An object with a mass of $8 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= 2x^2-x+7$ . How much work would it take to move the object over #x in [2, 5], where x is in meters?

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Answer 1 · 2017-06-09T05:57:23

The work is $=6938.4J$

The work done is

$W=F*d$

The frictional force is

$F_r=mu_k*N$

The normal force is $N=mg$

$F_r=mu_k*mg$

$=8(2x^2-x+7))g$

The work done is

$W=8gint_(2)^(5)(2x^2-x+7)dx$

$=8g*[2/3x^3-1/2x^2+7x]_(2)^(5)$

$=8g((250/3-25/2+35)-(16/3-2+14))$

$=8g(234/3-25/2+23)$

$=8g(177/2)$

$=6938.4J$

An object with a mass of 8 kg8 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 2x^2-x+7 u_k(x)= 2x^2-x+7 . How much work would it take to move the object over #x in [2, 5], where x is in meters?