What is the relativistic equation for finding kinetic energy?

[Ralphonsicus]

Let's say, I wanted to find the kinetic energy of a ball traveling at 99% the speed of light, what is the equation used for that calculation?

And also, do photons have kinetic energy?

Thanks.

 

[Pengwuino]

Let's say, I wanted to find the kinetic energy of a ball traveling at 99% the speed of light, what is the equation used for that calculation?

And also, do photons have kinetic energy?

Thanks.

The formula for a particle of mass m has a kinetic energy is given by $(\gamma - 1)mc^2$ where $\gamma = {{1}\over{\sqrt{1-{{v^2}\over{c^2}}}}}$ where c is the speed of light.

The energy of a photon with frequency $f$ is $E_{photon} = hf$ where h is Planck's constant.

 

[PAllen]

mc^2(γ - 1)

where γ = 1/(√(1- v^2/c^)

 

[Ryan_m_b]

Let's say, I wanted to find the kinetic energy of a ball traveling at 99% the speed of light, what is the equation used for that calculation?

Here you go http://bit.ly/xZN1YS

And also, do photons have kinetic energy?

I don't think so because they are massless.

 

[PAllen]

I missed the question about photons. What Pengwino says is correct, but (and we simul-posted, else I wouldn't have bothered) adding a little more, and disagreeing with Ryan_m_b:

Since a photon is massless it has no rest energy. Therefore all of its energy is kinetic. For a massive particle, you can say the frame dependent energy has a minimum - the rest energy; the frame dependent additional energy is kinetic. For a photon, there is no minimum - you can redshift to arbitrarily close to zero energy by choice of frame, consistent with its having no rest energy and all kinetic energy.

 

[Ryan_m_b]

disagreeing with Ryan_m_b...Since a photon is massless it has no rest energy. Therefore all of its energy is kinetic

I tried to make it clear I wasn't sure good to learn though, cheers.

 

[tom.stoer]

The relativistic energy-momentum relation reads

$$E^2 = (mc^2)^2 + p^2c^2$$

From this equation the kinetic energy can be determined directly

$$E_\text{kin} = E - mc^2 = \sqrt{(mc^2)^2 + p^2c^2} - mc^2$$

For photons we have m=0 and therefore

$$E_\text{kin} = E = pc$$

For m>0 one gets the equations with v<c mentioned above, of course