Let's have a look at a system with four external forces acting on it. The system consists of a block. The block can slide on an incline with friction. The four forces are an applied force _a, the gravitational force _g, the friction force _fr, and the normal force . The free-body diagram for the block is shown at top right in the applet window, along with the x,y axes that will be used in the calculations.

Question. Suppose the inclination angle q of the incline is 20^o, the coefficient of friction between block and incline is 0.5, the block's mass is 0.4 kg, and the applied force is equal to (2.0, 3.0) N with respect to the x,y axes shown. Then, if the block's initial velocity is 2 m/s up the incline, what is the block's speed after the block has moved a distance d = 2 m?

Take the magnitude g of the acceleration due to gravity equal to 10.0 m/s².

Hint. Use the CM-work theorem (see under Related Items). The normal force does no work on the block, because it is at right angles to the block's displacement. Thus, the combined CM-work done by the applied force, the friction force, and the gravitational force is equal to the change in (M/2)V², where m and v are the mass of the block and the speed of the block's center of mass (CM), respectively.