An object with a mass of $8 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= x^2+3x$ . How much work would it take to move the object over #x in [2, 3], where x is in meters?

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Answer 1 · 2017-08-24T04:58:45

The work is $=1084.5J$

We need

$intx^ndx=x^(n+1)/(n+1)+C (n!=-1)$

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 $m=8kg$

$F_r=mu_k*mg$

$=8*(x^2+3x)g$

The work done is

$W=8gint_(2)^(3)(x^2+3x)dx$

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

$=8g((9+27/2)-(8/3+6))$

$=8g(3+65/6)$

$=1084.5J$

An object with a mass of 8 kg8 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= x^2+3x u_k(x)= x^2+3x . How much work would it take to move the object over #x in [2, 3], where x is in meters?