# Friction

## Overview

• An equal and opposite force created when an object is slid across a surface
• Dependant on
• the normal force (usually the mass of the object)
• the co-efficient of friction (μ,"mu") between the surface and the object
• μ is an experimental value, when comparing the μ of different materials, it is best to test yourself
• The published μ for 2009 wheels was no found to be the actual value
• Two different co-efficients of friction depending if the object is already moving (kinetic) or not (static)
• You may have noticed when trying to slide a heavy object, it's really hard to get started, but once it starts moving, it's easy to continue moving

## Forces

• F = applied force
• The amount of force used to try and move the object across the surface
• Fg = gravitational force of object (Fg = m · g)
• The mass of the object multiplied by gravitational acceleration
• Fg = m · g
• g = 9.81ms2
• = 32.2fts2
• FF = friction force
• The amount of force the object and surface are resisting due to friction
• FN = normal force
• the amount of force the surface is providing to support the object ## Example

• General friction force equation
• FF = μ · FN
• In this example, Fg = FN
• FF = μ · m · g
• Static co-efficient of friction between wet concrete and rubber
• μstatic ≅ 0.3
• Assume rubber object weights 50 lbs
• FF = μstatic · m · g
• FF = 0.3 · 50 lbs = 15 lbs
• FF = 0.3 · 22.7 kg · 9.81 ms2 = 66.8 N
• In order to move this object, you must apply a force greater than 15 lbs or 66.8 N ## Testing Friction

• Testing static co-efficient of friction
• Place object on surface of interest material
• ie. place wheels on FRC carpet (or terrian for specific game)
• Increase the angle of the surface until the object begins to slide
• Ensure object cannot roll on surface
• Record the angle (θ, "theta") at which the object begins to slide
• μstatic = tanθ
• When the object begins to slide
• FN = Fg · sinθ
• Recall the general friction equation
• FF = μ · FN
• In this example, FN = Fg · cosθ
• μstatic = FgFg · sinθcosθ
• μstatic = tanθ ## Review of important equations

• Relationship between linear and angular velocity
• v = ω · π · D
• Relationship between torque and force
• τ = F · d
• Relating angular velocity, torque, and tooth count
• ω1ω2 = N2N1
• τ1τ2 = N1N2
• τ1τ2 = ω2ω1
• Friction force equation
• FF = μ · FN
• Measuring static co-efficient of friction
• μstatic = tanθ