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