An object with a mass of $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= 1+3cotx$ . How much work would it take to move the object over #x in [(pi)/12, (3pi)/8], where x is in meters?

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Answer 1 · 2018-03-16T07:17:22

The work is $=128.8J$

$"Reminder : "$

$intcotxdx=ln(|sinx|)+C$

The work done is

$W=F*d$

The frictional force is

$F_r=mu_k*N$

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

The normal force is $N=mg$

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

$F_r=mu_k*mg$

$=6*(1+3cotx)g$

The work done is

$W=6gint_(1/12pi)^(3/8pi)(1+3cot)dx$

$=6g*[x+3ln(sin(x) ] _(1/12pi)^(3/8pi)$

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

$=6*9.8*2.19$

$=128.8J$

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+3cotx u_k(x)= 1+3cotx . How much work would it take to move the object over #x in [(pi)/12, (3pi)/8], where x is in meters?