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/6, (3pi)/4], where x is in meters?

Question

1452 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-08T06:36:58

The work is $=344.57J$

$"Reminder : "$

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

The work done is

$W=F*d$

The frictional force is

$F_r=mu_k*N$

The coefficient of kinetic friction is $mu_k=(2+csc(x))$

The normal force is $N=mg$

The mass of the object is $m=6kg$

$F_r=mu_k*mg$

$=6*(2+csc(x))g$

The work done is

$W=6gint_(1/6pi)^(3/4pi)(2+csc(x))dx$

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

$=6g(3/2pi+ln(tan(3/8pi)))-(1/3pi+ln(tan(1/12pi))$

$=6g(5.86)$

$=344.57J$

An object with a mass of 6 kg6 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 2+cscx u_k(x)= 2+cscx . How much work would it take to move the object over #x in [pi/6, (3pi)/4], where x is in meters?