An object with a mass of #7 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 3+2sin(x) #. 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 · 2017-10-21T06:14:08

The work is #=1665J#

We need

#intsinxdx=-cosx+C#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

The normal force is #N=mg#

The mass is #m=7kg#

#F_r=mu_k*mg#

#=7*(3+2sinx)g#

The work done is

#W=7gint_(pi)^(4pi)(3+2sinx)dx#

#=7g*[3x-2cosx]_(pi)^(4pi)#

#=7g(12pi-2cos(4pi))-(3pi-2cospi)#

#=7g(9pi-2-2)#

#=7g(9pi-4)#

#=1665J#

The value of #g=9.8ms^-2#