An object with a mass of $4 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= 1+3cscx$ . How much work would it take to move the object over #x in [(pi)/12, (pi)/4], where x is in meters?

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Answer 1 · 2018-01-15T06:31:58

The work is $=155.2J$

$"Reminder : "$

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

The work done is

$W=F*d$

The frictional force is

$F_r=mu_k*N$

The coefficient of kinetic friction is $mu_k=(1+3csc(x))$

The normal force is $N=mg$

The mass of the object is $m=4kg$

$F_r=mu_k*mg$

$=4*(1+3csc(x))g$

The work done is

$W=4gint_(1/12pi)^(1/4pi)(1+3csc(x))dx$

$=4g*[x+3ln|(tan(x/2))|]_(1/12pi)^(1/4pi)$

$=4g(1/4pi+3ln(tan(pi/8)))-(1/12pi+3ln(tan(pi/24))$

$=4g(3.96)$

$=155.2J$

An object with a mass of 4 kg4 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 1+3cscx u_k(x)= 1+3cscx . How much work would it take to move the object over #x in [(pi)/12, (pi)/4], where x is in meters?