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8 FrictionIn many applications movement of objects over surfaces causes resistance due to friction. Reactions due to friction may also prevent movement completely. Hence, analysis of friction is an important part of mechanical analysis.

Type of surfaces:• Ideal (smooth) – contact force is normal.• Real (rough) – contact force has normal and tangential

components.

Friction Force

Friction force is the tangential component of the contact force.

Direction of friction force is opposite to sliding tendency.

Friction force is universal – any real contact has friction.

Example of Importance: at least one third of car fuelconsumption is spent on overcoming friction (http://phys.org/news/2012-01-one-third-car-fuel-consumption-due.html)

Effects of friction are generally negative:1. Prevents or slows motion

2. Induces loss of energy though heat dissipation

3. Wear of surfaces

Use of Friction

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While generally friction is sought to be minimized, there are applications where it is used:

1. Brakes, clutches, belt drives, wedges.

2. Heating by friction (earlier fire!).

3. Polishing (sand paper).

Types of friction• Dry – two sliding surfaces• Fluid – between layers moving at different velocities• Internal – during plastic deformation in solids.

Theory of Dry FrictionExperimental analysis:

As the P is increased, F is observed and two stages are apparent:

i. No sliding, static:

𝐅=𝐏 𝐚𝐧𝐝 𝐢𝐧𝐝𝐞𝐩𝐞𝐧𝐝𝐞𝐧𝐭 𝐨𝐟 𝐍F≤ Fmax=μs∗Nμs- static coefficient of friction

ii. Sliding, kinetic:Velocity increases with P!F k=constant (P )=μkN

-Kinetic friction, μk-kinetic coefficient of friction, μk<μsNote: both friction constants are material properties and depend on properties of the two surfacesPhysical Mechanism – friction is the result of interaction between asperities of rough surfaces.

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i. Close contact, at shallower angles, more horizontal:ii.

Sliding, means some elevation of the upper surface; contacts are more superficial; movement at steeper angles (horizontal components are smaller).

Effects of normal forceN 1<N2

As long as P<F 'max

There is no effect of the difference in the normal force

Dependency on Area

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=

F=∫ f∗dAFmax=∫ f max∗dA=∫ μs∗n∗dA=μs∫n∗dA=μ

s∗N

Fmax¿μs∗N

True for any contact area!

Note: f, n will, however be different, depending on the contact area

Angles of Friction

ϕ – Angle of friction

tan (φ )= FN

At impending motion F=Fmax, tan (φs )=

FmaxN

=μs

ϕs – Angle of static friction

When sliding occurs F=F k:

tan (φk )=F kN

=μk (kinetic)

Block on Inclined SurfaceIncrease angle till slippage occurs. Then, impeding motion: θ s- angle of repose

FNf

n

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N=Wcos (θs )F s=Wsin (θ s )

⇒ tan (θs )=F sN

=tan (φ s )⇒θs=φs

Can be used to measureμs:

μs=tan (θs )=tan(φs)

When slippage occurs, angles can be decreased a little, giving us the minimum angle θk. Similarly to before θk=φ k. Coefficient of kinetic friction can also be measured using:

μk=tan (θk)=tan(φk)

This experiment provides direct physical interpretation of angles of friction.

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Types of problems

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Example 1

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Example 2

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Example 3

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Example 4

Example 5

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Example 6

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Example 7

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Example 8

Example 9