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Friction Problems

Steven Vukazich

San Jose State University

A ruler is leaning on a wall.

How much can the ruler be

inclined, before it just starts

to move, if the coefficient

of static friction between

the ruler and the wall and

the ruler and the floor are

both 0.35?

Equations of Equilibrium 𝜃 N

B

N

A

L/ L/ W 𝐹

= 𝜇 & 𝑁

𝐹 ( = 𝜇 & 𝑁 ( 𝐿 cos 𝜃 𝐿 sin 𝜃

+ =^0

sin 𝜃 + 𝑁( 𝐿 sin 𝜃 − 𝜇&𝑁( 𝐿 cos 𝜃 = 0

Equations of Equilibrium 𝜃 N

B

N

A

L/ L/ W 𝐹

= 𝜇 & 𝑁

𝐹 ( = 𝜇 & 𝑁 ( 𝐿 cos 𝜃 𝐿 sin 𝜃

=^0

Solve Equations of Equilibrium −𝑊

sin 𝜃 + 𝑁( 𝐿 sin 𝜃 − 𝜇&𝑁( 𝐿 cos 𝜃 = 0

:

sin 𝜃 +

:

• 1 𝐿 sin 𝜃 − 𝜇&

:

• 1 𝐿 cos 𝜃 = 0

Solve Equations of Equilibrium −

tan 𝜃 +

:

• 1 tan 𝜃 −

:

• 1

Divide both sides by 𝑊𝐿 cos 𝜃 (recall that CDE F GHC F = tan 𝜃) −

:

• 1 tan 𝜃 =

:

• 1 𝜇& = 0. 35 tan 𝜃 =

𝜃 = tan

PQ

sin 𝜃 +

:

• 1 𝐿 sin 𝜃 − 𝜇&

:

• 1 𝐿 cos 𝜃 = 0