An object with a mass of $5 k g$ $5 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = x + 2$ $u_k(x)= x+2$ . 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 · 2017-06-01T08:43:26

The work is $= 220.5 J$ $=220.5J$

The work done is

$W = F \cdot d$ $W=F*d$

The frictional force is

$F_{r} = μ_{k} \cdot N$ $F_r=mu_k*N$

$N = m g$ $N=mg$

$F_{r} = μ_{k} \cdot m g$ $F_r=mu_k*mg$

$= 5 (x + 2)) g$ $=5(x+2))g$

The work done is

$W = 5 g \int_{2}^{3} (x + 2) d x$ $W=5gint_(2)^(3)(x+2)dx$

$= 5 g \cdot {[\frac{x^{2}}{2} + 2 x]}_{2}^{3}$ $=5g*[x^2/2+2x]_(2)^(3)$

$= 5 g ((\frac{9}{2} + 6) - (\frac{4}{2} + 4)$ $=5g((9/2+6)-(4/2+4)$

$= 5 g (\frac{21}{2} - 6)$ $=5g(21/2-6)$

$= 5 g (\frac{9}{2})$ $=5g(9/2)$

$= \frac{45}{2} g J$ $=45/2gJ$

$= 220.5 J$ $=220.5J$

An object with a mass of 5kg5 kg is pushed along a linear path with a kinetic friction coefficient of uk(x)=x+2u_k(x)= x+2 . How much work would it take to move the object over #x in [2, 3], where x is in meters?