Modern Physics - velocity of electron accelerated through 6 Mev

[shivam01anand]

Modern Physics -- velocity of electron accelerated through 6 Mev

Homework Statement

Electron accelerated through 6 Mev. from rest. My Answer was > speed of light

Homework Equations

Then our professor told us to not conserve KE only as mass was increased. Therefore use einstein's e=mc^2.

The Attempt at a Solution

he gave us the formulas of new mass vs old mass at rest.

I just don't get it why is mass increased as well as speed increased even though we're starting from rest

 

[tiny-tim]

hi shivam01anand! welcome to pf!

I just don't get it why is mass increased as well as speed increased even though we're starting from rest

mass is energy, energy is mass

in Newtonian physics, mass is constant, so (even though it's energy), we can ignore it in the conservation-of-energy equation!

in relativistic physics, mass is not constant, so the conservation-of-energy equation must include mass-after minus mass-before

 

[shivam01anand]

Wait, How come if this same question came when i studied electric field and applied the wrong method[ i.e energy conservation] it would have been correct?

 

[rude man]

Wait, How come if this same question came when i studied electric field and applied the wrong method[ i.e energy conservation] it would have been correct?

Because when you "studied electric field" you neglected relativistic effects.

Relativistic effects can be ignored for v< ~ 0.1c. If your computations using kinetic and potential energies indicate a velocity greater than about 0.1c then you must redo your computations using relativistic equations.

 

[tiny-tim]

yes, for ordinary speeds, the error is less than 1 in 10¹², way too small to take any notice of!

 

[haruspex]

I just don't get it why is mass increased as well as speed increased even though we're starting from rest

Just to anticipate a possible misunderstanding...
In relativity, what you used to think of as KE is the gain in mass. So don't go calculating a gain in KE (by Newton) and a gain in mass (by Einstein) and adding them together.

 

[rude man]

I just don't get it why is mass increased as well as speed increased even though we're starting from rest

Don't feel bad. No one else 'got it' either until Einstein explained it in 1905. Even then, it took a while before many physicists 'got it'!

 

[jtbell]

The argument about the validity of the concept of relativistic mass has been deleted. It's clear from the opening post that the answer is expected to be given using the framework of relativistic mass, so if you don't like relativistic mass, use it anyway or keep your fingers away from your keyboard.

Arguments about relativistic mass go in the relativity forum in the main Physics section.

 

[shivam01anand]

if you don't like relativistic mass, use it anyway or keep your fingers away from your keyboard.

.

lol funny