# How can I find the minimal work that can act on an object being pushed up a flight of stairs?

The question I have is that the object is being pushed up a flight of stairs (inclined at 42°) and I have to find the minimal work possible that can act on the object. I think it should be 0 joules because if the applied force is perpendicular to the displacement of the object, it would be cos90 in the formula which is equal to 0 and nothing can be inferior to 0. Is this correct? But when I draw the free body diagram for this, it doesn't seem to be right because then the applied force is sort of opposing the movement of the object, which seems wrong.

So I have a few questions: In the equation for work, would d be the height of the stairs or would it be the distance from the top to bottom on an incline? When I draw the free body diagram would the distance be pointing upwards or on an angle of 42° and would I have to draw it as if it's on an incline? How would I draw my applies force on the force diagram? Would the minimal force even be 0 joules?

Please let me know any solution anyone may have. Thank you!!!