For the side that looses motion is in the opposite direction of their force, so the dot product is negative. Does that mean they do negative work? If they do negative work, shouldn't they feel a boost of energy? Instead they feel like they did do work.


1 Answer 1


The "losing side" of a tug of war does negative work, which means they had work done to them. That work done to them is the work that needed to be done to pull them across the line.

However, if we're talking tug of war, we're talking humans. Humans are not simple machines so the work balances are far more complicated. In general, if you take a physics problem, and put a human in it, it becomes counter intuitive =)

In this case, the losing team does do work, but they're not doing work to the rope. The rope moved in the wrong direction to have had work done to it by the losing team. They actually did a tremendous amount of work to the protien structures in their muscles which are trying to contract as they pull on the rope. In "eccentric" motion (motion against the direction of a muscle's contraction), our muscles actually do a bunch of work on the protien crosslinks that pull in the fibers inside our muscle cells, elastically, then waste that work, turning it to heat, by letting those crosslinks break. This is actually why, when lifting a dumbbell, its far easier to lift it smoothly than it is to let it descent smoothly. At the cellular level, it's actually a much harder motion to get right!

But all of that is fancy human stuff. If you replace the losing side with a lump of rock on a sled, it's very easy to see that the winning team is doing work to the rope and the sled, thus the sled is having work done to it.


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