Conservation of Energy Problem: Where did it go?

• joelio36
In summary, during the conservation of energy problem where a boulder is shot into the air, its kinetic energy is converted into gravitational potential energy and KE of air particles. At a certain height above the ground, mgh represents the potential energy. When the boulder breaks orbit and is free from the Earth's gravitational pull, the potential energy does not disappear but rather reaches a maximum limit. This concept relates to the conservation of energy, where as the object's potential energy decreases, its kinetic energy increases in a way that maintains a net energy of zero.
joelio36
Conservation of Energy Problem: Where did it go??

Imagine I shoot a boulder vertically into the air with a massive cannon.

Its kinetic energy is converted into gravitational potential, and into KE of air particles (air resistance).

So at m metres above the ground, mgh is the Potential energy

But what happens once this boulder breaks orbit, free from the Earth's gravitational pull?

I think I am missing something but in my head, the Gravitation Potential just disappears, and the object carries on with any KE left.

Thanks for any help, got an exam heavy on conservation of energy in 2 days!

joelio36 said:
Imagine I shoot a boulder vertically into the air with a massive cannon.

Its kinetic energy is converted into gravitational potential, and into KE of air particles (air resistance).

So at m metres above the ground, mgh is the Potential energy

But what happens once this boulder breaks orbit, free from the Earth's gravitational pull?

I think I am missing something but in my head, the Gravitation Potential just disappears, and the object carries on with any KE left.

Thanks for any help, got an exam heavy on conservation of energy in 2 days!

The gravitational potential energy does not 'go' anywhere. Contrary to your impression, there is no point in space (except at 'infinity') at which the object is completely free of the Earth's gravitational field - however, since the force is inversely proportional to the square of the distance, at some point we can say that the field is negligible and the boulder appears 'free'. But we still have to put in (some vanishingly small amount of) energy to separate the masses further, and conversely we will gain energy if the masses are brought closer together.

How does this relate to conservation of energy? We define gravitational potential energies to be negative at finite distances (and zero at infinity). This definition means that as an initially-stationary object accelerates towards a mass from infinity, the potential energy 'decreases' (i.e. becomes more negative) whilst the kinetic energy increases (becomes more positive) in such a way that the net energy remains zero - energy is conserved.

Note that your formula GPE = mgh is an approximation only valid for small changes h in radial distance r such as one may achieve when jumping in the air on Earth, but for large changes in r we need to use the full formula GPE = -G/(M.m.r) (note the negative sign!)

joelio36 said:
in my head, the Gravitation Potential just disappears
The PE does not disappear, it goes to a finite maximum limit.

What is conservation of energy?

Conservation of energy is a fundamental principle in physics that states that energy cannot be created or destroyed, it can only be transferred or converted from one form to another.

Why is conservation of energy important?

Conservation of energy is important because it allows us to understand and predict the behavior of physical systems. It also helps us to make more efficient use of energy and resources.

Where does energy go when it is conserved?

When energy is conserved, it can be transferred to another object or system, or it can be converted into a different form of energy, such as thermal, kinetic, or potential energy.

What are some real-life examples of conservation of energy?

Examples of conservation of energy in everyday life include using a bike to generate kinetic energy, using solar panels to convert sunlight into electrical energy, and using a battery to store and transfer energy.

What happens when the principle of conservation of energy is violated?

If the principle of conservation of energy is violated, it means that energy has been created or destroyed, which goes against the fundamental laws of physics. This violation can lead to inconsistencies and errors in scientific theories and models.

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