Relativistic mass and work problem

[Liquidxlax]

Homework Statement

A body has rest mass of 10^5 Kg. Find how much work must be done on the body to give it a velocity such that the clocks on the body run at 1/10 of the rate of the lab clocks. compare the work energy with the rest energy of the body

Homework Equations

γ=1/√(1-(v/c)²)

E= T -m_oc²

The Attempt at a Solution

t'/10 = t where t' is the lab time and t is the rest frame time

so γ=10 (my prof assured me that i need not find the velocity)

E_rest = m_oc² = 3x10¹³J


So the object starts at rest and is accelerated up to a speed such that the clocks run at one tenth the time in the lab frame

the formula which i found in my textbook was

W=∫(dE/dt)dt = E_f-E_i

but this formula was not in the notes so I'm not sure if it is appropriate, yet I do have time end points t' -> t/10

yet I've seen other forumlas in which work was said to be

W = m_oc²(γ-1)


Some clarification would be nice :)

 

[BruceW]

the formula which i found in my textbook was

W=∫(dE/dt)dt = E_f-E_i

but this formula was not in the notes so I'm not sure if it is appropriate, yet I do have time end points t' -> t/10

The formula is correct, but is not really useful because you don't have time end points. You only know how fast the clocks are ticking relative to each other. So the work could have been done over a very long time or a very short time, you don't know.

yet I've seen other forumlas in which work was said to be

W = m_oc²(γ-1)Some clarification would be nice :)

This is correct, because it is the equation for the kinetic energy of a particle, and the particle was initially stationary, so the KE is equal to the work done on the particle.

Edit: I don't know why I'm saying particle, it could be any object.

 

[Liquidxlax]

The formula is correct, but is not really useful because you don't have time end points. You only know how fast the clocks are ticking relative to each other. So the work could have been done over a very long time or a very short time, you don't know.

This is correct, because it is the equation for the kinetic energy of a particle, and the particle was initially stationary, so the KE is equal to the work done on the particle.

Edit: I don't know why I'm saying particle, it could be any object.

heaviest particle in the universe :p

thanks for the help