An object with a mass of #8 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= x^2+3x #. How much work would it take to move the object over #x in [2, 6], where x is in meters?

1 Answer
Jun 19, 2017

Answer:

The work is #=9199J#

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(x^2+3x)g#

The work done is

#W=8gint_(2)^(6)(x^2+3x)dx#

#=8g*[1/3x^3+3/2x^2]_(2)^(6)#

#=8g((1/3*6^3+3/2*6^2)-(1/3*2^3+3/2*2^2))#

#=8g(72+54-8/3-6)#

#=8g*352/3#

#=9199J#