An object with a mass of #5 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= x+2 #. How much work would it take to move the object over #x in [2, 3], where x is in meters?

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Answer 1 · 2017-06-01T08:43:26

The work is #=220.5J#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

#N=mg#

#F_r=mu_k*mg#

#=5(x+2))g#

The work done is

#W=5gint_(2)^(3)(x+2)dx#

#=5g*[x^2/2+2x]_(2)^(3)#

#=5g((9/2+6)-(4/2+4)#

#=5g(21/2-6)#

#=5g(9/2)#

#=45/2gJ#

#=220.5J#