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Impending motion; friction force at different stages

Short answer

Impending motion is the state just before sliding where static friction reaches its maximum value F_max = μ_s N. As applied force increases, friction rises linearly with it (self-adjusting) until this peak, then drops slightly to a constant kinetic friction μ_k N once motion begins.

Illustrate impending motion state of friction and demonstrate the change in frictional force for different motion stages using relevant figure.

Impending motion

Impending motion is the state in which a body is just about to slide. The applied force has increased until the friction force has reached its maximum, limiting value F_max = μₛN. Any further increase of the applied force starts the motion.

Variation of friction force with the applied force

A block of weight W on a rough horizontal surface is pulled by a force P that is gradually increased from zero.

 F (friction)
  ^
  |               F_max = μs N
  |                +
  |              / |\
  |            /   |  \___________  F = μk N (motion)
  |          /     |
  |        /  F = P (45° line)
  |      /         |
  |    /           |
  +--/-------------+---------------> P (applied)
  O   static zone  impending   motion
      (no motion)  motion
StageApplied forceFriction force
No frictionP = 0F = 0
No motion (static)0 < P < F_maxF = P (increases with P)
Impending motionP = F_maxF = F_max = μₛN (maximum)
MotionP > F_maxF drops to μₖN and stays nearly constant

So the friction force first rises linearly with P (it is self-adjusting), reaches its peak at impending motion, then falls slightly to the kinetic value once sliding begins.

✓ Answer checked by Claude Opus 5.5 (high effort)

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