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## Main Question or Discussion Point

Oh no. My old mechanics teacher would probably disown me if he reads this. But today I was thinking about this puzzle, and I couldn't figure it.

A space vehicle of mass 2kg accelerates from 0 to 100m/s from it's rest frame. The energy required to do so is given by E = 0.5mv^2 = 10000 J. Then the space vehicle increases it's velocity to 101m/s.

From the initial rest frame, the total energy required to get a 2kg mass from rest to 101m/s is

E = 0.5*mv^2 = 0.5*2*101^2 = 10201 J

Taken with the fact that it takes 10000 J for a 2kg mass to reach 100m/s from rest, this implies it takes 201 J more for the mass to reach 101m/s than 100m/s

E(101)-E(100) = 0.5*2*(101^2 - 100^2) = 201 J

However, taking 100m/s as the rest frame, it only takes 1 J to acel from 100 to 101m/s.

How much energy does the space vehicle actually require to acel that last 1m/s? Why is one frame correct and the other wrong? This isn't an SR question is it? What is wrong with my understanding?

help me, please. I am feeling foolish. Right now I'm thinking it's an SR situation, but if so, it's the 1st time I've objectively realised SR effects are central to macro mechanics at v<<c.

A space vehicle of mass 2kg accelerates from 0 to 100m/s from it's rest frame. The energy required to do so is given by E = 0.5mv^2 = 10000 J. Then the space vehicle increases it's velocity to 101m/s.

From the initial rest frame, the total energy required to get a 2kg mass from rest to 101m/s is

E = 0.5*mv^2 = 0.5*2*101^2 = 10201 J

Taken with the fact that it takes 10000 J for a 2kg mass to reach 100m/s from rest, this implies it takes 201 J more for the mass to reach 101m/s than 100m/s

E(101)-E(100) = 0.5*2*(101^2 - 100^2) = 201 J

However, taking 100m/s as the rest frame, it only takes 1 J to acel from 100 to 101m/s.

How much energy does the space vehicle actually require to acel that last 1m/s? Why is one frame correct and the other wrong? This isn't an SR question is it? What is wrong with my understanding?

help me, please. I am feeling foolish. Right now I'm thinking it's an SR situation, but if so, it's the 1st time I've objectively realised SR effects are central to macro mechanics at v<<c.

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