Energy Needed To Go A Given Speed

[Sothh]

Hey, I don't have much of a physics background.

I have been searching for an equation that shows how much energy is needed to make a given mass go a given speed.

For example, let's say I want to send 1 gram at half light speed. How much energy is required?

Thanks!

 

[Doc Al]

Sounds like you want to calculate the kinetic energy of the mass.

For low speeds (compared to the speed of light) the kinetic energy is KE = ½mv². But for fast speeds, it's a bit more complicated:

(I can't seem to get Latex to work.)

 

[tiny-tim]

Welcome to PF!

Hi Sothh! Welcome to PF!

For a speed of v metres per second, the energy of a mass of m kilograms is mc²/√(1 - v²/c²) joules.

If v = 0 (the mass is at rest), that energy is obviously just mc², which is therefore called the rest-mass.

So the extra energy needed to get it to speed v (the kinetic energy) is mc²(1/√(1 - v²/c²) - 1) joules.

If v/c is very small, then that extra (kinetic) energy is approximately mc²(v²/2c²), ie mv²/2.

 

[Sothh]

Thanks!

Just to confirm I am using this correctly, it should take 20 kilograms around 9e+12 kilojoules to go .1c, correct?

 

[Doc Al]

Just to confirm I am using this correctly, it should take 20 kilograms around 9e+12 kilojoules to go .1c, correct?

Sounds about right.