Two particles have equal kenetic energies

[napier212121]

if two particles have equal kenetic energies, do they have the same momentum?

 

[lpfan4yrs04]

NO! Just because something has the same kinetic energy doesn't mean it has the same momentum. There are a number of factors that could affect it.

 

[HallsofIvy]

Kinetic energy of an object with mass m and velocity v is (1/2)mv². Momentum is mv.

Take for example, an object with mass 4kg and speed 1 m/s. Its kinetic energy is (1/2)(4)(1)²= 2 Joules and its momentum is (4)(1)= 4 kgm/s. Take a second object with mass 1kg and speed 2 m/s. It has kinetic energy (1/2)(1)(2)²= 2 Joules also but its momentum is (1)(2)= 2 kgm/s.

 

[GRQC]

Originally posted by HallsofIvy
Kinetic energy of an object with mass m and velocity v is (1/2)mv². Momentum is mv.

Take for example, an object with mass 4kg and speed 1 m/s. Its kinetic energy is (1/2)(4)(1)²= 2 Joules and its momentum is (4)(1)= 4 kgm/s. Take a second object with mass 1kg and speed 2 m/s. It has kinetic energy (1/2)(1)(2)²= 2 Joules also but its momentum is (1)(2)= 2 kgm/s.

Well, kinetic energy (for particles, as the question originally asked) is probably more likely to be K = (\gamma - 1) mc^2, i.e. relativistic kinetic energy, which reduces to the Newtonian expression in the limit of small v.