Energy conservation and e = mc^2

In summary, the equation E=mc² is a fundamental relation between mass and energy, while the equation for kinetic energy, k = 1/2 mv², involves the mass, velocity, and a constant. The intrinsic rest energy, Eo, is the energy a mass has with no relation to velocity or position. The c in E=mc² is a velocity related to the speed of light, while in k = 1/2 mv², the velocity is that of the particle of mass m. The two equations are not the same and serve different purposes. The derivation of k = 1/2 mv² involves integrating the force ma over a certain distance.
  • #1
iommi0028
2
0
If Kinetic Energy is mv²/2 how come E=mc² is a valid equation.. wouldn't it have to be divided by two also because c represents a velocity? Thanks for any help.
 
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  • #2
the equation e = mc^2 is a fundamental relation between mass and energy. A particle of mass m has an "intrinsic rest energy" Eo given by Eo = mc^2

im not 100% on the way that they derived k = 1/2 mv^2 but i do know that its only used when relating mass velocity and kinetic energy.

the Eo is the energy a mass has with no relation to velocity or position. the c is a velocity but its a relation to the speed of light your making, in 1/2 mv^2 the velocity your relating there is that of the particle of mass m.

basically the energies in the 2 equations are not the same, and in one your relating the speed of the mass, and in the other your relating a mass to a constant [the speed of light]

hope that helps.
 
  • #3
the 1/2mv^2 is derived by integrating the force ma over a certain distance:
[tex]
\int_{a}^{b}ma dx
[/tex]
 
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  • #4
hey thanks that really cleared things up
 

FAQ: Energy conservation and e = mc^2

What is energy conservation?

Energy conservation is the practice of reducing the amount of energy used in order to conserve natural resources and reduce the negative impact on the environment. It involves using energy efficiently, reducing waste, and finding alternative sources of energy.

What is the equation e = mc^2 and why is it important?

The equation e = mc^2, also known as the mass-energy equivalence equation, was proposed by Albert Einstein in his theory of special relativity. It states that energy (e) is equal to the mass (m) multiplied by the speed of light squared (c^2). This equation is important because it shows that mass and energy are interchangeable and that even small amounts of mass can contain a large amount of energy.

How does energy conservation relate to e = mc^2?

Energy conservation relates to e = mc^2 because it emphasizes the importance of using energy efficiently and reducing waste. By conserving energy, we can minimize the need for energy production, which often involves the conversion of mass to energy, as seen in nuclear power plants.

What are some practical ways to conserve energy?

There are many ways to conserve energy, including using energy-efficient appliances, turning off lights and electronics when not in use, using public transportation or carpooling, and using renewable energy sources such as solar or wind power. Simple daily habits like turning off the tap while brushing your teeth or using natural light instead of artificial light can also make a big impact.

How does energy conservation benefit the environment?

Energy conservation benefits the environment in many ways. It reduces the demand for energy production, which often involves the burning of fossil fuels and releases harmful pollutants into the environment. It also helps to preserve natural resources, such as water and forests, which are essential for maintaining a healthy ecosystem. Additionally, energy conservation reduces greenhouse gas emissions, helping to mitigate the effects of climate change.

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