Forces in Two Dimensions - Mission F2D2 Detailed Help

A box is being accelerated across a level surface. A force is being applied to the box in an upward and rightward direction (as shown below). In this situation, the normal force is ...

Newton's First and Second Law
Forces, when unbalanced, cause objects to accelerate; and the direction of the acceleration is in the same direction as the unbalanced force. If there is no acceleration in a given direction (horizontally or vertically), then one can be certain that all individual forces in that direction are balanced.

Since the box is not accelerating perpendicularly to the surface, the vertical forces must balance. The applied force has an upward component. Thus, there are three vertical pulls on the box - the down pull of gravity, the upward support force from the surface (Fnorm) and the upward component of the applied force. Since there are two upward pulls and one downward pull, the downward pull (gravity) must be bigger than each individual upward pull (normal and y-component of applied) in order to balance them out when combined.