An object with a mass of $7 k g$ $7 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 3 + sin (4 x)$ $u_k(x)= 3+sin(4x)$ . How much work would it take to move the object over #x in [pi, 4pi], where x is in meters?

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Answer 1 · 2017-05-13T09:44:17

The work done is $= 1939.62 J$ $=1939.62J$

The work done is

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

The frictional force is

$F_{r} = μ_{k} \cdot N$ $F_r=mu_k*N$

$N = m g$ $N=mg$

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

$= 7 (3 + sin 4 x) g$ $=7(3+sin4x)g$

The work done is

$W = 7 g \int_{π}^{4 π} (3 + sin 4 x) d x$ $W=7gint_(pi)^(4pi)(3+sin4x)dx$

$= 7 g \cdot {[3 x - \frac{1}{4} cos 4 x]}_{π}^{4 π}$ $=7g*[3x-1/4cos4x]_(pi)^(4pi)$

$= 7 g ((12 π - \frac{1}{4}) - (3 π - \frac{1}{4}))$ $=7g((12pi-1/4)-(3pi-1/4))$

$= 7 g (9 π)$ $=7g(9pi)$

$= 7 g \cdot 28.27$ $=7g*28.27$

$= 1939.62 J$ $=1939.62J$

An object with a mass of 7kg7 kg is pushed along a linear path with a kinetic friction coefficient of uk(x)=3+sin(4x)u_k(x)= 3+sin(4x) . How much work would it take to move the object over #x in [pi, 4pi], where x is in meters?