Joules required to accelerate 1kg of mass

[ally1h]

Homework Statement

how many joules of energy are required to accelerate 1 kg of mass from rest to a velocity of 0.866c?

I tried the relativistic kinetic energy equation, but I feel like it's totally incorrect.

Homework Equations

KE = [(m0c^2) / √(1-v^2/c^2)] - m0c^2
E = KE + m0c^2

The Attempt at a Solution

KE = [(1 kg*m^2/s^2) / √(1 - (0.866c)^2)] - (1 kg*m^2/s^2)
KE = [(1 kg*m^2/s^2) / √(1 -0.75 m^2/s^2) - (1 kg*m^2/s^2)
KE = [(1 kg*m^2/s^2) / (0.5 m/s)] - (1 kg*m^2/s^2)
KE = 2 kg*m/s - 1 kg*m^2/s^2
KE = 1 J

 

[tiny-tim]

Hi ally1h!

how many joules of energy are required to accelerate 1 kg of mass from rest to a velocity of 0.866c?
…
KE = [(m0c^2) / √(1-v^2/c^2)] - m0c^2
E = KE + m0c^2
…
KE = 1 J

one joule!

Hint: what happened to your c²?

 

[thomate1]

Your attempt at finding the solution is correct. However, it is important to note that the units for kinetic energy are not in joules (J), but rather in joules per kilogram (J/kg). Therefore, the correct answer would be 1 J/kg. Additionally, when using the relativistic kinetic energy equation, it is important to use the mass of the object at rest (m0), which is 1 kg in this case. Good job on using the correct equations and units!