Workdone on a mass moving on rough surface

The joints also produce a fluid (synovial fluid) that reduces friction and wear. The ends of the bones in the joint are covered by cartilage, which provides a smooth, almost-glassy surface. The hip is a ball (at the end of the femur) and socket (part of the pelvis) joint. The knee joint is formed by the lower leg bone (the tibia) and the thighbone (the femur). A joint is formed by the ends of two bones, which are connected by thick tissues. However, many parts of the body, especially the joints, have much smaller coefficients of friction-often three or four times less than ice. Many people have experienced the slipperiness of walking on ice. The actual value depends on the two surfaces that are in contact. Coefficient of friction is a unitless quantity with a magnitude usually between 0 and 1.0. If the floor is lubricated, both coefficients are considerably less than they would be without lubrication. These equations for static and kinetic friction are not vector equations.ДЇ k = Ој k N = ( 0.30 ) ( 980 N ) = 290 N f k = Ој k N = ( 0.30 ) ( 980 N ) = 290 N What follows is an approximate empirical (experimentally determined) model only. The magnitude of the frictional force has two forms: one for static situations (static friction), the other for situations involving motion (kinetic friction). (In fact, perfectly smooth, clean surfaces of similar materials would adhere, forming a bond called a вЂњcold weld.вЂќ) Much of the friction is actually due to attractive forces between molecules making up the two objects, so that even perfectly smooth surfaces are not friction-free. Some of the peaks will be broken off, also requiring a force to maintain motion. Thus, a force is required just to set the object in motion. For the object to move, it must rise to where the peaks of the top surface can skip along the bottom surface. Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view. At small but nonzero speeds, friction is nearly independent of speed.ДЇigure 6.10 Frictional forces, such as f в†’, f в†’, always oppose motion or attempted motion between objects in contact. Once an object is moving, there are fewer points of contact (fewer molecules adhering), so less force is required to keep the object moving. Adhesion varies with substances in contact and is a complicated aspect of surface physics. For example, rubber-soled shoes slip less than those with leather soles. Part of the friction is due to adhesive forces between the surface molecules of the two objects, which explains the dependence of friction on the nature of the substances. The harder the surfaces are pushed together (such as if another box is placed on the crate), the more force is needed to move them.

A considerable force can be resisted by friction with no apparent motion. Thus, when you push to get an object moving (in this case, a crate), you must raise the object until it can skip along with just the tips of the surface hitting, breaking off the points, or both. Close-up inspection of these surfaces shows them to be rough.

Furthermore, if you oiled the concrete you would find it easier to get the crate started and keep it going (as you might expect).ДЇigure 6.10 is a crude pictorial representation of how friction occurs at the interface between two objects. If you add mass to the crate, say by placing a box on top of it, you need to push even harder to get it started and also to keep it moving. Once in motion, it is easier to keep it in motion than it was to get it started, indicating that the kinetic frictional force is less than the static frictional force. Now static friction gives way to kinetic friction. If you finally push hard enough, the crate seems to slip suddenly and starts to move. This means that the static friction responds to what you do-it increases to be equal to and in the opposite direction of your push. Imagine, for example, trying to slide a heavy crate across a concrete floor-you might push very hard on the crate and not move it at all. If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction. If two systems are in contact and stationary relative to one another, then the friction between them is called static friction.

Workdone on a mass moving on rough surface