Help With Conservation Of Energy Concept

In summary, the conversation discusses the concept of energy in a situation where an asteroid is heading towards the Earth. The equations for kinetic energy and gravitational potential energy are mentioned, with a focus on the latter. The correct equation for gravitational potential energy is given and it is explained that as the asteroid gets closer to the Earth, the gravitational potential energy decreases. The difference in size between the asteroid and Earth is also discussed in relation to the impact of gravitational potential energy. The conversation concludes by mentioning the significant speed that an object falling towards Earth can reach due to the conversion of gravitational potential energy into kinetic energy.
  • #1
bobbles22
17
0
Hi guys,

Can someone help explain something to me.

In a situation of an asteroid heading straight towards the Earth, I'm trying to understand where the energy comes and goes (using just gravitational potential energy and kinetic energy). Consider the energy of the asteriod some distance away from the surface of the Earth, then just before impact.

I'm using the following equations:

Kinetic Energy = Ek = 0.5mv2

Gravitational Potential Energy = Eg = (GMm)/r

My question is that, ignoring friction/sound etc, initially the asteroid has a certain speed and thus a certain kinetic energy, simple to work out. It also has a gravitational potential energy based on G and the masses involved and the separation. However, as it gets closer, the force from the Earth increased, as the separation 'r' off the objects decreases, the gravitational potential energy increases. At the same time, as the force on the asteroid increases, we expect the speed to increase so in effect, both Ek and Eg are both increasing. If both are increasing, then where is the energy coming from.

Surely it should be Eearly = Ek + Eg = Elater = Ek + Eg

Can anyone give me a basic idea of where I'm going wrong with this idea please.

Many thanks

Bob
 
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  • #2
Where you are going wrong is with your equation for Gravitational Potential Energy:
bobbles22 said:
Gravitational Potential Energy = Eg = (GMm)/r
You left out the all-important minus sign in front:
GPE = -(GMm)/r
However, as it gets closer, the force from the Earth increased, as the separation 'r' off the objects decreases, the gravitational potential energy increases.
Using the correct expression, you'll see that the GPE decreases (becomes more negative) as objects approach and r decreases.

See: Gravitational Potential Energy
 
  • #3
bobbles22 said:
Gravitational Potential Energy = Eg = (GMm)/r

You omitted a minus sign. In this situation, we consider Eg to be negative.

However, as it gets closer, the force from the Earth increased, as the separation 'r' off the objects decreases, the gravitational potential energy increases.

No, the gravitational potential energy decreases as the object approaches the Earth, the same as an object close to the Earth for which we usually use Eg = +mgh. Including a minus sign in your equation for Eg takes care of this.
 
  • #4
just a though to put out there ( I am not a maths guy )

you haven't given an example of the size/mass of an asteroid for your calcs

I would consider that the difference in size of say an asteroid up to ~ 1km across compared to the size of the earth, the gravitational PE may not be a large factor compared to the KE of the incoming asteroid.
average incoming velocity of a meteor/asteroid ... 30 - 40 km / sec
acceleration due to gravity 9.81m/s2 ... big difference, orders of magnitude

some one more knowledgeable than me will hopefully clarify more

Dave
 
  • #5
Thanks Doc and JT

that gave me some insight too :)

Dave
 
  • #6
davenn said:
I would consider that the difference in size of say an asteroid up to ~ 1km across compared to the size of the earth, the gravitational PE may not be a large factor compared to the KE of the incoming asteroid.
average incoming velocity of a meteor/asteroid ... 30 - 40 km / sec
acceleration due to gravity 9.81m/s2 ... big difference, orders of magnitude

But look at the units... The acceleration is measured in meters per second per second, meaning that every second the speed increases by 9.8 meters/sec... Let that go for a few hundred seconds and you've built up some serious speed. (note: gravitational acceleration is only 9.8 m/sec at the surface of the earth; it declines steadily the further away from Earth you are).

It turns out that an object falling from infinity to the surface of the Earth will reach a speed of about 11 km/sec; that's its gravitational potential energy being converted into kinetic energy. It's a lot.
 

What is conservation of energy?

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

Why is conservation of energy important?

Conservation of energy is important because it helps us understand and predict how energy behaves in various systems. It also allows us to make informed decisions about how to use and conserve energy resources.

What are some examples of conservation of energy in everyday life?

Some examples of conservation of energy in everyday life include turning off lights when leaving a room, using energy-efficient appliances, and carpooling to reduce fuel consumption.

How can I help with conservation of energy?

There are many ways to help with conservation of energy, such as using renewable energy sources, reducing energy consumption, and properly insulating your home. Additionally, supporting policies and initiatives that promote energy conservation can also make a difference.

What are some challenges to achieving conservation of energy?

One challenge to achieving conservation of energy is the high initial cost of implementing energy-efficient technologies. Another challenge is changing societal attitudes and behaviors towards energy use. Additionally, there may be political and economic barriers to implementing conservation measures.

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