An object with a mass of #6 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 2+cscx #. How much work would it take to move the object over #x in [pi/4, (3pi)/4], where x is in meters?

1 Answer
Dec 22, 2017

Answer:

The work is #=288.1J#

Explanation:

We need

#intcscxdx=ln|tan(x/2)|+C#

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=6kg#

#F_r=mu_k*mg#

#=6*(2+cscx)g#

The work done is

#W=6gint_(1/4pi)^(3/4pi)(2+cscx)dx#

#=6g*[2x+ln|tan(x/2)|]_(1/4pi)^(3/4pi)#

#=6g((3/2pi+ln|tan(3/8pi)|+sec(pi/6))-(1/2pi+ln|tan(pi/8)|)#

#=6g(*4.9)#

#=288.1J#