(a) The strings of the racquet exert a force and thus an impulse which is perpendicular to the face of the racquet, that is, along the +x – axis in the figure above. Therefore the change in momentum of the ball is also only along the +x – axis:
(b) Since the force is applied in the +x – direction, the average acceleration is must also be directed along the +x – axis, that is, there is no acceleration along the y-axis.
The Principle of Conservation of Linear Momentum
We’ve seen that if you want to change the momentum of an object or a system of objects, Newton’s second law says that you have to apply an unbalanced force. This implies that if there are no unbalanced forces acting on a system, the total momentum of the system must remain constant. This is another way of stating Newton’s first law, the law of inertia, discussed in chapter 4. If the total momentum of a system remains constant during a process, such as an explosion or collision, we say that the momentum is conserved. The principle of conservation of linear momentum states that the total linear momentum of an isolated system remains constant (is conserved). An isolated system is one for which the vector sum of the external forces acting on the system is zero.
Typically, the AP Physics B exam includes the following types of problems which use the principle of conservation of linear momentum: recoil in one and two dimensions, inelastic collisions in one and two dimensions, and elastic collisions in one and two dimensions. Remember, if a momentum vector is conserved, its components are also conserved.
