Chapter 5 FRICTION W A horizontal force P applied to a block will not at first cause it to move. This is because the friction force F balances P.
P
N F
Equilibrium
F Motion
Fm Fk
P
As the magnitude of P increases, the magnitude of F increases until it reaches a maximum value Fm. If P is increased further, the magnitude of F drops to Fk and the block begins to slide.
W
F
Equilibrium
Motion
Fm
P
Fk
N
F
P
The forces Fm and Fk are proportional to the normal component N of the reaction of the surface. We have
Fm = μs N
F k = μk N
where μs is the coefficient of static friction and μk is the coefficient of kinetic friction. These coefficients depend on the nature and the condition of the surfaces in contact.
W P
N
R
φ F
F = R sin φ N = R cos φ
It is sometimes convenient to replace the normal force N and the friction force F by their resultant R. As the friction force increases and reaches its maximum value Fm =μsN, the angle φ that R forms with the normal to the surface increases and reaches a maximum value φs, called the angle of static friction.
W P
N
R
φ F
F = R sin φ N = R cos φ
If motion actually takes place, the magnitude of F drops to Fk; similarly the angle φ drops to a lower value φk , called the angle of kinetic friction. The coefficient of friction and the angle of friction are related by
tan φs = μs tan φk = μk
W
P
Frequired N The magnitude F of the friction force is equal to Fm = ÎźsN only if the body is about to slide. If motion is not impending, F and N should be considered as independent unknowns to be determined from the equilibrium equations. The value of F required to maintain equilibrium should be checked to insure that it does not exceed Fm.
W
P
Fm = ÎźsN N If motion is known to be impending, F has reached its maximum value Fm = ÎźsN , and this expression may be substituted for F in the equilibrium equations.