# Conservation of energy question

• aftershock
In summary, the conversation discusses a conceptual question about the conservation of energy, specifically in the scenario of two charged spheres with one being glued in place and the other being kicked away. The question is how fast the negative sphere needs to be kicked to prevent it from coming back. The equation KE + PE = constant is mentioned, with the clarification that the constant is not always zero and that potential energy at infinity is defined as zero. The concept of escape velocity is also brought up.

#### aftershock

This is a conceptual question I've been thinking about dealing with conservation of energy.

For example, say you have two charged spheres, one positive and one negative. The positive one is glued in place while you kick the negative one away. How fast would you have to kick the negative one so that it won't come back?

I'm aware these types of problems are pretty simple. potential + kinetic = 0

What I don't understand is how the final energy of the system is zero. Where'd it go?

EDIT: Is it because the potential energy is negative, so the sum is zero initial energy also? That's a weird concept to me to be honest.

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hi aftershock!
aftershock said:
I'm aware these types of problems are pretty simple. potential + kinetic = 0

What I don't understand is how the final energy of the system is zero. Where'd it go?

i don't know where you got that equation from …

the correct equation is KE + PE = constant, not zero

in other words, KEi + PEi = KEf + PEf

if you define PE at ∞ to be zero, then PE at distance r is minus kqQ/r, so escape velocity (defined as the speed that you need to reach infinity at speed zero) is the speed corresponding to KE = kqQ/r

tiny-tim said:
hi aftershock!

i don't know where you got that equation from …

the correct equation is KE + PE = constant, not zero

in other words, KEi + PEi = KEf + PEf

if you define PE at ∞ to be zero, then PE at distance r is minus kqQ/r, so escape velocity (defined as the speed that you need to reach infinity at speed zero) is the speed corresponding to KE = kqQ/r

Yeah I meant in this particular problem the constant is 0. If we define PE to be 0 at ∞ like you said.

Not that it is always equal zero, of course I know that's not true.

## What is conservation of energy?

The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another.

## Why is conservation of energy important?

Conservation of energy is important because it allows us to understand and predict how energy behaves in different systems. It also helps us to develop more efficient and sustainable energy sources.

## What are some examples of conservation of energy?

Examples of conservation of energy include a pendulum swinging back and forth, a roller coaster going up and down, and a light bulb converting electrical energy into light and heat energy.

## How is conservation of energy related to the environment?

Conservation of energy is closely tied to environmental concerns because the use and transformation of energy can have significant impacts on the environment. By conserving energy, we can reduce our carbon footprint and help mitigate climate change.

## What are some ways to conserve energy?

Some ways to conserve energy include using energy-efficient appliances, turning off lights and electronics when not in use, using public transportation or biking instead of driving, and using renewable energy sources such as solar or wind power.