An object with a mass of #7 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 3+sin(4x) #. How much work would it take to move the object over #x in [pi, 4pi], where x is in meters?

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Answer 1 · 2017-05-13T09:44:17

The work done is #=1939.62J#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

#N=mg#

#F_r=mu_k*mg#

#=7(3+sin4x)g#

The work done is

#W=7gint_(pi)^(4pi)(3+sin4x)dx#

#=7g*[3x-1/4cos4x]_(pi)^(4pi)#

#=7g((12pi-1/4)-(3pi-1/4))#

#=7g(9pi)#

#=7g*28.27#

#=1939.62J#