A question about friction

abc666

Explain why the coefficient of kinetic friction is smaller than that of static friction.

AL PHY TAS A1 Q.3

上堂好像講過,但忘記了=.=

sapphire

consider a moving block on a rough plane

let:
N be the normal reaction of the block
F be the force acting on it
f be the frictional force acting on it
mg be the weight of the block
R be the reaction of the block when moving

static friction f = (μ1)N

when the block is moving, R is the force that need to balance the resultant force of F and mg
so that R is not a vertical force
in fact, R = Ncosθ (the value of cosθ is refered to the vector sum of F and mg, but it is always less than 1)
so that, R < N for all values of cosθ

kinetic friction f = (μ1)Ncosθ = (μ2)N     where μ2 = (μ1)cosθ

as a result, kinetic friction is always less than static friction