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+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 · 2017-05-23T13:48:17

The work is #=408.3J#

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+2)g#

The work done is

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

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

#=5g((9+6)-(8/3+4))#

#=5g(15-20/3)#

#=5g*25/3#

#=408.3J#