An object with a mass of #3 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= e^x-2x+3 #. How much work would it take to move the object over #x in [1, 4], where x is in meters?

1 Answer
Apr 16, 2018

Answer:

The work is #=1348.9J#

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-2x+3)#

The normal force is #N=mg#

The mass of the object is #m=3kg#

#F_r=mu_k*mg#

#=3*(e^x-2x+3)g#

The work done is

#W=3gint_(1)^(4)(e^x-2x+3)dx#

#=3g*[e^x-x^2+3x ] _(1)^(4)#

#=3g((e^4-16+12)-(e-1+3))#

#=3xx9.8xx45.88#

#=1348.9J#