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

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Answer 1 · 2017-05-15T12:25:47

The work is #=867.69J#

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+sinx)g#

The work done is

#W=5gint_(0)^(5pi)(1+sinx)dx#

#=5g*[x-cosx]_(0)^(5pi)#

#=5g((5pi+1)-(0-1))#

#=5g(2+5pi)#

#=5g*17.71#

#=867.69J#