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 a rightward direction (as shown below). This force makes an angle of 30 degrees with the horizontal. If the angle at which the force is exerted is increased to 45 degrees, then the normal force would ...

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.

The applied force has a rightward and an upward component or effect on the box. The magnitude of the upward component can be calculated as Fapp• sine(Θ) where Θ is the angle that the force makes with the horizontal.

For objects accelerating across level surfaces, the vertical forces balance. There are three vertical forces - the downward pull of gravity, the upward support force from the surface (normal force) and the upward component of the applied force (Fapp-y). The normal force is the support force and always supplies sufficient support to make up for the difference between the down pull of gravity and the upward component of the applied force. For instance, if the gravity force was 100 N and the Fapp-y was 20 N, then the normal force makes up for the difference and supplies 80 N of support. And of course if the Fapp-y changed, the amount of support provided by the surface would have to change accordingly. So if the 20 N for Fapp-y became 40 N, then the 80 N for normal force would decrease to 60 N. Understanding the role of the normal force in balancing out the forces allows you to predict how a change in angle would alter the Fapp-y value (see Math Magic section) and in turn affect the Fnorm.