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)/6, (3pi)/8], where x is in meters?

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Answer 1 · 2017-05-01T08:24:28

The work is $=146.7J$

The work done is

$W=F*d$

The frictional force is

$F_r=mu_k*N$

$N=mg$

$F_r=mu_k*mg$

$=6(1+3cotx)g$

The work done is

$W=int_(pi/6)^(3/8pi)6(1+3cotx)gdx$

$=6gint_(pi/6)^(3/8pi)(1+3cotx)dx$

$=6g*[x+3ln(|sinx|)]_(pi/6)^(3/8pi)$

$=6g(3/8pi+3lnsin(3/8pi)-(pi/6+3lnsin(pi/6))$

$=6g(5/24pi+1.84)$

$=6g*2.49$

$=146.7J$

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)/6, (3pi)/8], where x is in meters?