Friction Formulas

1. Static friction (f_s)

Self adjusting in nature means magnitude of this is equal to external force applied on body and vary with external force.
0 Γëñ f_s Γëñ ┬╡_s N

2. Kinetic friction (f_k)

f_k = ┬╡_kN
µ_k → coefficient of kinetic friction
N → normal reaction
does not depends on external force depends only on normal reaction and ┬╡_k

3. Graphical representation

Note – If ┬╡_R is rolling friction coefficient then

4. Angle of friction (╬▒)

tan ╬▒ = \(\frac{f}{N}\) = ┬╡

5. Angle of repose (╬╕)

The angle of plane at which a body placed on it begins to slide,
tan ╬╕ = ┬╡ = tan ╬▒ (╬╕ = ╬▒)

6. Minimum force required to move a block

(i) On horizontal rough plane:

F cos ╬╕ = ┬╡ N ; N + F sin ╬╕ = mg
F = \(\frac{\mu \mathrm{mg}}{\cos \theta+\mu \sin \theta}\)
For F_min, ╬╕ = angle of friction = tan^-1┬╡
F_min = \(\frac{\mu \mathrm{mg}}{\sqrt{\mu^{2}+1}}\)

(ii) On inclined rough plane:
(a) To move down wards F = ┬╡mg cos ╬╕ – mg sin ╬╕
(b) To move upwards F = ┬╡mg cos ╬╕ + mg sin ╬╕
Note: – To move down ward or upward with minimum force the angle ╬ª = tan^-1┬╡ in fig (i) and (ii) respectively and corresponding


F_min = \(\frac{\mu m g \cos \theta-m g \sin \theta}{\sqrt{\mu^{2}+1}}\) (For downward motion)
F_min = \(\frac{\mu \mathrm{mg} \cos \theta+\mathrm{mg} \sin \theta}{\sqrt{\mu^{2}+1}}\) (For upward motion)

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