Static and kinetic friction.
Version: 0.2 10-27-06

m_s = coefficient of static friction; m_k = coefficient of kinetic friction; m = mass of block; g = acceleration due to gravity.

m_s=1.4,m_k=1.1,m=1,g=3

F_A = applied force; F_F = friction force; F_N = normal force

f=slider([0,8])

F_A=vector(f,0)

vector(1.5,1),vector(1.5,1)+F_A

F_N=m*g

function(F_F,x)=branch(if(x,x<m_s*F_N),if(m_k*F_N,x>m_s*F_N))

vector(-1.5,1),vector(-1.5,1)-vector(function(F_F,f),0)

function(F_F,prime(x))

if(function(F_F,prime(x)),prime(x)<f)

Block and surface:

[x/1.5]^40+[y-1]^40=1

y=0

Block accelerates when applied force exceeds maximum static friction:

function(G,x)=0.05*[cos(10*x)]^2

function(X,x,a)=branch(if(function(G,x)-0.05,a<m_s*F_N),if(function(G,x+[1/(200*m)*[f-(m_k*F_N)]]*n^2)-0.05,a>m_s*F_N))

function(X,x,f)



Author: David A. Craig <http://web.lemoyne.edu/~craigda/>

Graph of the formula

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