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We cannot talk about magnitudes in case of work, but if someone did (-42 J of work) by stopping a moving object. And if someone did 42 J of work, by pushing something, who did more work? Does it even make sense to ask that?

Also, consider Gravitational Potential Energy (GPE), Gravitational kinetic energy of orbiting body (GKE) and Total Energy(TE)

GPE = 2TE and GKE = - TE

If a body is Just gravitationally bound, it takes more energy than if it is moving, to knock it out

But is GKE greater than other two?

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  • $\begingroup$ We can't talk about the magnitude of work if by magnitude you mean the norm of a vector. But you can talk about it if by magnitude you mean absolute value. The same word, magnitude, used with two different meanings in two different contexts. $\endgroup$ – garyp Nov 25 '15 at 16:06
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The one with the greater magnitude or absolute value is greater. The sign has no bearing. Negative work only tells us about the direction in which the work is being done, positive along the direction of motion, and negative anti-parallel to the direction of motion.

An object in a gravitational field can escape to infinity if TE>0. GKE has to be greater than GPE for this to happen.

see: http://tutor4physics.com/positivenegativework.htm

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