Friction
December 8, 2016
Categorised in: 1st Year Mechanics
Coefficient of Static Friction
$μ_s = {F_s}/{R}$ …For impending motion
Coefficient of Kinetic Friction
$μ_k = {F_k}/{R}$ For actual motion
R -> Magnitude of normal reaction
Angle of Friction
φ = $tan^{-1} μ $
For impending motion the angle between normal reaction and resultant reaction is called as angle of static friction.
For actual motion when P = $F_k$ the angle between normal reaction and resultant reaction is called angle of kinetic friction.
Angle of Respose
Angle of inclined plane with horizontal at which body is just on verge of sliding (impending motion) and so $F_s$ = $μ_s$ R
Angle of respose is denoted by α.
Note: $ ϕ_s$ = α
${\text"Tight side"}/{\text"Slack side"} = e^{μ_s β}$
Lap angle or angle of contact β must be in radians.
Above relation is used only when belt is about to slip.
Tight side represents the larger tension in part of belt which pulls and slack side represents the smaller tension in part which resists.
For V-belt ${T_1}/{T_2}$ = $e^{(μ_s β cosec α/2)}$
Band Brake
Breaking Torque $T_B$ = $(T_1 – T_2) r$
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