An object with a mass of $5 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= 1+sinx$ . How much work would it take to move the object over #x in [0, 5pi], where x is in meters?

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Answer 1 · 2017-05-15T12:25:47

The work is $=867.69J$

The work done is

$W=F*d$

The frictional force is

$F_r=mu_k*N$

$N=mg$

$F_r=mu_k*mg$

$=5(1+sinx)g$

The work done is

$W=5gint_(0)^(5pi)(1+sinx)dx$

$=5g*[x-cosx]_(0)^(5pi)$

$=5g((5pi+1)-(0-1))$

$=5g(2+5pi)$

$=5g*17.71$

$=867.69J$

An object with a mass of 5 kg5 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 1+sinx u_k(x)= 1+sinx . How much work would it take to move the object over #x in [0, 5pi], where x is in meters?