Forces in Two Dimensions - Mission F2D2 Detailed Help

A box is being accelerated across a rough, 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 friction force would ...


The force of friction experienced by an object is often calculated using the equation:
Ffrict= mu • Fnorm
where muis the coefficient of friction (dependent predominantly upon the nature of the two surfaces that are in contact) and Fnorm is the normal force. The equation predicts that an increase in normal force would lead to an increase in the amount of friction force.

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). Quite amazingly, the horizontal friction force is dependent upon the magnitude of the vertical normal force (see Formula Frenzy section). As such, this question can be reduced to how would a change in the angle of Fapp affect the normal force? If the normal forces increases, then the friction force increases and if the normal force decreases, the friction force decreases.
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 and ultimately Ffrict.

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.