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 #. How much work would it take to move the object over #x in [2, 3], where x is in meters?

1 Answer
Oct 28, 2017

Answer:

The work is #=797.1J#

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)g#

The acceleration due to gravity is #g=9.8ms^-2#

The work done is

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

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

#=8g(2/3*3^3-9/2))-(2/3*8-2)#

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

#=8g(20-59/6)#

#=797.1J#