Question

1. How much work W must be done on a particle with a mass of m to accelerate it from rest to a speed of 0.895c?
(in units of mc^2)

2. How much work W must be done on a particle with a mass of m to accelerate it from a speed of 0.895c to a speed of 0.990c?

Answer 1

Given thatInitial speed of particle u = 0final speed of partilcle v = 0.895 c----------------------------------------------------1) According to work energy theoremWork done = Change in kinetic energyW = [1/√[1- (v/c)^2] -1] mc^2 - [1/√[1- (u/c)^2] -1] mc^2=[1/√[1- ((0.895c)/c)^2] -1] mc^2 - [1/√[1-(0/c)^2] -1] mc^2= 1.24 mc^22) According to work energy theoremWork done = Change in kinetic energyW = [1/√[1- (v/c)^2] -1] mc^2 - [1/√[1- (u/c)^2] -1] mc^2Here v= 0.990c and u = 0.895cW =[1/√[1- ((0.990c )/c)^2] -1] mc^2 - [1/√[1- (0.895c/c)^2] -1] mc^2=6.09 mc^2 -1.24 mc^2= 4.85 mc^2