# Fundamentals Of Energy

#### Delzac

Hi all,

being a long time since i last posted( because of exams).

The question is what actually happens when i lift, lets say a tennis ball, up in the air? We say GPE increases, but what actually changes within the atom or what does it means went one object has more energy that another. (other that mass) ?.

Any help will be appreciated.

Delzac

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#### The Bob

Delzac said:
Hi all,

being a long time since i last posted( because of exams).

The question is what actually happens when i lift, lets say a tennis ball, up in the air? We say GPE increases, but what actually changes within the atom or what does it means went one object has more energy that another. (other that mass) ?

Any help will be appreciated.

Delzac
When you lift a tennis ball up you are lifting the ball through the Earth's 'gravity field'. In doing this you are increasing the GPE because the 'effect' of gravity will be great on the tennis ball at a greater height. Just look at the formulae for constant acceleration. If s, the height in this case, is greater in the equation s = (v-at)t + 0.5at2, then the end velocity, v, will be greater for a higher s (well too a point anyway). You can see this because t is squared and so is not directly proportional to velocity.

I do hope this helps and I hope that anyone that knows this in more detail will be able to enlighten me or even correct what I have done.

Cheers,

#### Delzac

So we all agree that GPE increase if we move an object to a higher level/ height. But what is the DIFFERENCE between 2 identical object at different height. We know that GPE is different, but where is this energy stored? inside the atom?

#### Delzac

erm..... any help?

#### PhanthomJay

Homework Helper
Gold Member
Delzac said:
erm..... any help?
That's a good question.

Gravitational potential energy is the energy stored in an object as the result of its vertical position, just like elastic spring potential energy of a compressed or stretched spring is energy stored in the spring as a result of its position only. In both cases, there is a force that keeps it in this position in equilibrium...the force prevents movement. When, as in a spring or crossbow, the force is released, the potential energy is released to become energy of motion. In the GPE case, once the force holding the object at rest is removed (like the Normal force of a book on a table keeping the book off terra firma and giving it energy of position, then the book is allowed to drop from the table when the force is removed) , then the gravity force is allowed to do its thing and convert the stored energy to energy of motion. There is no actual physical change to the object when it possesses GPE in the cases where g is assumed constant over a reasonable distance of several miles.

#### Delzac

Thanks, but how can we explain one object having a higher kinetic energy than another?

#### PhanthomJay

Homework Helper
Gold Member
Delzac said:
Thanks, but how can we explain one object having a higher kinetic energy than another?
Not counting the Einstein apparent mass increase with speed, which is significant at relativistic speeds of sub-atomic particles, but miniscule at ordinary speeds, there is no physical change in an object moving at constant velocity, regardless of its speed. The one with the higher speed, however, and hence higher energy, has greater ability to do work. That's sort of the definition of energy. But it is all relative, you know. A person in a plane that is moving at 600 mph w/ respect to ground, also has that same speed, and each has kinetic energy of motion w/ respect to the ground. However, w/ respect to each other, they each have no kinetic energy, since there is no movemnt between the 2. Nothing at all. So although the plane and the person would do plenty of work if they crashed, they are harmless one to the other, and can do no non-conservative work at all in that frame.

#### turdferguson

Some work was done on object 1 to raise it to height 1. If more work was done on object 2 to get it to a higher height 2, it will have more GPE stored. Energy is conserved, so the object with heigher GPE will have higher KE returned to it and it will have a higher speed. Gravity does more work on the higher object. Does this help?

#### student85

Subquestion:
Let's say we have a 5kg object and a 2kg object at exactly the same height above ground. We all know that when released, they will accelarate at the same rate (g) until pounding on the ground with the same velocity. So, using the equation for PE we have that the 5kg object has more PE than the ligher object. But they both reach the same speed so how can we say one has more mechanical energy. Please someone explain, this has been bugging for quite a while.
I think that the higher mass by itself means more energy, but we're talking about mechanical energy so isnt it supposed that speed's what matters.

Help is greatly appreciated.

#### PhanthomJay

Homework Helper
Gold Member
student85 said:
Subquestion:
Let's say we have a 5kg object and a 2kg object at exactly the same height above ground. We all know that when released, they will accelarate at the same rate (g) until pounding on the ground with the same velocity. So, using the equation for PE we have that the 5kg object has more PE than the ligher object. But they both reach the same speed so how can we say one has more mechanical energy. Please someone explain, this has been bugging for quite a while.
I think that the higher mass by itself means more energy, but we're talking about mechanical energy so isnt it supposed that speed's what matters.

Help is greatly appreciated.
In each case, energy is conserved prior to ground contact. But the initial potential and final kinetic energy for the bigger mass is greater than the corresponding initial PE and final KE of the lighter mass, since energy is a function not only of position (potential energy), or speed (kinetic energy), but also of mass. PE=mgh, or KE =1/2mv^2. So although they both have the same speed prior to contact, the larger has more energy, and will do more damage when coming to a stop in the ground. Is this the answer you are looking for?

#### student85

thanks PhantomJay
But still more "damage". I mean how can you physically explain the larger having more energy. So is that the answer? Because one will hit the ground harder than the other?

#### student85

On second thought, maybe what we really need is to define what mechanical energy is..?

#### turdferguson

student85 said:
thanks PhantomJay
But still more "damage". I mean how can you physically explain the larger having more energy. So is that the answer? Because one will hit the ground harder than the other?
Momentum is also based on both mass and velocity. The more massive object has more momentum, so it indergoes a greater change in momentum when being brought to rest

#### Delzac

But shouldn't there be a difference in 2 identical object with dif. velocity?

He the 1st place is it possible to express/describe energy diference between objects using physical diference, or any diference so as to speak.

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#### turdferguson

If youre trying to ask what energy is, the answer is we don't know. We can only define energy by what it does. This happened...so now it has energy

#### verty

Homework Helper
Delzac, velocity is not something "in" the object, velocity is relative. Velocity means that, as time passes, the object will move. The object changes location in time, but location is also relative. Then, acceleration is the rate of change of velocity, and it is also relative.

For instance, if I am standing in a train but don't know that it is moving at constant velocity, I might say that I was standing still, and I am standing still relative to the train. Relative to the train, my position is constant over time.

Potential energy is also not something in the object, it is a calculation of the potential for gravity to do work on that object. F = MA and work is force * distance, so we can say that work = MAS. Now when the force is gravity and it acts over some falling height, the formula becomes: gravity's work = MGH. That is what potential energy is: it represents the work that gravity will do if given the chance.

Sorry, I don't know how to derive the kinetic energy formula.

#### Delzac

Thx for the help.

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