An object with a mass of #8 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 2x^2-x+7 #. How much work would it take to move the object over #x in [2, 3], where x is in meters?

1 Answer
Jul 11, 2017

Answer:

The work is #=1009.4J#

Explanation:

We need

#intx^ndx=x^(n+1)/(n+1)+C(n!=-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=8kg#

#F_r=mu_k*mg#

#=8(2x^2-x+7)g#

The work done is

#W=8gint_(2)^(3)(2x^2-x+7)dx#

#=8g*[2/3x^3-1/2x^2+7x]_(2)^(3)#

#=8g((18-9/2+21)-(16/3-2+14))#

#=8g(27-59/6)#

#=6g(103/6)#

#=1009.4J#