# Coefficients of Friction for Aluminum

Friction is the force between two surfaces in contact that opposes motion or intended motion. Friction can be found by using

*f* = *µF _{n}*

where µ is the coefficient of friction and *N* is the normal force.

In order to calculate the static coefficient of friction (µ_{s}), the angle of an inclined plane was increased gradually until the object first
begins to slide downward. At that angle, the weight of the object (*F _{g}*) would have succeeded in overcoming the force of static friction (

*f*). Using trigonometry, it can be shown that …

_{s}*f _{s}* =

*F*sin θ

_{g}until the time when the object begins to slip. Therefore …

µ_{s}*F _{n}* =

*F*sin θ

_{g}The normal force (*F _{n}*) that the object exerts on the plane surface is equivalent to the weight of
the object perpendicular to the plane …

*F _{n}* =

*F*cos θ

_{g}Substituting into the previous equation will produce a new equation …

µ_{s} = tan θ

helpful for determining the coefficient of static friction, with the angle of the inclined plane being an important component.

Procedure:

- Setup equipment as shown as in the diagram. (The ramp is covered in aluminum foil)
- Place an object of any material (ex. penny = copper) at the top of the board, which is initially level.
- Lift board up on one end, pivoting it on the table, until the the object starts slipping.
- Determine the parallel component of the acceleration due to gravity using Logger Pro.

LoggerPro determined the acceleration due to gravity parallel to the ramp. Using trigonometry we can determine the angle of inclination …

*sin θ* = *g _{parallel}*/

*g*

*θ*= sin

^{-1}(

*g*/

_{parallel}*g*)

Material | g (m/s_{parallel}^{2}) |
θ (°) | µ_{static} |
---|---|---|---|

Plastic | 3.67 | 21.9 | 0.40 |

Cardboard | 3.9 | 23.45 | 0.43 |

Leather | 6.75 | 43.53 | 0.95 |

Copper | 4.84 | 29.59 | 0.57 |

Leo Tam, Jenny Hua, Stephanie Ma -- 2005

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