Question

physics 211:

a block is placed on an adjustable ramp and then the tilt of the ramp is increased slowly until the block begins to slide. why exactly does the block refuse to slide at some angles, but once the tilt is large enough it always slides down the ramp?

Answer 1

The forces on the block are,

Component of gravitational force parallel to the incline, down the incline

Component of gravitational force perpendicular to the incline, towards it

Normal reaction due to incline perpendicular to the incline, away from it

Frictional force parallel to the incline, upwards.

Net force perpendicular to the incline is zero. Hence  .

Frictional force has two different phases, static and kinetic.

During the static phase,

Initially when the angle is small, also is small. Hence the downward force trying to move the block is small and friction has exctly the same magnitude but opposite direction hence the block does not move. This phase is called static phase of friction since the block does not move. During this phase, .

Later, as the angle is being increased, the friction will reach the limiting value. . When the angle is increased slightly beyond this, friction will enter the kinetic phase. in this phase . . During this phase, the block slides down the incline as friction is not sufficient to keep the block at rest in equilibrium.