How do you find work when given weight, distance and incline?

How much work is needed to push a 100. -kg packing crate a distance of 10.0 m up a frictionless inclined plane that makes an angle of 30. degrees with the horizontal?

How do you find work when given weight, distance and incline?
Before nothing, I say to you that this it is not my native language, so it excuses the grammar.





In order to begin, we must clarify that, on an inclined plane the amount of work does not change, only varies the force necessary to do it; therefore, the only thing that you must do is to multiply the weight of the packing crate by the height of the plane, it is to say:





W = w * h -------- (1)





where:





W, work necessary to raise


w, weight of the load


h, height of the plane





Since h = L*sin(theta), finally we have:





W = w*L*sin(theta) ----------- (2)





where


L, length of the plane


theta, angle formed by the plane with the horizontal





In order to verify the previous thing, you can make a decomposition of the forces that act in the system. The weight has two components, that is to say: one that is parallel to the plane and another perpendicular to the same one. This last one, is annulled with the normal force to the plane.





The weight component parallel to the plane, according to the Third Newton's Law -and supposing that the applied force is parallel to the plane also- is of equal magnitude and direction but in opposed sense to which you must apply to transfer the weight, so:





F = w*sin(theta) -------------- (3)





and, as the work is defined by:





W = F*d ----------- (4)





in this case d = L, therefore:





W = F*L ---------- (5)





Replacing (3) in (5):





W = w*L*sin(theta)





Q. E. D.
Reply:Work is defined as F*d*cos(theta)


(where theta is the angle between force and the direction of motion)