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

1 Answer
Aug 21, 2017

Answer:

The work is #=254.8J#

Explanation:

We need

#intx^ndx=x^(n+1)/(n+1)+C (x!=-1)#

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=1kg#

#F_r=mu_k*mg#

#=1*(3x^2-x+2)g#

The work done is

#W=gint_(1)^(3)(3x^2-x+2)dx#

#=g*[3x^3/3-x^2/2+2x]_(1)^(3)#

#=g((3^3-9/2+6)-(1-1/2+2))#

#=g(33-3-4)#

#=(26g)J#

#=254.8J#