An object with a mass of $4 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= 5+tanx$ . How much work would it take to move the object over #x in [(-3pi)/12, (pi)/3], where x is in meters?

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Answer 1 · 2018-03-14T16:46:59

The work is $=372.8J$

$"Reminder : "$

$inttanxdx=-ln(cosx)+C$

The work done is

$W=F*d$

The frictional force is

$F_r=mu_k*N$

The coefficient of kinetic friction is $mu_k=(5+tanx)$

The normal force is $N=mg$

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

$F_r=mu_k*mg$

$=4*(5+tanx)g$

The work done is

$W=4gint_(-3/12pi)^(1/3pi)(5+tanx)dx$

$=4g*[5x-ln(cos(x)]_(-3/12pi)^(1/3pi)$

$=4g((5/3pi-ln(cos(1/3pi))-(-15/12pi-ln(cos(-3/12pi))))$

$=4g(35/12pi+1/12ln64)$

$=4*9.8*9.51$

$=372.8J$

An object with a mass of 4 kg4 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 5+tanx u_k(x)= 5+tanx . How much work would it take to move the object over #x in [(-3pi)/12, (pi)/3], where x is in meters?