Friction (conceptual)

two people push on the crate, parallel to the surface of the incline, and it moves at constant speed up the incline. how does the force exerted by the two people on the crate compare with the force of friction on the crate?

force of two people is greater than force of friction

force of friction acting on crate at rest on an incline

frictional force points up the incline

when a board with a box on it is slowly tilted to a larger and larger angle, common experience shows that the box will at some point "break loose" and start to accelerate down the board. the box begins to slide once the component of its weight parallel to the board, w||, equals the maximum force of static friction. what explains why the box accelerates down the board after it begins to slide (rather than sliding with constant speed)?

the coefficient of kinetic friction is less than the coefficient of static friction. at the point when the box finally does "break loose," the component of the box's weight that is parallel to the board, w||, is equal to μsn (the maximum force of static friction). For the box to then accelerate, there must be a nonzero net force acting on the box parallel to the board. In other words, w|| must be greater than the force of kinetic friction, fk=μkn. Therefore the force of kinetic friction, μkn , must be less than the force of static friction, μsn, which implies μk<μs, as expected.

when two objects slide against one another...

the magnitude of the frictional force is always equal to μkn

when two surfaces slide against each other, experiments show three things about the resulting kinetic frictional force fk

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, fk, is proportional to the magnitude of the normal force, n. 3. the ratio of fk to n is fairly constant over a wide range of speeds. the constant of proportionality is called the coefficient of kinetic friction and is often designated μk. As long as the sliding continues, the frictional force is fk=μkn. 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 μsn, where μs is known as the coefficient of static friction; μs is, invariably, larger than μk. The frictional force for surfaces that do not move relative to each other is therefore fs≤μsn. The equality fs=μsn holds only when the surfaces are on the verge of sliding.

force of kinetic friction (plot)

only an object that is sliding with respect to a surface can be acted upon by the force of kinetic friction. - fk points in a direction that is parallel to the surface of contact and opposes the motion of the object. - fk=μkn, where μk is the coefficient of kinetic friction and N is the magnitude of the normal force

force is applied to the crate to move it up an incline so the frictional force...

points down the incline

when two objects are in contact with no relative motion...

the magnitude of the frictional force may be either equal to or less than μsn for static friction, the actual magnitude of the friction force is such that it, together with any other forces present, will cause the object to have zero acceleration. The magnitude of the force due to static friction cannot, however, exceed μsn. If the magnitude of static friction needed to keep the acceleration equal to zero exceeds μsn, then the object will slide and will be subject to the force of kinetic friction.

force of static friction (plot)

until the pulling force Fx exceeds fs,max, the force of static friction is exactly equal in magnitude to the pulling force - plot shows how fs remains constant at some positive value from Fx equal to 0 until Fx equal to fm and then decreases linearly to 0 = triangle