Hello,

I hope you are doing well!

While watching the 7/19 class on AP Physics, around the 28 minute mark where a problem about how much work was done on a floor with friction, I got kind of confused about the solving. The problem:

How much work did the movers do (horizontally) pushing a 46.0 kg crate  10.3 m across a rough floor without accelerating if the effective coefficent of friction was 0.5?

I would think that the answer should be W_1 + W_2, where

W_1 = the work needed to displace the box on a frictionless field (W = m * g * d)

w_2 = the work needed to compensate for the friction (which would be the W  = friction * m * g* d

I think what I'm unsure about is: if I push something (and it moves) on a frictionless surface, is any work being done? If so, then in this question, why may I just consider W_2 as my answer rather than doing the calculation as I think above?

Thank you.