An object with a mass of $3 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= e^x-2x+3$ . How much work would it take to move the object over #x in [1, 4], where x is in meters?

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Answer 1 · 2018-04-16T05:52:20

The work is $=1348.9J$

$"Reminder : "$

$inte^xdx=e^x+C$

The work done is

$W=F*d$

The frictional force is

$F_r=mu_k*N$

The coefficient of kinetic friction is $mu_k=(e^x-2x+3)$

The normal force is $N=mg$

The mass of the object is $m=3kg$

$F_r=mu_k*mg$

$=3*(e^x-2x+3)g$

The work done is

$W=3gint_(1)^(4)(e^x-2x+3)dx$

$=3g*[e^x-x^2+3x ] _(1)^(4)$

$=3g((e^4-16+12)-(e-1+3))$

$=3xx9.8xx45.88$

$=1348.9J$

An object with a mass of 3 kg3 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= e^x-2x+3 u_k(x)= e^x-2x+3 . How much work would it take to move the object over #x in [1, 4], where x is in meters?