) max s f = µ s N . Therefore, tan θ max = µ s or θ max = tan – µ s When θ becomes just a little more than θ max , there is a small net force on the block and it begins to slide. Note that θ max depends only on µ s and is independent of the mass of the block. For θ max = ° , µ s = tan ° = .
Example . What is the acceleration of the block and trolley system shown in a Fig. . (a), if the coefficient of kinetic friction between the trolley and the surface is .
? What is the tension in the string? (Take g = m s - ). Neglect the mass of the string.
(a) (b) (c) Fig. . is the reason why discovery of the wheel has been a major milestone in human history. Rolling friction again has a complex origin, though somewhat different from that of static and sliding friction.
During rolling, the surfaces in contact get momentarily deformed a little, and this results in a finite area (not a point) of the body being in contact with the surface. The net effect is that the component of the contact force parallel to the surface opposes motion. We often regard friction as something undesirable. In many situations, like in a machine with different moving parts, friction does have a negative role.
It opposes relative motion and thereby dissipates power in the form of heat, etc. Lubricants are a way of reducing kinetic friction in a machine. Another way is to use ball bearings between two moving parts of a machine [Fig. .
(a)]. Since the rolling friction between ball bearings and the surfaces in contact is very small, power dissipation is reduced. A thin cushion of air maintained between solid surfaces in relative motion is another effective way of reducing friction (Fig. .
(a)). In many practical situations, however, friction is critically needed. Kinetic friction that dissipates power is nevertheless important for quickly stopping relative motion. It is made use of