy must be stored somewhere. This is now what we call the potential energy. You see, it's kind of like a bookkeeping trick. At all times, the total energy in the system must be the same (this is conservation of energy). If I drop a brick from some height, at the bottom it will have some kinetic energy -- and hence total energy -- E. Just before I dropped it, it didn't have kinetic energy though, but the total energy should still be E (I don't "make" energy during the fall, or something like that). That's the potential energy, which it gets just by being about to be dropped, basically. Somewhere halfway through the fall, the brick does have kinetic energy, but it's not at its final velocity yet. A part of the potential energy has been converted to kinetic energy, but the sum of the two is still E.

In numbers, suppose a mass m hits the ground with a velocity $v_0$. Then it's kinetic energy is $E_k = \tfrac12 m v_0^2$ and potential energy $E_p = 0$, hence total energy $E = E_k + E_p$. Before it fell, it must have had the same total energy, but it wasn't moving, so $E_p = \tfrac12 m v_0^2$ and $E_k = 0$. Halfway the fall, neither $E_p$ nor $E_k$ are zero, but the sum is still E.

Actually, from the above you (could/should) see that it's actually useless to talk about an object "not having potential energy", as potential energy itself is not observable. What we can measure, is a difference in potential energy. In the case of the mass, if it has kinetic energy $E_k$ when it hits the ground, we can define it to have potential energy $E_p$ at the top and it will have a potential energy $E_p - E_k$ at the bottom; it's common to pick $E_p$ such that this is zero though. I don't know if this works confusing or not, if so - please forget it until you understand the rest written here.

I get what you tried to say. Potential energy is sort of like an object stores an energy until it does some actual motion. Then, its PE converts to KE. For answering you guys what I don't understand is that I think potential energy is just so abstract for me because unlike kinetic energy, I know it's when an object is in motion. But PE is like something just stays there and if it stays in some height in relative to a zero level, then it has potential energy..If it is on zero level, then it doesn't have PE? SO what exactly potential energy does? It converts to another energy? What's the use?

 

[MIA6]

Potential energy is the energy available within a physical system due to an object's position in conjunction with a conservative force which acts upon it.

What is conservative force? PE=mgh, so it just relates to gravity.

 

[turdferguson]

To an extent, we can't really define energy by what it is, only from what we observe it to do. We see something falling off a shelf and say it has kinetic energy. But where did the energy come from? Someone did work against a gravitational field to put it on the shelf, and that was stored as potential energy. Its a convenient way of explaining something

There are two main forces in physics: conservative and non-conservative forces. Conservative forces do not depend on the path taken, only the initial and final positions. If you move an object from point A to a higher point B it has gained potential energy, and if you move it back down to A, it loses an equal amount of energy to get back where it started

Non-conservative forces like friction depend on the path taken from point A to point B. Going from point A to B back to A on a rough surface, even more work is done. There are many ways to go from point A to B, all with different amount of energy lost because of a different distance traveled

 

[HIMANSHU777]

Is Law Of Conservation Of Mass-energy Applicable In Individual Systems? IN OTHER WORDS, IS ENERGY CONSERVED IN INDIVIDUAL SYSTEMS?

 

[CompuChip]

What do you mean by individual systems?

It is always applicable in closed systems. That is, if there is nowhere energy can "leak" away, it's conserved.

 

[HIMANSHU777]

if a bucket of hot water is kept in space (where there no atmosphere) then will the water cool?

 

[Doc Al]

if a bucket of hot water is kept in space (where there no atmosphere) then will the water cool?

Such a bucket of water is not an isolated system--energy will radiate out.

 

[CompuChip]

The universe with the bucket in it is closed though (that is, assuming there is no energy transfer between this universe and another one), the energy from the cooling water will heat up the universe (only problem is that the universe is a little bigger and a little colder than the bucket, so the effect won't be really noticeable).

And if you put the bucket in a completely isolated room, that would be a closed system.

 

[learningphysics]

I get what you tried to say. Potential energy is sort of like an object stores an energy until it does some actual motion. Then, its PE converts to KE. For answering you guys what I don't understand is that I think potential energy is just so abstract for me because unlike kinetic energy, I know it's when an object is in motion. But PE is like something just stays there and if it stays in some height in relative to a zero level, then it has potential energy..If it is on zero level, then it doesn't have PE? SO what exactly potential energy does? It converts to another energy? What's the use?

I agree with you that PE is more abstract in a sense than kinetic energy.

PE is just used to take into account the work done by a conservative force (the path taken by the object while the work is done doesn't matter... only the final position and initial position matter)...

The work-energy theorem is:

Work done by all forces (including gravity) = Change in kinetic energy

Work done by gravity + work done by nongravity forces = change in kinetic energy

work done by nongravity forces = -work done by gravity + change in kinetic energy

Gravitational potential energy (or any potential energy) is a bookkeeping trick as Compuchip said, to take into account this work done by gravity...

absolute potential energy doesn't make sense... it is only the change in potneital energy from one point to another that is significant...

suppose an object rises from a height h2 to h3... let h1 be any height

work done by gravity = -mg(h3-h2) = -mg(h3-h1+h1-h2)=-[mg(h3-h1)-mg(h2-h1)]

-work done by gravity = mg(h3-h1)-mg(h2-h1)

So we can choose any height h1 we want, and let grav. potential energy = 0 there... then the grav. potential energy at any height h is defined to be mg(h-h1)...

So by these definitions: -work done by gravity = GPE at h3 -GPE at h1. I could have chosen any height I wanted for...

It is the work energy theorem that is fundamental (in classical mechanics anyway)... and conservation of energy is in a sense... defining energy in a way to take into account for work...

The reason we're able to take into account the work by done by gravity as potential energy is because it is a conservative force... There are nonconservative forces but all the fundamental forces are conservative (ie they can be taken into account by a potential energy...eg electrical potential energy gravitational potential energy)... which is why energy is conserved...