Coefficient of kinetic friction Steel on Steel

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Coefficient of Kinetic friction is the ratio of friction force that arises when there is relative motion between the bodies, to the compressive force that acts on the body normally.
 
Let two steel block kept one over another and the upper block is moving towards right, over the lower steel block.

The coefficient of friction is given by      µ =   f/ R    ,  f is friction force and  R isa normal reactionn exerted by the lower block on the upper steel block.  
 
By Newton’s third law,     mg  =  R
 
Also can write,            µk   = f/mg,      where R is mg, Notice here that I add subscript to represent the coefficient of kinetic friction.
 
The force of friction arises when we try to move the body with respect to any other surface or body in contact.
 
The force of kinetic friction comes into play when the body starts moving unless the friction is said to be static friction or limiting friction.
 
The friction force always acts tangentially to the surface in contact between the bodies.  & the weight of the body is normal compressive force.   
 
Example1. Calculate force of friction between the moving two block, as shown in the fig. If the upper block is of mass m 5 kg. where µ the coefficient of kinetic friction between steel and steel is 0.42  
 
Solution:    As we know,          µk =   f/ R  =   f/mg 
                                   0.42 =   f/ 5×10                so that  f = 21 N
 
Example 2.  Find  out µk if R is  250 N and f is 105 N. These data are for two heavy blocks of moving steel.
 
Solution:                           µk     =   f/R  on substituting we get   µk  = 0.42
 
 
Thus these two examples are given to find out the µk for steel manually.

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