An object with a mass of $6 k g$ $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 2 + sin x$ $u_k(x)= 2+sinx$ . 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 · 2017-07-19T14:35:57

The work is $= 311.7 J$ $=311.7J$

We need

$\int sin x d x = - cos x + C$ $intsinxdx=-cosx+C$

The work done is

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

The frictional force is

$F_{r} = μ_{k} \cdot N$ $F_r=mu_k*N$

The normal force is $N = m g$ $N=mg$

The mass is $m = 6 k g$ $m=6kg$

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

$= 6 (2 + sin x) g$ $=6(2+sinx)g$

The work done is

$W = 6 g \int_{2}^{5} (2 + sin x) d x$ $W=6gint_(2)^(5)(2+sinx)dx$

$= 6 g \cdot {[2 x - cos x]}_{2}^{5}$ $=6g*[2x-cosx]_(2)^(5)$

$= 6 g ((10 - cos 5) - (4 - cos 2))$ $=6g((10-cos5)-(4-cos2))$

$= 6 g (6 - cos 5 + cos 2)$ $=6g(6-cos5+cos2)$

$= 6 g (\cdot 5.3)$ $=6g(*5.3)$

$= 311.7 J$ $=311.7J$

An object with a mass of 6 kg6kg6 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 2+sinx uk(x)=2+sinxu_k(x)= 2+sinx . How much work would it take to move the object over #x in [2, 5], where x is in meters?