An object with a mass of $7 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= 4+secx$ . How much work would it take to move the object over #x in [(-5pi)/12, (pi)/6], where x is in meters?

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Answer 1 · 2017-09-30T06:42:52

The work is $=679.83J$

We need

$intsecxdx=ln(tanx+secx)+C$

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 $m=7kg$

$F_r=mu_k*mg$

$=7*(4+secx)g$

The work done is

$W=7gint_(-5/12pi)^(1/6pi)(4+secx)dx$

$=7g*[4x+ln(tanx+secx)]_(-5/12pi)^(1/6pi)$

$=7g(4/6pi+ln(tan(pi/6)+sec(pi/6))-(-20/12pi+ln(tan(-5/12pi)+sec(-5/12pi))$

$=7g(9.91)$

$=679.83J$

An object with a mass of 7 kg7 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 4+secx u_k(x)= 4+secx . How much work would it take to move the object over #x in [(-5pi)/12, (pi)/6], where x is in meters?