Box sliding down wall at constant speed

[ayjakk]

Homework Statement

The 2.0 kg wood box in the figure slides down a vertical wood wall while you push on it at a 45 ∘angle.
https://session.masteringphysics.com/problemAsset/1070374/4/06.P51.jpg

Homework Equations

ΣF_Y = F_PY - mg

The Attempt at a Solution

I know that since there is a constant velocity, the acceleration will be zero. I then have
0 = F_Psin45 - mg
F_Psin45 = mg
F_P = (mg)/sin45
F_P = ((2kg)*(9.8m/s²))/sin45
F_P = 27.719 N

Which is wrong. Am I correct in assuming that the only forces in the Y direction (taking up as positive Y) are the y-component of the pushing force and gravity? What am I missing here?

 

[ehabmozart]

Your approach just misses the friction component which acts against the relative motion of box/wall (i.e. downwards).. Therefore the equation will be

F(push)sin45 - mu*N - mg = 0 ; where mu is coefficient of friction and N= F(push) cos 45 ...