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, 6], where x is in meters?

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Answer 1 · 2017-06-19T13:15:13

The work is $=9199J$

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

$W=8gint_(2)^(6)(x^2+3x)dx$

$=8g*[1/3x^3+3/2x^2]_(2)^(6)$

$=8g((1/3*6^3+3/2*6^2)-(1/3*2^3+3/2*2^2))$

$=8g(72+54-8/3-6)$

$=8g*352/3$

$=9199J$

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, 6], where x is in meters?