Say I push a box with a constant force $F$ causing a displacement $d$. So magnitude of work done by me on the box is $W=Fd$, and the kinetic energy gained by the box is $W$. But according to N3L, the box exerts an equal and opposite force $F$ on me, but since I am moving opposite to direction of force exerted by box, the box does $-W$ work on me, but does this mean that the box gains even more work $W$, and I am losing more energy equal to $W$? But that is paradoxical as I only applied force $F$ along displacement $d, and my interpretation leads to me constantly losing energy and unintentionally doing more work because of N3L. How does this make sense? How should I treat Newton's third law in this context?
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Only forces on a body determine the work done on the body. In your case, work done on the box depends on the force applied to the box by you. For your case, the reaction force is not on the box, it is on you and has nothing to do with the work done on the box. The work done on you depends on all the forces acting on you, including the force from the ground on you when you push the box. Work is not stored in the system, it is energy applied that changes the kinetic energy of the system.
John Darby
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You do work W on the box and the box does work -W on you. That much is true. It is also true that the total work done on the system consisting of you plus box is $W_{total}=W+(-W)=0$.
In some respects work and energy resemble money. Say you borrow \$10 from me. If your reasoning holds, then I should expect you to pay me back \$20.
AdHoc
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