Question

1. What is the momentum (p) of a 960-MeV proton (that is, its kinetic energy is 960 MeVMeV )?

Express your answer with the appropriate units.

2. An electron (mmm = 9.11×10⁻³¹ kg ) is accelerated from rest to speed vv by a conservative force. In this process, its potential energy decreases by 6.70×10⁻¹⁴ JJ . Determine the electron's speed, v. (in term of c.)

Answer 1

1. Given,

kinetic energy is  

mass of proton is  

let momentum be  

we have, total energy

also, we have

in another units,

2. Given

mass of an electron is  

change in potential energy is  

As the work is done by a conservative force, its change in kinetic energy is the same as its change in kinetic energy

that is,

where is the Lorentz factor

we have,

squaring both sides, we get