1  

                               

By:    Ece  Fulya  ERDEN  −  11-­‐154-­‐034  

               Canan  PİR  −  11-­‐154-­‐062  

 

   

     

 

 

   

 

 

To:          Mersin  University  Food  Engineering  Department  

Prof.  Dr.  Mahir  TURHAN  

Fall   ‘13  

Determination  of  Coefficient  of  Friction  

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Table  of  Content  

DETERMINATION  OF  COEFFICIENT  OF  FRICTION .......................................... 3  FRICTION................................................................................................................................................ 3  Kinetic  Friction.....................................................................................................................................3  Static  Friction .......................................................................................................................................3  

Determining  the  Static  Coefficient  of  Friction ........................................................................ 4  Determining  the  Kinetic  Coefficient  of  Friction..................................................................... 5  METHOD ................................................................................................................................................. 5  Static  Coefficient  of  Friction...........................................................................................................5  Kinetic  Coefficient  of  Friction ........................................................................................................7  

Bibliography................................................................................................ 9  

 

 

 

 

 

 

 

 

 

 

 

   

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DETERMINATION  OF  COEFFICIENT  OF  FRICTION  

FRICTION  

When  two  surfaces  touch,  they  exert  forces  on  each  other.  Friction  is  the  resisting  force  encountered  when  one  tries  to  slide  (static)  or  does  slide  (kinteic)  one  surface  over  another.  This  force  acts  parallel  to  the  surfaces  in  contact.  The  force  necessary   to  overcome   friction  depends  on   the  nature  of   the  materials   in  contact,   their   roughness   or   smoothness,   and   on   the   normal   force.  Experimentally,   the   force   of   friction   is   found   to  be  directly  proportional   to   the  normal   force.   The   ratio   of   the   frictional   force   to   the   normal   force   is   called  coefficient  of  friction  (μ).  

                                                                                                   

μ:  Coefficient  of  friction  f  :  Frictional  force  

FN:  Normal  force                                                                                                  

Kinetic  Friction  

Kinetic   friction   is   the   friction  between  surfaces   in  relative  motion.  When  sliding  an  object  across  another  surface,  small  bumps  or  defects  tend  to  resist  the  motion   (even   the   smoothest   surfaces   are   rough   on   the  microscopic   scale).  We  can  say  that  kinetic  friction  is  the  type  of  force  that  brings  rolling  ball  to  rest  or  coasting  car  to  a  stop.    

Experimentally,   it   is   observed   that   the   force   of   kinetic   friction   is  proportional   to   the  normal   force  acting  between   the   surfaces.  Therefore   if   you  increase  the  normal  force,  the  surfaces  are  crushed  more  together,  increasing  the  contact   area,   and   thus   increasing   frictional   force.  Mathematically  we   can  write  the  force  of  kinetic  friction  as;  

                                                                                                 The  coefficient  of  kinetic   friction   (μk)   is  a  dimensionless  quality,   and   it  

only   depends   on   the   properties   of   two   surfaces.   μk   ranges   from   0.01   (very  smooth  surfaces)  to  1.5  (very  rough  surfaces).  

Static  Friction  

Static  friction  (fs) acts  when  two  surfaces  are  at  rest  relative  to  each  other  and   resists   any   sliding.   It   is   a   bonding   force   that   tries   to   keep   the   surfaces  together.  The  direction  of  static  force  is  opposite  to  that  of  any  external  force  that  tries   to   make   the   surfaces   move.   Up   to   certain   limit,   the   magnitude   of   static  friction  remains  equal  to  the  external  forces,  so  that  the  net  force  on  the  surfaces  remain  zero  which  keeps   the   surfaces   still.  The   static   friction  between   the   two  surfaces  is  described  by  the  coefficient  of  static  friction  (μs).    

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Experimentally,  it  is  found  that  the  maximum  value  for  the  static  frictional  force   is  proportional   to   the  normal   force  between  two  surfaces.  Thus  the  static  frictional  force  Fs  is;  

                                                   Since  in  this  case,  the  objects  are  at  rest  with  one  another,  more  molecular  

bonds   are   able   to   form   and   this  makes   the   object   harder   to  move.   So,   greater  force  will  be  needed  to  start  motion  when  compared  to  the  kinetic  friction  case.  Therefore  μs  is  generally  greater  than  μk.    

1  Figure  1:  Force  of  friction  (fr)  as  a  function  of  an  external  force  F  applied  to  an  object  that  is  

initally  at  rest.  

Figure  1  shows  that;  as  you  increase  the  force,  the  static  friction  force  will  increase   linearly   until   the   applied   force   F   equals   to   μsFN.   After   this   point   the  object  “breaks  away”  and  the  friction  force  falls  to  the  kinetic  friction  value.  

Determining  the  Static  Coefficient  of  Friction    

The   one   way   of   determining   the   static   coefficient   of   friction   is   limiting  angle  repose  method.  The  principle    of   this  method   is;  we  put   the  block  on  the  plank   and   raise   one   end   of   the   plank   so   that   it   makes   an   angle   θ   with   the  horizontal.    When  the  angle  is  large  enough,  the  block  will  slide  down  the  incline.  

     Diagram  1  

                                                                                                               1http://www.iit.edu/csl/phy/resources/pdfs/2013_physics_123_friction_

lab.pdf  

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      Diagram  1  

The  installation  of  the  experiment  will  be  like  Diagram  2.  At  an  angle  just  before   the  block  begins   to  slide  (called   the   limiting  angle  of   repose),   the   forces  are  still  balanced  and  we  have:  

        and      

When  we  take  the  ratio  of  these  two,  we  will  be  left  with:  

       

 

Determining  the  Kinetic  Coefficient  of  Friction  

In   our   experiment   we   will   first   determine   the   coefficients   of   static   and  kinetic  friction  between  two  wanted  surfaces.  Diagram  1  illustrates  the  set-­‐up  we  will  use.    The  block  (m)  is  our  sample,  it  can  be  in  any  geometrical  shape.  To  find  the  magnitude  of  kinetic  friction,  we  change  the  angle  from  horizontal  until  the  sample  begins   to  move  at   constant   speed.  While  doing   this  we  need   to   tap   the  surface  just  to  be  able  to  give  that  firt  push  so  we  can  neglect  static  coefficient  of  friction.    

The  calculations  will  be  same  as   the     calculations   for  static  coefficient  of  friction.  

METHOD  

Static  Coefficient  of  Friction  

 Diagram  2  

1. Set  up  the  apparatus  shown  above.  (Diagram  2)  

2. Measure   the  mass  of   the  sample  and  record   it  as   “m”   in   the  chart  

provided  below.  (Table  1)  

3. Increase  the  angle  of  the  ramp  slowly  until  the  sample  just  begins  

to  slip.  

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 Diagram  3  

4. Measure  the  angle  θ  with  protractor  and  record  it  as  θ(degree)  in  

the  chart  provided  below.  (Table  1)  

5. Repeat   this  process  5   times  with   the  same  amount  of   sample  and  

record  the  angles  as  θ(degree)  in  the  chart  provided  below.  (Table  

1)  

6. Insert   the   “m”   values   to   the   equation   below   to   find   “W”   (N)   and  

record  the  result  in  the  chart  provided  below  (Table  1)                            

        W=m  ×  g  

7. Insert   the  W   calculated   above   to   the   equations  below  and   record  

the   result   in   the   chart   provided   below   (Table   1)   as   Wx   and   Wy  

respectively.    

          Wx    =  W  ×  sinθ  

          Wy    =  W  ×  cosθ  

8. Using  the  Wx  and  Wy  calculated,  calculate  the  μs  (coefficient  of  static  

friction)  with   equation  below  and   record   it   in   the   chart   provided  

below  (Table  1)  as  μs.                                                                                  

        μs  =    Wx/Wy  

9. Take   the  average  of  μs     and  record   it   in   the  chart  provided  below  

(Table  1)  as  μs  ave.  

 

 

 

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m  (kg)   W  (N)   θ  (degree)   Wx   Wy   μs  

           

           

           

           

           

        μs  ave    

Table  1  

 

Kinetic  Coefficient  of  Friction  

1. Set  up  the  apparatus  shown  above.  (Diagram  2)  

2. Measure   the  mass  of   the  sample  and  record   it  as   “m”   in   the  chart  

provided  below.  (Table  2)  

3. While  tapping  on  the  ramp  with  your   finger   increase  the  angle  of  

the  ramp  slowly  until  the  sample  just  begins  to  slip.  

4. Measure  the  angle  θ  with  protractor  and  record  it  as  θ(degree)  in  

the  chart  provided  below.  (Table  2)  

5. Repeat   this  process  5   times  with   the  same  amount  of   sample  and  

record  the  angles  as  θ(degree)  in  the  chart  provided  below.  (Table  

2)  

6. Insert   the   “m”   values   to   the   equation   below   to   find   “W”   (N)   and  

record  the  result  in  the  chart  provided  below  (Table  2)                            

        W=m  ×  g  

7. Insert   the  W   calculated   above   to   the   equations  below  and   record  

the   result   in   the   chart   provided   below   (Table   2)   as   Wx   and   Wy  

respectively.    

          Wx    =  W  ×  sinθ  

          Wy    =  W  ×  cosθ  

8. Using   the   Wx   and   Wy   calculated,   calculate   the   μk   (coefficient   of  

kinetic   friction)   with   equation   below   and   record   it   in   the   chart  

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provided  below  (Table  2)  as  μk.                                                                                  

        μk  =    Wx/Wy  

9. Take   the  average  of  μk    and  record   it   in   the  chart  provided  below  

(Table  2)  as  μk  ave.  

m  (kg)   W  (N)   θ  (degree)   Wx   Wy   μk  

           

           

           

           

           

        μk  ave    

Table  2  

                                       

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Bibliography    Curtis,   John.   Friction.   Rep.   Missisippi   College,   n.d.   Web.   Dec.   2013.  

<http://www.mc.edu/academics/departments/physics/files/8413/2163/3128/PHY251L_Friction.pdf>.  

 Blau,  P.  J.  Friction  Science  and  Technology:  From  Concepts  to  Applications.  

Boca  Raton,  FL:  CRC,  2009.  Print.    "Lab   5."   FrictionLab.   Penn   State   University,   n.d.   Web.   Nov.   2013.  

<http://www.personal.psu.edu/bqw/physics_150/phy_150_4/FrictionLab2.html>.  

 Duffy,   Andrew.   "Measuring   Friction."   Boston   University,   n.d.   Web.   Dec.  

2013.  <http://physics.bu.edu/~duffy/semester1/c6_measuremus.html>.    Rabinowicz,   Ernest.   "The   nature   of   the   static   and   kinetic   coefficients   of  

friction."  Journal  of  applied  physics  22.11  (1951):  1373-­‐1379.    Berthoud,   P.,   et   al.   "Physical   analysis   of   the   state-­‐and   rate-­‐dependent  

friction  law:  Static  friction."  Physical  review  B  59.22  (1999):  14313.