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 a downward 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 a downward component. Thus, there are three vertical pulls on the box - the down pull of gravity, the downward component of the applied force, and the upward support force from the surface (Fnorm). Since there are two downward pulls and one upward pull, the upward pull (normal force) must be bigger than each individual downward pull (gravity and y-component of applied) in order to balance them out when combined.