An object with a mass of $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= 1+cotx$ . How much work would it take to move the object over #x in [(pi)/4, (3pi)/8], where x is in meters?

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Answer 1 · 2017-09-03T07:08:37

The work is $=38.8J$

We need

$intcotxdx=ln|sin(x)|+C$

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 $m=6kg$

$F_r=mu_k*mg$

$=6*(1+cotx)g$

The work done is

$W=6gint_(1/4pi)^(3/8pi)(1+cotx)dx$

$=6g*[x+ln|sin(x)|]_(1/4pi)^(3/8pi)$

$=6g(3/8pi+ln|sin(3/8pi)|-1/4pi-ln|sin(1/4pi)|)$

$=6g(0.66)$

$=38.8J$

An object with a mass of 6 kg6 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 1+cotx u_k(x)= 1+cotx . How much work would it take to move the object over #x in [(pi)/4, (3pi)/8], where x is in meters?