Relativity - Mass/Energy/Speed

[ZedCar]

Homework Statement

A spaceship of rest mass 7.5 x 10^3 Kg has a kinetic energy that is 0.12 times it's rest energy.

a) Calculate it's total energy
b) Calculate it's speed

Homework Equations

The Attempt at a Solution

a)
E = E0 + K
E = mc^2 + K
E = 7.5 x 10^3 x (3 x10^8)^2 + 0.12(7.5 x 10^3)
E = 6.75 x 10^20 J


b)
E = γmc^2
substituting above values in and solving for v, I get v = 0

 

[ehild]

a)
E = E0 + K
E = mc^2 + K
E = 7.5 x 10^3 x (3 x10^8)^2 + 0.12(7.5 x 10^3)

Correct the red part. It is the rest mass now, not the rest energy.


ehild

 

[ZedCar]

Correct the red part. It is the rest mass now, not the rest energy.


ehild

So should it be...

E = 7.5 x 10^3 x (3 x10^8)^2 + 0.12(7.5 x 10^3 x (3 x10^8)^2)
E = 7.56 x 10^20 J

 

[ehild]

Yes.

ehild

 

[ZedCar]

Thanks very much ehild.

 

[ehild]

You can save calculations if you not multiply with c^2 at the beginning:

E= γmc^2 = mc^2+0.12mc^2

γmc^2=mc^2(1.12)

y=1.12ehild