# Homework Help: Energy conservation

1. Dec 12, 2005

### iommi0028

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.

2. Dec 12, 2005

### naeblis

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. Dec 12, 2005

### daniel_i_l

the 1/2mv^2 is derived by integrating the force ma over a certain distance:
$$\int_{a}^{b}ma dx$$

Last edited: Dec 12, 2005
4. Dec 12, 2005

### iommi0028

hey thanks that really cleared things up