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 · 2017-11-07T13:57:20

The work is $=435.6J$

We need

$intxe^xdx=e^x(x-1)+C$

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

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

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

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

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

$=435.6J$

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?