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Define coefficient of kinetic & statics friction & law of friction
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This constant is referred to as coefficient of static friction, denoted as 𝜇s
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𝝁𝐤 =

𝐅𝐤
𝐍

Since 𝐹𝑘 is less than 𝐹max , we have 𝜇𝑘 < 𝜇s

Coefficient of friction 𝜇s or 𝜇k depend on the nature of surfaces of contact and have value less than 1
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2 to 0
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The
corresponding coefficient of kinetic friction (𝜇k ) is around 25% lower
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2

The value of frictional force F increases as the applied disturbing force increases till it reaches the limiting
value 𝐹max
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3

The ratio of limiting frictional force 𝐹max and the normal reaction N is a constant and it is referred to as
coefficient of static friction (𝜇𝑠 )
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The ratio
of 𝐹𝑘 and the normal reaction 𝑁 is a constant and is referred to as coefficient of kinetic friction (𝜇𝑘 )
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Define Angle of Friction, Cone of Friction and Angle of Repose
Angle of Friction:
"It is the angle made by the resultant of the limiting frictional force 𝐹max and the normal reaction 𝑁 with the normal
reaction"
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4
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Let 𝑁 be the normal reaction
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Let 𝑅 be the resultant of 𝐹max and 𝑁, making an angle 𝜙 with the normal reaction
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Here 𝑅 = √𝔽max 2 + N2
= √(𝜇s N)2 + N2
also tan 𝜙 =

Fmax
N

=

𝜇s N
N

tan 𝜙 = 𝜇𝑠

∴ 𝜙 = tan−1 𝜇s … … … 4
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4
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Let 𝑅 be the resultant
reaction at the contact surface acting at an angle of
friction 𝜙
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This right circular cone is known as the cone of friction
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Consider a block of weight W resting on a rough horizontal plane
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4
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The angle of inclination of the plane at this position is known as the angle of
repose
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Angle of repose is independent of the weight of the body and depends only on the
coefficient of static friction
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Applying COE
Σ𝐹𝑥 = 0 Π + 𝑣𝑒
𝐹max − Wsin 𝛼 = 0
∴ 𝜇s N − Wsin 𝛼 = 0 … … 1
ΣFy = 0 + +ve
N − Wcos 𝛼 = 0
∴ N = Wcos 𝛼 … … 2
Substituting (2) in (1)
𝜇𝑠 ( Wcos 𝛼)
tan 𝛼

−Wsin 𝛼 = 0
=𝜇

or 𝛼 = tan−1 𝜇𝑠 … …
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4
but we have seen that

𝜙
∴
i
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Angle of Repose

= tan−1 𝜇s
𝛼=𝜙
= Angle of Friction

Though magnitude wise both angle of repose and angle of friction have the same value, their meaning and
application are different, as we have seen

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