An object with a mass of $5 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= xe^x-x$ . How much work would it take to move the object over #x in [1, 2], where x is in meters?

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Answer 1 · 2017-08-23T05:13:40

The work is $=288.6J$

We need

$intxe^xdx=xe^x-e^x+C$

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 $m=5kg$

$F_r=mu_k*mg$

$=5*(xe^x-x)g$

The work done is

$W=5gint_(1)^(2)(xe^x-x)dx$

$=5g*[xe^x-e^x-x^2/2]_(1)^(2)$

$=5g((2e^2-e^2-2)-(e-e-1/2))$

$=5g(e^2-2+1/2)=5g(e^2-3/2)$

$=288.6J$

An object with a mass of 5 kg5 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= xe^x-x u_k(x)= xe^x-x . How much work would it take to move the object over #x in [1, 2], where x is in meters?