Friction

#### Coefficient of friction

• The coefficient of friction($\mu$) is the ratio of the friction force compared to the normal reaction.
• That is:
(1)
\begin{align} \mu = \frac{Fr}{N} \end{align}
(2)
\begin{align} \therefore Fr = \mu N \end{align}
• It can be found by finding the angle of repose($\theta_R$) (see below) in that:
(3)
\begin{align} \mu = \tan{\theta_R} \end{align}

#### Normal Reaction

• This is the force that always acts perpendicular to the surface of the object.
• It is a reaction to all the forces in that direction (see right for example)
• In a general case (top picture), it can usually be found through
(4)
\begin{align} N = mg\cos{\theta} \end{align}

#### Friction

• Friction can usually found using this value $Fr = \mu N$
• It always opposes the direction of motion

NB: Be very careful that one does not treat the weight's sliding force ($mg\sin{\theta}$) as friction, nor ignore it.

#### Limiting friction

• This is the frictional resistance just as the object is about to move.
• It is what determines the angle of repose

#### Angle of Static Friction/Repose

• The angle of static friction ($\phi_s$) is the angle to the normal reaction that the resultant of the Friction and the normal makes.
• When the limiting friction is used, this angle is known as the angle of repose($\theta_R$) and will equal the angle of inclination($\theta$).
page revision: 1, last edited: 04 Oct 2011 12:04
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.970207154750824, "perplexity": 1431.1373059192056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945584.75/warc/CC-MAIN-20180422100104-20180422120104-00592.warc.gz"}