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

1 Answer
Mar 14, 2018

Answer:

The work is #=523.1J#

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+3)#

The normal force is #N=mg#

The mass of the object is #m=1kg#

#F_r=mu_k*mg#

#=1*(e^x-x+3)g#

The work done is

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

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

#=1g((e^4-8+12)-(e^1-1/2+3))#

#=1g(e^4-e+3/2)#

#=523.1J#