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, 3], where x is in meters?

1 Answer
Aug 24, 2017

Answer:

The work is #=1084.5J#

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)^(3)(x^2+3x)dx#

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

#=8g((9+27/2)-(8/3+6))#

#=8g(3+65/6)#

#=1084.5J#