An object with a mass of $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= 2+cscx$ . How much work would it take to move the object over #x in [(3pi)/4, (7pi)/8], where x is in meters?

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Answer 1 · 2017-07-29T06:40:15

The work is $=89.3J$

We need

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

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 $m=6kg$

$F_r=mu_k*mg$

$=6(2+cscx)g$

The work done is

$W=6gint_(3/4pi)^(7/8pi)(2+cscx)dx$

$=6g*[2x+ln|tan(x/2)|]_(3/4pi)^(7/8pi)$

$=6g((2*7/8pi+ln|tan(7/16pi)|)-(2*3/4pi+ln|tan(3/8pi)|))$

$=6g(7/4pi-6/4pi+1.61)$

$=6g(1/4pi+0.73)$

$=89.3J$

An object with a mass of 6 kg6 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 2+cscx u_k(x)= 2+cscx . How much work would it take to move the object over #x in [(3pi)/4, (7pi)/8], where x is in meters?