# 0.7 3.8 friction  (Page 2/10)

 Page 2 / 10 Frictional forces, such as f size 12{f} {} , always oppose motion or attempted motion between objects in contact. Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view. In order for the object to move, it must rise to where the peaks can skip along the bottom surface. Thus a force is required just to set the object in motion. Some of the peaks will be broken off, also requiring a force to maintain motion. Much of the friction is actually due to attractive forces between molecules making up the two objects, so that even perfectly smooth surfaces are not friction-free. Such adhesive forces also depend on the substances the surfaces are made of, explaining, for example, why rubber-soled shoes slip less than those with leather soles.

The magnitude of the frictional force has two forms: one for static situations (static friction), the other for when there is motion (kinetic friction).

When there is no motion between the objects, the magnitude of static friction ${\mathbf{f}}_{\text{s}}$ is

${f}_{s}\le {\mu }_{s}N,$

where ${\mu }_{\text{s}}$ is the coefficient of static friction and $N$ is the magnitude of the normal force (the force perpendicular to the surface).

## Magnitude of static friction

Magnitude of static friction ${f}_{\text{s}}$ is

${f}_{\text{s}}\le {\mu }_{\text{s}}N,$

where ${\mu }_{\text{s}}$ is the coefficient of static friction and $N$ is the magnitude of the normal force.

The symbol $\le$ means less than or equal to , implying that static friction can have a minimum and a maximum value of ${\mu }_{\text{s}}N$ . Static friction is a responsive force that increases to be equal and opposite to whatever force is exerted, up to its maximum limit. Once the applied force exceeds ${f}_{\text{s}\left(\text{max}\right)}$ , the object will move. Thus

${f}_{\text{s}\left(\text{max}\right)}={\mu }_{\text{s}}N.$

Once an object is moving, the magnitude of kinetic friction ${\mathbf{f}}_{\text{k}}$ is given by

${f}_{\text{k}}={\mu }_{\text{k}}N,$

where ${\mu }_{\text{k}}$ is the coefficient of kinetic friction. A system in which ${f}_{\text{k}}={\mu }_{\text{k}}N\phantom{\rule{0.25em}{0ex}}$ is described as a system in which friction behaves simply .

## Magnitude of kinetic friction

The magnitude of kinetic friction ${f}_{\text{k}}$ is given by

${f}_{\text{k}}={\mu }_{\text{k}}N,$

where ${\mu }_{\text{k}}$ is the coefficient of kinetic friction.

As seen in [link] , the coefficients of kinetic friction are less than their static counterparts. That values of $\mu$ in [link] are stated to only one or, at most, two digits is an indication of the approximate description of friction given by the above two equations.

Coefficients of static and kinetic friction
System Static friction ${\mu }_{\text{s}}$ Kinetic friction ${\mu }_{\text{k}}$
Rubber on dry concrete 1.0 0.7
Rubber on wet concrete 0.7 0.5
Wood on wood 0.5 0.3
Waxed wood on wet snow 0.14 0.1
Metal on wood 0.5 0.3
Steel on steel (dry) 0.6 0.3
Steel on steel (oiled) 0.05 0.03
Teflon on steel 0.04 0.04
Bone lubricated by synovial fluid 0.016 0.015
Shoes on wood 0.9 0.7
Shoes on ice 0.1 0.05
Ice on ice 0.1 0.03
Steel on ice 0.4 0.02

The equations given earlier include the dependence of friction on materials and the normal force. The direction of friction is always opposite that of motion, parallel to the surface between objects, and perpendicular to the normal force. For example, if the crate you try to push (with a force parallel to the floor) has a mass of 100 kg, then the normal force would be equal to its weight, $W=\mathrm{mg}=\left(\text{100 kg}\right)\left(9\text{.}\text{80}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)=\text{980 N}$ , perpendicular to the floor. If the coefficient of static friction is 0.45, you would have to exert a force parallel to the floor greater than ${f}_{\text{s}\left(\text{max}\right)}={\mu }_{\text{s}}N=\left(0.45\right)\left(\text{980}\phantom{\rule{0.25em}{0ex}}\text{N}\right)=\text{440}\phantom{\rule{0.25em}{0ex}}\text{N}\phantom{\rule{0.25em}{0ex}}$ to move the crate. Once there is motion, friction is less and the coefficient of kinetic friction might be 0.30, so that a force of only 290 N ( ${f}_{\text{k}}={\mu }_{\text{k}}N=\left(0\text{.}\text{30}\right)\left(\text{980}\phantom{\rule{0.25em}{0ex}}\text{N}\right)=\text{290}\phantom{\rule{0.25em}{0ex}}\text{N}$ ) would keep it moving at a constant speed. If the floor is lubricated, both coefficients are considerably less than they would be without lubrication. Coefficient of friction is a unit less quantity with a magnitude usually between 0 and 1.0. The coefficient of the friction depends on the two surfaces that are in contact.

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is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
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William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
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Bhagvanji
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Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
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narayan
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ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
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Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
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Alexandre
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Rafiq
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Damian
How we are making nano material?
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What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
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Mahi
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Rafiq
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Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
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