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Say that a ball is sitting in front of a compressed spring launcher. The spring is then released. The spring applies a force on the ball for a certain distance. This force is accompanied by an equal and opposite force from the ball. Thus, the spring does some work $W$ on the ball, while the ball does exactly $-W$ work on the spring, correct? So, work is transfer of energy and always accompanied by a negative work on behalf of what is gaining kinetic energy, right?

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  • $\begingroup$ Yes. The conception of work as transfer of energy is an important concept in thermodynamics, so keep it in mind. $\endgroup$ – garyp Aug 19 '14 at 20:34
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Yes - the coiled spring has a certain amount of (potential) energy. When it gives up the energy to the ball, you could say the ball does negative work on the spring, so it loses (potential) energy.

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  • $\begingroup$ So, generally, positive work is always accompanied by negative work, as an extension of Newton's third law? $\endgroup$ – RustyDoorknobs Aug 19 '14 at 20:38
  • $\begingroup$ Yes - or if you like as a consequence of conservation of energy. $\endgroup$ – Floris Aug 19 '14 at 20:49
  • $\begingroup$ I'm not so sure negative work is always accompanied by positive work (and vice versa). Consider a ball and Earth system initially at rest with respect to each other. Go to an inertial frame. Now let the two accelerate toward each other. There is positive work done on each object. (In fact, there is considerably more work done on the ball by the Earth than work done on the Earth by the ball; think of displacements.) No negative work to be found. Yes? $\endgroup$ – BMS Aug 19 '14 at 20:54
  • $\begingroup$ Negative work done on the earth-ball system as it loses potential energy?... $\endgroup$ – Floris Aug 19 '14 at 20:56
  • $\begingroup$ @BMS You forget the invisible spring in between, called gravitation. Actually not a spring, but a rubber band. A bit as if the spring had a ball on each end before being released, except that the spring is repulsive, while the rubber band is attractive. - - - - Negative work: only a force going backward. $\endgroup$ – babou Aug 19 '14 at 21:00

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