When two objects slide against one another, which of the following statements about the force of friction between them is true? The magnitude of the frictional force is always equal to kn . The magnitude of the frictional force is always less than kn . The magnitude of the frictional force is determined by other forces on the objects so it can be either equal to or less than kn .

Learning Goal: To introduce contact forces: the normal force and the force due to friction.. Two types of contact forces operate in typical mechanics problems: the normal force (usually designated by 7) and frictional forces = (designated by f ). The normal force is always perpendicular to the plane of contact, whereas the force due to friction is parallel to the plane of contact. When two surfaces slide against each other, experiments show three things about the resulting kinetic frictional force f ,: 1. The frictional force opposes the relative motion of the two surfaces at their point of contact. 2. The magnitude of the kinetic frictional force, fx, is proportional to the magnitude of the normal force, 7. 3. The ratio of f,, to nis fairly constant over a wide range of speeds. The constant of proportionality is called the coefficient of kinetic friction and is often designated jz. As long as the sliding continues, the frictional force is fy, = ban. When there is no relative motion of the two surfaces, the magnitude of the static frictional force can assume any value from zero up to a maximum jisn, where [ts is known as the coefficient of static friction; [Us is, invariably, larger than ,. The frictional force for surfaces that do not move relative to each other is therefore fs