An object with a mass of #3 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= x^2-3x+6 #. How much work would it take to move the object over #x in [1, 3], where x is in meters?

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Answer 1 · 2016-07-12T12:39:51

We know that the work done against variable frictional force is

#w=int_1^3mu_k(x)mgdx#

#=mgint_1^3(x^2-3x+6)dx#

#=mg[1/3*x^3-3/2*x^2+6x]_1^3#

#=3*9.8[(1/3*3^3-3/2*3^2+6*3)-(1/3*1^3-3/2*1^2+6*1)#
#=29.4*(13.5-4.8)=255.78J#