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There is a similar looking equation coming for Newton's second law
being applied to the changing motion of the skater's centre of mass.
It is: F(net) delta s(centre of mass) = delta (1/2 mv(center of
mass)*2. That relates the change in kinetic energy of the body to
something that, on quick inspection, could be mistaken for the work
done on the skater but is not that. Ian Sefton, in his useful
contribution to this thread noted that this term is sometimes called
psuedo-work. Whatever we choose to call it, it certainly is not the
work done by the net force (which happens to be equal to the force
applied by the contact force from the wall) because that work is zero.