An object with a mass of #5 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 1-cos(x/3) #. How much work would it take to move the object over #x in [0, 8pi], where x is in meters?

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Answer 1 · 2017-05-29T06:22:02

The work is #=1104.2J#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

#N=mg#

#F_r=mu_k*mg#

#=5(1-cos(x/3))g#

The work done is

#W=5gint_(0)^(8pi)(1-cos(x/3))dx#

#=5g*[x-3sin(x/3)]_(0)^(8pi)#

#=5g((8pi-3sin(8/3pi))-(0-0))#

#=5g(8pi-3/2sqrt3)#

#=1104.2J#