An object with a mass of $5 k g$ $5 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = x^{2} + 2$ $u_k(x)= x^2+2$ . 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 · 2017-05-23T13:48:17

The work is $= 408.3 J$ $=408.3J$

The work done is

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

The frictional force is

$F_{r} = μ_{k} \cdot N$ $F_r=mu_k*N$

$N = m g$ $N=mg$

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

$= 5 (x^{2} + 2) g$ $=5(x^2+2)g$

The work done is

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

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

$= 5 g ((9 + 6) - (\frac{8}{3} + 4))$ $=5g((9+6)-(8/3+4))$

$= 5 g (15 - \frac{20}{3})$ $=5g(15-20/3)$

$= 5 g \cdot \frac{25}{3}$ $=5g*25/3$

$= 408.3 J$ $=408.3J$

An object with a mass of 5kg5 kg is pushed along a linear path with a kinetic friction coefficient of uk(x)=x2+2u_k(x)= x^2+2 . How much work would it take to move the object over #x in [2, 3], where x is in meters?