An object with a mass of #4 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 5+tanx #. How much work would it take to move the object over #x in [(pi)/12, (pi)/3]#, where x is in meters?

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Answer 1 · 2017-05-31T08:18:40

The work is #=179.75J#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

#N=mg#

#F_r=mu_k*mg#

#=4(5+tanx))g#

The work done is

#W=4gint_(1/12pi)^(1/3pi)(5+tanx)dx#

#=4g*[5x-ln|cosx|)]_(1/12pi)^(1/3pi)#

#=4g((5/3pi-ln|cos(1/3pi)|)-(5/12pi-ln|cos(1/12pi)|))#

#=4g(5/4pi+ln2+ln(cos(1/12pi))#

#=4g(5/4pi+ln2(cos(1/12pi)))#

#=4g*4.59J#

#=179.75J#