Question

How much work must be done on a particle with a mass of mm to accelerate it from rest to a speed of 0.084 cc ? (Express the answer in terms of mc2mc2.)

Answer 1

Work = 0.68 mc²

Step-by-step explanation:

given data

speed = 0.084 cc

solution

as kinetic energy of mass particle is

KE = mc²(
`\gamma` - 1 ) ............1

here
`\gamma` is lorentz constant

`\gamma` =
`\frac{1}{\sqrt{1-((v)/(c))^2 } }`

`\gamma` =
`\frac{1}{\sqrt{1-((0.084c)/(c))^2 } }`

`\gamma` = 1.68

as here particle start from rent so initial KE is 0

and final KE = mc²(1.68 - 1 )

final KE = 0.68mc²

so here work done to increase speed of particle

W = final KE - initial KE

Work = 0.68 mc²