6.1: Dry Friction
- Page ID
- 50594
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Dry friction is the force that opposes one solid surface sliding across another solid surface. Dry friction always opposes the surfaces sliding relative to one another, and it can have the effect of either opposing motion or causing motion in bodies.
![A training sled, consisting of a wooden platform attached on top of a series of metal rods in contact lengthwise with the ground, is on a grassy field.](https://eng.libretexts.org/@api/deki/files/42419/sled.jpg?revision=1)
![Front view of a helmeted motorcycle rider leaning to their right to perform a right turn.](https://eng.libretexts.org/@api/deki/files/42420/motorcycle.jpg?revision=1)
The most commonly used model for dry friction is coulomb friction. This type of friction can further be broken down into static friction and kinetic friction. These two types of friction are illustrated in the diagram below. First, imagine a box sitting on a surface. A pushing force is applied parallel to the surface and is constantly being increased. A gravitational force, a normal force, and a frictional force are also acting on the box.
![Diagram of a book lying flat on a table, experiencing an applied force pushing it to the right, a friction force pushing it to the left, and an upwards normal force from the table. A graph of the book's magnitude of friction force experienced vs. the magnitude of push force applied, and a combination of words and equations, both show that as the magnitude of the push force increases the friction force magnitude increases to match it, until the point where the friction force magnitude equals the coefficient of static friction times the magnitude of the normal force. Afterwards, the magnitude of friction force drops to stay at a value equal to the coefficient of kinetic friction times the magnitude of the normal force.](https://eng.libretexts.org/@api/deki/files/42421/coulombfriction.png?revision=1)
Static friction occurs prior to the box slipping and moving. In this region, the friction force will be equal in magnitude and opposite in direction to the pushing force itself. As the magnitude of the pushing force increases, so does the magnitude of the friction force.
If the magnitude of the pushing force continues to rise, eventually the box will begin to slip. As the box begins to slip, the type of friction opposing the motion of the box changes from static friction to what is called kinetic friction. The point just before the box slips is known as impending motion. This can also be thought of as the maximum possible static friction force before slipping. The magnitude of the maximum static friction force is equal to the static coefficient of friction times the normal force existing between the box and the surface. This coefficient of friction is a property that depends on both materials and can usually be looked up in tables.
Kinetic friction occurs beyond the point of impending motion, when the box is sliding. With kinetic friction, the magnitude of the friction force opposing motion will be equal to the kinetic coefficient of friction times the normal force between the box and the surface. The kinetic coefficient of friction also depends upon the two materials in contact, but will almost always be less than the static coefficient of friction.
Example \(\PageIndex{1}\)
A 500 lb box is sitting on concrete floor. If the static coefficient of friction is 0.7 and the kinetic coefficient of friction is 0.6:
- What is the friction force if the pulling force is 150 lbs?
- What pulling force would be required to get the box moving?
- What is the minimum force required to keep the box moving once it has started moving?
![A box weighing 500 lbs, on a flat floor. A pulling force towards the right is applied to the middle of the right edge of the box.](https://eng.libretexts.org/@api/deki/files/42422/P1.png?revision=1)
- Solution
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Video \(\PageIndex{2}\): Worked solution to example problem \(\PageIndex{1}\), provided by Dr. Jacob Moore. YouTube source: https://youtu.be/7R7kvKBxUjw.
Example \(\PageIndex{2}\)
A 30 lb sled is being pulled up an icy incline of 25 degrees. If the static coefficient of friction between the ice and the sled is 0.4 and the kinetic coefficient of friction is 0.3, what is the required pulling force needed to keep the sled moving at a constant rate?
![A 25-degree incline slants up and to the left. A sled lies on that incline facing uphill, with a pulling force applied at its front.](https://eng.libretexts.org/@api/deki/files/42423/P2.png?revision=1)
- Solution
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Video \(\PageIndex{3}\): Worked solution to example problem \(\PageIndex{2}\), provided by Dr. Jacob Moore. YouTube source: https://youtu.be/oPMx-SZyiy4.
Example \(\PageIndex{3}\)
A plastic box is sitting on a steel beam. One end of the steel beam is slowly raised, increasing the angle of the surface until the box begins to slip. If the box begins to slip when the beam is at an angle of 41 degrees, what is the static coefficient of friction between the steel beam and the plastic box?
![A box sitting on a steel beam, whose left end has been raised until the beam is inclined at 41 degrees above the horizontal.](https://eng.libretexts.org/@api/deki/files/42424/P3.png?revision=1)
- Solution
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Video \(\PageIndex{4}\): Worked solution to example problem \(\PageIndex{3}\), provided by Dr. Jacob Moore. YouTube source: https://youtu.be/ShGP5rzIHN4.