An object with a mass of #5 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= e^x+x #. How much work would it take to move the object over #x in [3, 4], where x is in meters?

1 Answer
Feb 27, 2018

Answer:

The work done is #=1862.5J#

Explanation:

#"Reminder : "#

#inte^xdx=e^x+C#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

The coefficient of kinetic friction is #mu_k=(e^x+x)#

The normal force is #N=mg#

The mass of the object is #m=5kg#

#F_r=mu_k*mg#

#=5*(e^x+x)g#

The work done is

#W=5gint_(3)^(4)(e^x+x)dx#

#=5g*[e^x+x^2/2]_(3)^(4)#

#=5g((e^4+8)-(e^3+9/2))#

#=5g(38.01)#

#=1862.5J#