Question

a) If the momentum of a nonrelativistic particle is doubled, its kinetic energy increases by a factor of 4. Explain why. If the momentum of a photon is doubled, by what factor does its energy increase

b) The theory of relativity sets an upper limit on the speed that a particle can have. Are there also limits on its energy and momentum? Explain

c) In what ways do photons resemble other particles such as electrons? Do photons have mass? Can they be accelerated? Do they have electric charge?

Answer 1

a) Kinetic energy is given as

E = P² / 2m

where P is momentum

Now, if P is doubled, we have

keeping mass constant

E₁ / P₁² = E₂ / (2P)²

E₂ / 4P = E₁ / P

E₂ = 4E₁

SO, kiNETIC ENERGY INCREASES BY 4 TIMES WHEN MOMENTUM IS DOUBLED.

b) A particle's energy approaches infinity as its velocity approaches the speed of light. Thus, in order for the particle to move faster than the speed of light would require it to attain infinite kinetic energy, which can't happen and isn't possible. so yes , momentum and energy do have a limit

c) photons have zero mass. photon doesn't carry a charge thus cannot be accelerated. Photons have no charge, electrons are charged. They have no mass but an electron is about 9 x 10^-31 kg. The photons have limit to their speed which is speed of light.