Your moving company is to load a crate of books on a truck with the help of some planks that slope upward 33°. The mass of the crate is 98.0 kg, and the coefficient of sliding friction between it and the planks is 0.500. You and your employees push horizontally with a combined net force . Once the crate has started to move, how large must F be in order to keep the crate moving at constant speed?
Since the crate has started to move, we know that the friction coef to use is the static one. Since the crate is moving at constant speed, the net force on the crate is zero. Let's chose axes with the x axis along the incline and the y axis perpendicular to the incline.
Three forces act on the crate: The Fpushx, Friction and the x component of gravity. These forces must add to zero. Fgx = mg*sin 33. Fnormal = mgcos 33 and Friction = uFnormal.
So FpushX = 98*g*sin 33 + 0.5*98*g*cos 33.
Having found the X component of the Force, we can find the full magnitude Fpush = FpushX/cos 33.