Gravitational potential energy conflict

[donaldparida]

I know that when an object A a does positive work on another object B, object A loses energy and object B gains energy(there is transfer of energy from object A to object B) and when object A does negative work on object B, it gains energy and object B loses energy(there is transfer of energy from object B to object A).
Now, when we lift an object(standing on the Earth), we do positive work on the object and so the energy of the object should increase (and our energy should decrease) while the Earth by its gravitational force does negative work on the object and so the energy of the object should decrease(and the energy of the Earth should increase).
Now my question is, is the energy of the object increasing or decreasing since it cannot be both at the same time.

 

[Dale]

Now my question is, is the energy of the object increasing or decreasing since it cannot be both at the same time.

It can be both at the same time. Think of a rope where one end of the rope is attached to a horse and the other end is attached to a cart. The horse is doing positive work on the rope, transferring energy into the rope, and the cart is doing negative work on the rope, transferring energy out of the rope at the same rate.

Similarly, it is perfectly acceptable for you to be transferring energy into a rock at the same rate as gravity is transferring energy out of the rock.

However, that is usually not the conceptual error that is being made. Usually the error is that the system under consideration is being changed. You can arbitrarily define the system, but then you have to be consistent.

One possibility is to define the system as the object+earth. In this case as you lift the object you transfer energy into the object+earth system, which is stored in the PE of the system. The gravity is an internal force, so it doesn't transfer any energy.

The other possibility is to define the system as the object only. In that case as you lift the object you transfer energy into the system. The gravity is an external force and the energy is transferred out of the system and into the gravitational field (fields store energy).

The confusion usually comes by considering the object+earth to be the system in one step and then accidentally switching to considering the object only system in the middle.

 

[donaldparida]

If the object is now released (system: object only) then the gravitational field will do positive work on the object and the energy of the object will increase( and the energy of the field will decrease) and the object will fall down. Will the object have more energy now compared to the starting?

 

[Doc Al]

Sure. It's speeding up.

 

[donaldparida]

What will happen to the energy of the object when it hits the ground?Will it be transformed to heat energy or remain with the object?

 

[Doc Al]

What will happen to the energy of the object when it hits the ground?Will it be transformed to heat energy or remain with the object?

Assuming a typical object/ground collision--like dropping a book, for example--the kinetic energy of the book will end up as random thermal energy (for the most part).

 

[G. Cavazzini]

Donaldparida wrote:
[...] when we lift an object(standing on the Earth),
OK
we do positive work on the object
These words are improper: in this case we do work against gravitation, not on the object.
and so the energy of the object should increase
No, if we exclude the transient we lift the object.
(and our energy should decrease)
Yes, we spend energy to lift the object, against gravitation.
while the Earth by its gravitational force does negative work on the object
No, not on the object. On us (on our hands and arms), who are lifting the body.
and so the energy of the object should decrease
The object has no (kinetic) energy, except in the transient we lift it.
The energy of the object does not decrease.
(and the energy of the Earth should increase).
No.
Now my question is, is the energy of the object increasing or decreasing since it cannot be both at the same time.
The body has kinetic energy only in the time-span you spend to lift it.

 

[donaldparida]

Your post is obscure. Could you please elaborate.

 

[jbriggs444]

Donaldparida wrote:
we do positive work on the object
These words are improper: in this case we do work against gravitation, not on the object.

You should learn to use the quote functionality built into these forums. When replying to a post, you can either hit "reply" and have the post to which you are responding surrounded in a quote tag and your cursor positioned ready for you to key in a response. Or you can highlight individual sections to which you want to reply, right-click and select "quote". Then, in your reply, click "Insert quotes". Now back to the matter at hand...

When we lift an object, we most certainly do work on the object. Whether a separate gravitational force extracts work from the object has nothing to do with it.

and so the energy of the object should increase
No, if we exclude the transient we lift the object.

Our contribution to the objects's energy is positive. There are other contributions. If we count gravitation as a potential, the object's potential energy increases and its kinetic energy remains constant. The object gains energy. If we count gravitation as an external force, it subtracts from the object's energy. The object does not gain kinetic energy.

(and our energy should decrease)

There may be other contributions to our own energy. For instance, if we are standing on an escalator holding a shopping bag, we can do positive work on the shopping bag without losing energy in the process. The escalator steps under our feet are doing positive work on us even while the shopping bag is doing negative work. In such a case, we are gaining potential energy in the process.

 

[vanhees71]

The energy-conservation law in the most simple case of a conservative force is immediately derived from Newton's equation of moation. A force is called conservative, if it is described by a scalar time-independent potential,
$$\vec{F}(\vec{r})=-\vec{\nabla} \phi(\vec{r}).$$
Then the EoM reads
$$m \ddot{\vec{r}}=-\vec{\nabla} \phi(\vec{x}) \qquad (*).$$
Now multiply this equation with $\dot{\vec{r}}$ (scalar product). The left-hand side becomes
$$m \dot{\vec{r}} \ddot{\vec{r}}=\frac{\mathrm{d}}{\mathrm{d} t} \left ( \frac{m}{2} \dot{\vec{r}}^2 \right),$$
and the right-hand side
$$-\dot{\vec{r}} \cdot \vec{\nabla} \phi(\vec{r})=-\frac{\mathrm{d}}{\mathrm{d} t} \phi(\vec{r}).$$
Subtracting both equations leads, together with (*) to
$$\frac{\mathrm{d}}{\mathrm{d} t} \left (\frac{m}{2} \dot{\vec{r}}^2+\phi(\vec{r}) \right )=0.$$
This means that the quantity in the bracket, called the energy of the particle, is constant, i.e.,
$$E=\frac{m}{2} \dot{\vec{r}}^2 + \phi(\vec{r})=\text{const}.$$
As an example take gravity of the Earth on an object. Close to Earth you can write the force as
$$\vec{F}=m \vec{g},$$
Obviously this is a conservative force with
$$\phi=-m \vec{r} \cdot \vec{g},$$
and thus the energy reads
$$E=\frac{m}{2} \dot{\vec{r}}^2 -m \vec{r} \cdot \vec{g}=\text{const}.$$

 

[Vanadium 50]

B thread...B thread...

 

[donaldparida]

What do you mean by B thread?

 

[Vanadium 50]

The level of the thread - basic.

 

[vanhees71]

Well, B thread means you have to explain something with so many words and so little math that it becomes incomprehensible even to the expert...

 

[hmmm27]

Potential Energy, per se, is a relationship, not a solo act.

Within the context of the object itself, no internal energy is gained by raising it up a few feet : the molecules didn't wind themselves up tighter, the amount of heat being emitted (or absorbed) didn't change, etc.

Within the context of the object and the Earth, some Potential Energy is gained in the relationship (though we just refer to the object as owning it to make sentences shorter).

As an aside you could increase the PE by digging a hole in the ground under the object so it has farther to travel. Or, for fun, you could stand on your head, balance the object on your feet and lift the Earth, it works out the same, though the latter involves much longer numbers to get the same answer.

Help any ? or too basic.

 

[MicroCosmos]

Sure. It's speeding up.

Sorry but i don't think so. When you release an object it transfers its potential to cinematic energy. it doesn't win anything.

 

[MicroCosmos]

It can be both at the same time. Think of a rope where one end of the rope is attached to a horse and the other end is attached to a cart. The horse is doing positive work on the rope, transferring energy into the rope, and the cart is doing negative work on the rope, transferring energy out of the rope at the same rate.

Similarly, it is perfectly acceptable for you to be transferring energy into a rock at the same rate as gravity is transferring energy out of the rock.

However, that is usually not the conceptual error that is being made. Usually the error is that the system under consideration is being changed. You can arbitrarily define the system, but then you have to be consistent.

One possibility is to define the system as the object+earth. In this case as you lift the object you transfer energy into the object+earth system, which is stored in the PE of the system. The gravity is an internal force, so it doesn't transfer any energy.

The other possibility is to define the system as the object only. In that case as you lift the object you transfer energy into the system. The gravity is an external force and the energy is transferred out of the system and into the gravitational field (fields store energy).

The confusion usually comes by considering the object+earth to be the system in one step and then accidentally switching to considering the object only system in the middle.

And sorry again but it cannot be both at the same time. You can get energy and give at the same time. The addition determines wheter you are losing, gaining, or remaining with the same energy.

 

[jbriggs444]

Sorry but i don't think so. When you release an object it transfers its potential to cinematic energy. it doesn't win anything.

Are you sure? http://www.space.com/24880-gravity-oscars-wins-academy-awards.html

 

[MicroCosmos]

Are you sure? http://www.space.com/24880-gravity-oscars-wins-academy-awards.html

lol, i scrolled the whole page looking for what i was missing until i got it

 

[jbriggs444]

lol, i scrolled the whole page looking for what i was missing until i got it

I should apologize for poking fun at an unintentional mistake made by a non-native English speaker. The term is "kinetic" energy, not "cinematic" energy. Kinetic energy is the energy associated with motion. "Cinematic" has to do with motion pictures.

 

[MicroCosmos]

i knew it wasnt right, just to lazy to google another Word today... but thanks anyways. i will come to you with an interesting question next days, if you are prepared :)

 

[donaldparida]

@Dale If i consider the system as the object only, then since the work done in lifting the body is ultimately getting stored in the gravitational field of the Earth will the object have no change in energy when it is lifted to a particular height?

 

[Dale]

@Dale If i consider the system as the object only, then since the work done in lifting the body is ultimately getting stored in the gravitational field of the Earth will the object have no change in energy when it is lifted to a particular height?

Correct. The increased gravitational energy is external to the system.

 

[donaldparida]

Do you mean to say that the energy is drained to an external source(The Earth)?

 

[Dale]

Do you mean to say that the energy is drained to an external source(The Earth)?

An external source, yes. You could label this external system "the Earth" if you include the gravitational field as part of it. Again, system definitions are arbitrary, you just need to be consistent.

I am a little concerned why you keep asking the same question.